Module gplately.reconstruction
Tools that wrap up pyGplates and Plate Tectonic Tools functionalities for reconstructing features, working with point data, and calculating plate velocities at specific geological times.
Expand source code
"""Tools that wrap up pyGplates and Plate Tectonic Tools functionalities for reconstructing features,
working with point data, and calculating plate velocities at specific geological times.
"""
import math
import os
import warnings
import numpy as np
import pygplates
from . import tools as _tools
from .gpml import _load_FeatureCollection
from .pygplates import FeatureCollection as _FeatureCollection
from .pygplates import RotationModel as _RotationModel
class PlateReconstruction(object):
"""The `PlateReconstruction` class contains methods to reconstruct topology features to specific
geological times given a `rotation_model`, a set of `topology_features` and a set of
`static_polygons`. Topological plate velocity data at specific geological times can also be
calculated from these reconstructed features.
Attributes

rotation_model : str, or instance of <pygplates.FeatureCollection>, or <pygplates.Feature>, or sequence of <pygplates.Feature>, or instance of <pygplates.RotationModel>, default None
A rotation model to query equivalent and/or relative topological plate rotations
from a time in the past relative to another time in the past or to present day. Can be
provided as a rotation filename, or rotation feature collection, or rotation feature, or
sequence of rotation features, or a sequence (eg, a list or tuple) of any combination of
those four types.
topology_features : str, or a sequence (eg, `list` or `tuple`) of instances of <pygplates.Feature>, or a single instance of <pygplates.Feature>, or an instance of <pygplates.FeatureCollection>, default None
Reconstructable topological features like trenches, ridges and transforms. Can be provided
as an optional topologyfeature filename, or sequence of features, or a single feature.
static_polygons : str, or instance of <pygplates.Feature>, or sequence of <pygplates.Feature>,or an instance of <pygplates.FeatureCollection>, default None
Presentday polygons whose shapes do not change through geological time. They are
used to cookiecut dynamic polygons into identifiable topological plates (assigned
an ID) according to their presentday locations. Can be provided as a static polygon feature
collection, or optional filename, or a single feature, or a sequence of
features.
"""
def __init__(
self,
rotation_model,
topology_features=None,
static_polygons=None,
anchor_plate_id=0,
):
if hasattr(rotation_model, "reconstruction_identifier"):
self.name = rotation_model.reconstruction_identifier
else:
self.name = None
self.anchor_plate_id = int(anchor_plate_id)
self.rotation_model = _RotationModel(
rotation_model, default_anchor_plate_id=anchor_plate_id
)
self.topology_features = _load_FeatureCollection(topology_features)
self.static_polygons = _load_FeatureCollection(static_polygons)
def __getstate__(self):
filenames = {"rotation_model": self.rotation_model.filenames,
"anchor_plate_id": self.anchor_plate_id}
if self.topology_features:
filenames["topology_features"] = self.topology_features.filenames
if self.static_polygons:
filenames["static_polygons"] = self.static_polygons.filenames
# # remove unpicklable items
# del self.rotation_model, self.topology_features, self.static_polygons
# # really make sure they're gone
# self.rotation_model = None
# self.topology_features = None
# self.static_polygons = None
return filenames
def __setstate__(self, state):
# reinstate unpicklable items
self.rotation_model = _RotationModel(state["rotation_model"], default_anchor_plate_id=state["anchor_plate_id"])
self.anchor_plate_id = state["anchor_plate_id"]
self.topology_features = None
self.static_polygons = None
if "topology_features" in state:
self.topology_features = _FeatureCollection()
for topology in state["topology_features"]:
self.topology_features.add(_FeatureCollection(topology))
if "static_polygons" in state:
self.static_polygons = _FeatureCollection()
for polygon in state["static_polygons"]:
self.static_polygons.add(_FeatureCollection(polygon))
def tessellate_subduction_zones(
self,
time,
tessellation_threshold_radians=0.001,
ignore_warnings=False,
return_geodataframe=False,
**kwargs
):
"""Samples points along subduction zone trenches and obtains subduction data at a particular
geological time.
Resolves topologies at `time`, tessellates all resolved subducting features to within 'tessellation_threshold_radians'
radians and obtains the following information for each sampled point along a trench:
`tessellate_subduction_zones` returns a list of 10 verticallystacked tuples with the following data per sampled trench point:
* Col. 0  longitude of sampled trench point
* Col. 1  latitude of sampled trench point
* Col. 2  subducting convergence (relative to trench) velocity magnitude (in cm/yr)
* Col. 3  subducting convergence velocity obliquity angle (angle between trench normal vector and convergence velocity vector)
* Col. 4  trench absolute (relative to anchor plate) velocity magnitude (in cm/yr)
* Col. 5  trench absolute velocity obliquity angle (angle between trench normal vector and trench absolute velocity vector)
* Col. 6  length of arc segment (in degrees) that current point is on
* Col. 7  trench normal azimuth angle (clockwise starting at North, ie, 0 to 360 degrees) at current point
* Col. 8  subducting plate ID
* Col. 9  trench plate ID
Parameters

time : float
The reconstruction time (Ma) at which to query subduction convergence.
tessellation_threshold_radians : float, default=0.001
The threshold sampling distance along the subducting trench (in radians).
Returns

subduction_data : a list of verticallystacked tuples
The results for all tessellated points sampled along the trench.
The size of the returned list is equal to the number of tessellated points.
Each tuple in the list corresponds to a tessellated point and has the following tuple items:
* Col. 0  longitude of sampled trench point
* Col. 1  latitude of sampled trench point
* Col. 2  subducting convergence (relative to trench) velocity magnitude (in cm/yr)
* Col. 3  subducting convergence velocity obliquity angle (angle between trench normal vector and convergence velocity vector)
* Col. 4  trench absolute (relative to anchor plate) velocity magnitude (in cm/yr)
* Col. 5  trench absolute velocity obliquity angle (angle between trench normal vector and trench absolute velocity vector)
* Col. 6  length of arc segment (in degrees) that current point is on
* Col. 7  trench normal azimuth angle (clockwise starting at North, ie, 0 to 360 degrees) at current point
* Col. 8  subducting plate ID
* Col. 9  trench plate ID
Notes

Each sampled point in the output is the midpoint of a great circle arc between two adjacent points in the trench polyline.
The trench normal vector used in the obliquity calculations is perpendicular to the great circle arc of each point
(arc midpoint) and pointing towards the overriding plate (rather than away from it).
Each trench is sampled at approximately uniform intervals along its length (specified via a threshold sampling distance).
The sampling along the entire length of a trench is not exactly uniform. Each segment along a trench is sampled
such that the samples have a uniform spacing that is less than or equal to the threshold sampling distance. However each
segment in a trench might have a slightly different spacing distance (since segment lengths are not integer multiples of
the threshold sampling distance).
The trench normal (at each arc segment midpoint) always points *towards* the overriding plate.
The obliquity angles are in the range (180 180). The range (0, 180) goes clockwise (when viewed from above the Earth)
from the trench normal direction to the velocity vector. The range (0, 180) goes counterclockwise.
You can change the range (180, 180) to the range (0, 360) by adding 360 to negative angles.
The trench normal is perpendicular to the trench and pointing toward the overriding plate.
Note that the convergence velocity magnitude is negative if the plates are diverging (if convergence obliquity angle
is greater than 90 or less than 90). And note that the absolute velocity magnitude is negative if the trench
(subduction zone) is moving towards the overriding plate (if absolute obliquity angle is less than 90 or greater
than 90)  note that this ignores the kinematics of the subducting plate.
The delta time interval used for velocity calculations is, by default, assumed to be 1Ma.
"""
from . import ptt as _ptt
anchor_plate_id = kwargs.pop("anchor_plate_id", self.anchor_plate_id)
if ignore_warnings:
with warnings.catch_warnings():
warnings.simplefilter("ignore")
subduction_data = _ptt.subduction_convergence.subduction_convergence(
self.rotation_model,
self.topology_features,
tessellation_threshold_radians,
float(time),
anchor_plate_id=anchor_plate_id,
**kwargs
)
else:
subduction_data = _ptt.subduction_convergence.subduction_convergence(
self.rotation_model,
self.topology_features,
tessellation_threshold_radians,
float(time),
anchor_plate_id=anchor_plate_id,
**kwargs
)
subduction_data = np.vstack(subduction_data)
if return_geodataframe:
import geopandas as gpd
from shapely import geometry
coords = [
geometry.Point(lon, lat)
for lon, lat in zip(subduction_data[:, 0], subduction_data[:, 1])
]
d = {"geometry": coords}
labels = [
"convergence velocity (cm/yr)",
"convergence obliquity angle (degrees)",
"trench velocity (cm/yr)",
"trench obliquity angle (degrees)",
"length (degrees)",
"trench normal angle (degrees)",
"subducting plate ID",
"overriding plate ID",
]
for i, label in enumerate(labels):
index = 2 + i
d[label] = subduction_data[:, index]
gdf = gpd.GeoDataFrame(d, geometry="geometry")
return gdf
else:
return subduction_data
def total_subduction_zone_length(self, time, use_ptt=False, ignore_warnings=False):
"""Calculates the total length of all midocean ridges (km) at the specified geological time (Ma).
if `use_ptt` is True
Uses Plate Tectonic Tools' `subduction_convergence` module to calculate trench segment lengths on a unit sphere.
The aggregated total subduction zone length is scaled to kilometres using the geocentric radius.
Otherwise
Resolves topology features ascribed to the `PlateReconstruction` model and extracts their shared boundary sections.
The lengths of each trench boundary section are appended to the total subduction zone length.
The total length is scaled to kilometres using a latitudedependent (geocentric) Earth radius.
Parameters

time : int
The geological time at which to calculate total midocean ridge lengths.
use_ptt : bool, default=False
If set to `True`, the PTT method is used.
ignore_warnings : bool, default=False
Choose whether to ignore warning messages from PTT's `subduction_convergence` workflow. These warnings alert the user
when certain subduction subsegments are ignored  this happens when the trench segments have unidentifiable subduction
polarities and/or subducting plates.
Raises

ValueError
If neither `use_pygplates` or `use_ptt` have been set to `True`.
Returns

total_subduction_zone_length_kms : float
The total subduction zone length (in km) at the specified `time`.
"""
from . import ptt as _ptt
if use_ptt:
with warnings.catch_warnings():
warnings.simplefilter("ignore")
subduction_data = self.tessellate_subduction_zones(
time, ignore_warnings=ignore_warnings
)
trench_arcseg = subduction_data[:, 6]
trench_pt_lat = subduction_data[:, 1]
total_subduction_zone_length_kms = 0
for i, segment in enumerate(trench_arcseg):
earth_radius = _tools.geocentric_radius(trench_pt_lat[i]) / 1e3
total_subduction_zone_length_kms += np.deg2rad(segment) * earth_radius
return total_subduction_zone_length_kms
else:
resolved_topologies = []
shared_boundary_sections = []
pygplates.resolve_topologies(
self.topology_features,
self.rotation_model,
resolved_topologies,
time,
shared_boundary_sections,
)
total_subduction_zone_length_kms = 0.0
for shared_boundary_section in shared_boundary_sections:
if (
shared_boundary_section.get_feature().get_feature_type()
!= pygplates.FeatureType.gpml_subduction_zone
):
continue
for (
shared_sub_segment
) in shared_boundary_section.get_shared_sub_segments():
clat, clon = (
shared_sub_segment.get_resolved_geometry()
.get_centroid()
.to_lat_lon()
)
earth_radius = _tools.geocentric_radius(clat) / 1e3
total_subduction_zone_length_kms += (
shared_sub_segment.get_resolved_geometry().get_arc_length()
* earth_radius
)
return total_subduction_zone_length_kms
def total_continental_arc_length(
self,
time,
continental_grid,
trench_arc_distance,
ignore_warnings=True,
):
"""Calculates the total length of all global continental arcs (km) at the specified geological time (Ma).
Uses Plate Tectonic Tools' `subduction_convergence` workflow to sample a given plate model's trench features into
point features and obtain their subduction polarities. The resolved points are projected out by the `trench_arc_distance`
and their new locations are linearly interpolated onto the supplied `continental_grid`. If the projected trench
points lie in the grid, they are considered continental arc points, and their arc segment lengths are appended
to the total continental arc length for the specified `time`. The total length is scaled to kilometres using the geocentric
Earth radius.
Parameters

time : int
The geological time at which to calculate total continental arc lengths.
continental_grid: Raster, array_like, or str
The continental grid used to identify continental arc points. Must
be convertible to `Raster`. For an array, a global extent is
assumed [180,180,90,90]. For a filename, the extent is obtained
from the file.
trench_arc_distance : float
The trenchtoarc distance (in kilometres) to project sampled trench points out by in the direction of their
subduction polarities.
ignore_warnings : bool, default=True
Choose whether to ignore warning messages from PTT's subduction_convergence workflow that alerts the user of
subduction subsegments that are ignored due to unidentified polarities and/or subducting plates.
Returns

total_continental_arc_length_kms : float
The continental arc length (in km) at the specified time.
"""
from . import grids as _grids
if isinstance(continental_grid, _grids.Raster):
graster = continental_grid
elif isinstance(continental_grid, str):
# Process the continental grid directory
graster = _grids.Raster(
data=continental_grid,
realign=True,
time=float(time),
)
else:
# Process the masked continental grid
try:
continental_grid = np.array(continental_grid)
graster = _grids.Raster(
data=continental_grid,
extent=[180, 180, 90, 90],
time=float(time),
)
except Exception as e:
raise TypeError(
"Invalid type for `continental_grid` (must be Raster,"
+ " str, or array_like)"
) from e
if (time != graster.time) and (not ignore_warnings):
raise RuntimeWarning(
"`continental_grid.time` ({}) ".format(graster.time)
+ "does not match `time` ({})".format(time)
)
# Obtain trench data with Plate Tectonic Tools
trench_data = self.tessellate_subduction_zones(
time, ignore_warnings=ignore_warnings
)
# Extract trench data
trench_normal_azimuthal_angle = trench_data[:, 7]
trench_arcseg = trench_data[:, 6]
trench_pt_lon = trench_data[:, 0]
trench_pt_lat = trench_data[:, 1]
# Modify the trencharc distance using the geocentric radius
arc_distance = trench_arc_distance / (
_tools.geocentric_radius(trench_pt_lat) / 1000
)
# Project trench points out along trencharc distance, and obtain their new latlon coordinates
dlon = arc_distance * np.sin(np.radians(trench_normal_azimuthal_angle))
dlat = arc_distance * np.cos(np.radians(trench_normal_azimuthal_angle))
ilon = trench_pt_lon + np.degrees(dlon)
ilat = trench_pt_lat + np.degrees(dlat)
# Linearly interpolate projected points onto continental grids, and collect the indices of points that lie
# within the grids.
sampled_points = graster.interpolate(
ilon,
ilat,
method="linear",
return_indices=False,
)
continental_indices = np.where(sampled_points > 0)
point_lats = ilat[continental_indices]
point_radii = _tools.geocentric_radius(point_lats) * 1.0e3 # km
segment_arclens = np.deg2rad(trench_arcseg[continental_indices])
segment_lengths = point_radii * segment_arclens
return np.sum(segment_lengths)
def tessellate_mid_ocean_ridges(
self,
time,
tessellation_threshold_radians=0.001,
ignore_warnings=False,
return_geodataframe=False,
**kwargs
):
"""Samples points along resolved spreading features (e.g. midocean ridges) and calculates spreading rates and
lengths of ridge segments at a particular geological time.
Resolves topologies at `time`, tessellates all resolved spreading features to within 'tessellation_threshold_radians'
radians. Returns a 4column vertically stacked tuple with the following data.
* Col. 0  longitude of sampled ridge point
* Col. 1  latitude of sampled ridge point
* Col. 2  spreading velocity magnitude (in cm/yr)
* Col. 3  length of arc segment (in degrees) that current point is on
All spreading feature types are considered. The transform segments of spreading features are ignored.
Note: by default, the function assumes that a segment can deviate 45 degrees from the stage pole before it is
considered a transform segment.
Parameters

time : float
The reconstruction time (Ma) at which to query subduction convergence.
tessellation_threshold_radians : float, default=0.001
The threshold sampling distance along the subducting trench (in radians).
ignore_warnings : bool, default=False
Choose to ignore warnings from Plate Tectonic Tools' ridge_spreading_rate workflow.
Returns

ridge_data : a list of verticallystacked tuples
The results for all tessellated points sampled along the trench.
The size of the returned list is equal to the number of tessellated points.
Each tuple in the list corresponds to a tessellated point and has the following tuple items:
* longitude of sampled point
* latitude of sampled point
* spreading velocity magnitude (in cm/yr)
* length of arc segment (in degrees) that current point is on
"""
from . import ptt as _ptt
anchor_plate_id = kwargs.pop("anchor_plate_id", self.anchor_plate_id)
if ignore_warnings:
with warnings.catch_warnings():
warnings.simplefilter("ignore")
spreading_feature_types = [pygplates.FeatureType.gpml_mid_ocean_ridge]
ridge_data = _ptt.ridge_spreading_rate.spreading_rates(
self.rotation_model,
self.topology_features,
float(time),
tessellation_threshold_radians,
spreading_feature_types,
anchor_plate_id=anchor_plate_id,
**kwargs
)
else:
spreading_feature_types = [pygplates.FeatureType.gpml_mid_ocean_ridge]
ridge_data = _ptt.ridge_spreading_rate.spreading_rates(
self.rotation_model,
self.topology_features,
float(time),
tessellation_threshold_radians,
spreading_feature_types,
anchor_plate_id=anchor_plate_id,
**kwargs
)
if not ridge_data:
# the _ptt.ridge_spreading_rate.spreading_rates might return None
return
ridge_data = np.vstack(ridge_data)
if return_geodataframe:
import geopandas as gpd
from shapely import geometry
points = [
geometry.Point(lon, lat)
for lon, lat in zip(ridge_data[:, 0], ridge_data[:, 1])
]
gdf = gpd.GeoDataFrame(
{
"geometry": points,
"velocity (cm/yr)": ridge_data[:, 2],
"length (degrees)": ridge_data[:, 3],
},
geometry="geometry",
)
return gdf
else:
return ridge_data
def total_ridge_length(self, time, use_ptt=False, ignore_warnings=False):
"""Calculates the total length of all midocean ridges (km) at the specified geological time (Ma).
if `use_ptt` is True
Uses Plate Tectonic Tools' `ridge_spreading_rate` workflow to calculate ridge segment lengths. Scales lengths to
kilometres using the geocentric radius.
Otherwise
Resolves topology features of the PlateReconstruction model and extracts their shared boundary sections.
The lengths of each GPML midocean ridge shared boundary section are appended to the total ridge length.
Scales lengths to kilometres using the geocentric radius.
Parameters

time : int
The geological time at which to calculate total midocean ridge lengths.
use_ptt : bool, default=False
If set to `True`, the PTT method is used.
ignore_warnings : bool, default=False
Choose whether to ignore warning messages from PTT's `ridge_spreading_rate` workflow.
Raises

ValueError
If neither `use_pygplates` or `use_ptt` have been set to `True`.
Returns

total_ridge_length_kms : float
The total length of global midocean ridges (in kilometres) at the specified time.
"""
from . import ptt as _ptt
if use_ptt is True:
with warnings.catch_warnings():
warnings.simplefilter("ignore")
ridge_data = self.tessellate_mid_ocean_ridges(time)
ridge_arcseg = ridge_data[:, 3]
ridge_pt_lat = ridge_data[:, 1]
total_ridge_length_kms = 0
for i, segment in enumerate(ridge_arcseg):
earth_radius = _tools.geocentric_radius(ridge_pt_lat[i]) / 1e3
total_ridge_length_kms += np.deg2rad(segment) * earth_radius
return total_ridge_length_kms
else:
resolved_topologies = []
shared_boundary_sections = []
pygplates.resolve_topologies(
self.topology_features,
self.rotation_model,
resolved_topologies,
time,
shared_boundary_sections,
)
total_ridge_length_kms = 0.0
for shared_boundary_section in shared_boundary_sections:
if (
shared_boundary_section.get_feature().get_feature_type()
!= pygplates.FeatureType.gpml_mid_ocean_ridge
):
continue
for (
shared_sub_segment
) in shared_boundary_section.get_shared_sub_segments():
clat, clon = (
shared_sub_segment.get_resolved_geometry()
.get_centroid()
.to_lat_lon()
)
earth_radius = _tools.geocentric_radius(clat) / 1e3
total_ridge_length_kms += (
shared_sub_segment.get_resolved_geometry().get_arc_length()
* earth_radius
)
return total_ridge_length_kms
def reconstruct(self, feature, to_time, from_time=0, anchor_plate_id=None, **kwargs):
"""Reconstructs regular geological features, motion paths or flowlines to a specific geological time.
Parameters

feature : str, or instance of <pygplates.FeatureCollection>, or <pygplates.Feature>, or sequence of <pygplates.Feature>
The geological features to reconstruct. Can be provided as a feature collection, or filename,
or feature, or sequence of features, or a sequence (eg, a list or tuple) of any combination of
those four types.
to_time : float, or :class:`GeoTimeInstant`
The specific geological time to reconstruct to.
from_time : float, default=0
The specific geological time to reconstruct from. By default, this is set to present day. Raises
`NotImplementedError` if `from_time` is not set to 0.0 Ma (present day).
anchor_plate_id : int, default=None
Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made
with respect to the absolute reference frame (anchor_plate_id = 0), like a stationary object in the mantle,
unless otherwise specified.
**reconstruct_type : ReconstructType, default=ReconstructType.feature_geometry
The specific reconstruction type to generate based on input feature geometry type. Can be provided as
pygplates.ReconstructType.feature_geometry to only reconstruct regular feature geometries, or
pygplates.ReconstructType.motion_path to only reconstruct motion path features, or
pygplates.ReconstructType.flowline to only reconstruct flowline features.
Generates :class:`reconstructed feature geometries<ReconstructedFeatureGeometry>’, or :class:`reconstructed
motion paths<ReconstructedMotionPath>’, or :class:`reconstructed flowlines<ReconstructedFlowline>’ respectively.
**group_with_feature : bool, default=False
Used to group reconstructed geometries with their features. This can be useful when a feature has more than one
geometry and hence more than one reconstructed geometry. The output *reconstructed_geometries* then becomes a
list of tuples where each tuple contains a :class:`feature<Feature>` and a ``list`` of reconstructed geometries.
Note: this keyword argument only applies when *reconstructed_geometries* is a list because exported files are
always grouped with their features. This is applicable to all ReconstructType features.
**export_wrap_to_dateline : bool, default=True
Wrap/clip reconstructed geometries to the dateline.
Returns

reconstructed_features : list
Reconstructed geological features (generated by the reconstruction) are appended to the list.
The reconstructed geometries are output in the same order as that of their respective input features (in the
parameter “features”). The order across input feature collections is also retained. This happens regardless
of whether *features* and *reconstructed_features* include files or not. Note: if keyword argument
group_with_feature=True then the list contains tuples that group each :class:`feature<Feature>` with a list
of its reconstructed geometries.
Raises

NotImplementedError
if the starting time for reconstruction `from_time` is not equal to 0.0.
"""
from_time, to_time = float(from_time), float(to_time)
reconstructed_features = []
if not anchor_plate_id:
anchor_plate_id = self.anchor_plate_id
pygplates.reconstruct(
feature,
self.rotation_model,
reconstructed_features,
to_time,
anchor_plate_id=anchor_plate_id,
**kwargs
)
return reconstructed_features
def get_point_velocities(self, lons, lats, time, delta_time=1.0):
"""Generates a velocity domain feature collection, resolves them into points, and calculates the north and east
components of the velocity vector for each point in the domain at a particular geological `time`.
Notes

Velocity domain feature collections are MeshNodetype features. These are produced from `lons` and `lats` pairs
represented as multipoint geometries (projections onto the surface of the unit length sphere). These features are
resolved into domain points and assigned plate IDs which are used to obtain the equivalent stage rotations of
identified tectonic plates over a time interval (`delta_time`). Each velocity domain point and its stage rotation
are used to calculate the point's plate velocity at a particular `time`. Obtained velocities for each domain point
are represented in the northeastdown coordinate system.
Parameters

lons : array
A 1D array of point data's longitudes.
lats : array
A 1D array of point data's latitudes.
time : float
The specific geological time (Ma) at which to calculate plate velocities.
delta_time : float, default=1.0
The time increment used for generating partitioning plate stage rotations. 1.0Ma by default.
Returns

all_velocities : 1D list of tuples
For each velocity domain feature point, a tuple of (north, east, down) velocity components is generated and
appended to a list of velocity data. The length of `all_velocities` is equivalent to the number of domain points
resolved from the latlon array parameters.
"""
# Add points to a multipoint geometry
time = float(time)
multi_point = pygplates.MultiPointOnSphere(
[(float(lat), float(lon)) for lat, lon in zip(lats, lons)]
)
# Create a feature containing the multipoint feature, and defined as MeshNode type
meshnode_feature = pygplates.Feature(
pygplates.FeatureType.create_from_qualified_string("gpml:MeshNode")
)
meshnode_feature.set_geometry(multi_point)
meshnode_feature.set_name("Velocity Mesh Nodes from pygplates")
velocity_domain_features = pygplates.FeatureCollection(meshnode_feature)
# NB: at this point, the feature could be written to a file using
# output_feature_collection.write('myfilename.gpmlz')
# All domain points and associated (magnitude, azimuth, inclination) velocities for the current time.
all_domain_points = []
all_velocities = []
# Partition our velocity domain features into our topological plate polygons at the current 'time'.
plate_partitioner = pygplates.PlatePartitioner(
self.topology_features, self.rotation_model, time
)
for velocity_domain_feature in velocity_domain_features:
# A velocity domain feature usually has a single geometry but we'll assume it can be any number.
# Iterate over them all.
for velocity_domain_geometry in velocity_domain_feature.get_geometries():
for velocity_domain_point in velocity_domain_geometry.get_points():
all_domain_points.append(velocity_domain_point)
partitioning_plate = plate_partitioner.partition_point(
velocity_domain_point
)
if partitioning_plate:
# We need the newly assigned plate ID
# to get the equivalent stage rotation of that tectonic plate.
partitioning_plate_id = (
partitioning_plate.get_feature().get_reconstruction_plate_id()
)
# Get the stage rotation of partitioning plate from 'time + delta_time' to 'time'.
equivalent_stage_rotation = self.rotation_model.get_rotation(
time, partitioning_plate_id, time + delta_time
)
# Calculate velocity at the velocity domain point.
# This is from 'time + delta_time' to 'time' on the partitioning plate.
velocity_vectors = pygplates.calculate_velocities(
[velocity_domain_point],
equivalent_stage_rotation,
delta_time,
)
# Convert global 3D velocity vectors to local (magnitude, azimuth, inclination) tuples
# (one tuple per point).
velocities = pygplates.LocalCartesian.convert_from_geocentric_to_north_east_down(
[velocity_domain_point], velocity_vectors
)
all_velocities.append(
(velocities[0].get_x(), velocities[0].get_y())
)
else:
all_velocities.append((0, 0))
return np.array(all_velocities)
def create_motion_path(
self,
lons,
lats,
time_array,
plate_id=None,
anchor_plate_id=None,
return_rate_of_motion=False,
):
"""Create a path of points to mark the trajectory of a plate's motion
through geological time.
Parameters

lons : arr
An array containing the longitudes of seed points on a plate in motion.
lats : arr
An array containing the latitudes of seed points on a plate in motion.
time_array : arr
An array of reconstruction times at which to determine the trajectory
of a point on a plate. For example:
import numpy as np
min_time = 30
max_time = 100
time_step = 2.5
time_array = np.arange(min_time, max_time + time_step, time_step)
plate_id : int, default=None
The ID of the moving plate. If this is not passed, the plate ID of the
seed points are ascertained using pygplates' `PlatePartitioner`.
anchor_plate_id : int, default=0
The ID of the anchor plate.
return_rate_of_motion : bool, default=False
Choose whether to return the rate of plate motion through time for each
Returns

rlons : ndarray
An ndimensional array with columns containing the longitudes of
the seed points at each timestep in `time_array`. There are n
columns for n seed points.
rlats : ndarray
An ndimensional array with columns containing the latitudes of
the seed points at each timestep in `time_array`. There are n
columns for n seed points.
StepTimes
StepRates
Examples

To access the latitudes and longitudes of each seed point's motion path:
for i in np.arange(0,len(seed_points)):
current_lons = lon[:,i]
current_lats = lat[:,i]
"""
lons = np.atleast_1d(lons)
lats = np.atleast_1d(lats)
time_array = np.atleast_1d(time_array)
# ndarrays to fill with reconstructed points and
# rates of motion (if requested)
rlons = np.empty((len(time_array), len(lons)))
rlats = np.empty((len(time_array), len(lons)))
if plate_id is None:
query_plate_id = True
else:
query_plate_id = False
plate_ids = np.ones(len(lons), dtype=int) * plate_id
if not anchor_plate_id:
anchor_plate_id = self.anchor_plate_id
seed_points = zip(lats, lons)
for i, lat_lon in enumerate(seed_points):
seed_points_at_digitisation_time = pygplates.PointOnSphere(
pygplates.LatLonPoint(float(lat_lon[0]), float(lat_lon[1]))
)
# Allocate the presentday plate ID to the PointOnSphere if
# it was not given.
if query_plate_id:
plate_id = _tools.plate_partitioner_for_point(
lat_lon, self.topology_features, self.rotation_model
)
else:
plate_id = plate_ids[i]
# Create the motion path feature. enforce float and int for C++ signature.
motion_path_feature = pygplates.Feature.create_motion_path(
seed_points_at_digitisation_time,
time_array,
valid_time=(time_array.max(), time_array.min()),
relative_plate=int(plate_id),
reconstruction_plate_id=int(anchor_plate_id),
)
reconstructed_motion_paths = self.reconstruct(
motion_path_feature,
to_time=0,
reconstruct_type=pygplates.ReconstructType.motion_path,
anchor_plate_id=int(plate_id),
)
# Turn motion paths in to latlon coordinates
for reconstructed_motion_path in reconstructed_motion_paths:
trail = reconstructed_motion_path.get_motion_path().to_lat_lon_array()
lon, lat = np.flipud(trail[:, 1]), np.flipud(trail[:, 0])
rlons[:, i] = lon
rlats[:, i] = lat
# Obtain stepplot coordinates for rate of motion
if return_rate_of_motion is True:
StepTimes = np.empty(((len(time_array)  1) * 2, len(lons)))
StepRates = np.empty(((len(time_array)  1) * 2, len(lons)))
# Get timestep
TimeStep = []
for j in range(len(time_array)  1):
diff = time_array[j + 1]  time_array[j]
TimeStep.append(diff)
# Iterate over each segment in the reconstructed motion path, get the distance travelled by the moving
# plate relative to the fixed plate in each time step
Dist = []
for reconstructed_motion_path in reconstructed_motion_paths:
for (
segment
) in reconstructed_motion_path.get_motion_path().get_segments():
Dist.append(
segment.get_arc_length()
* _tools.geocentric_radius(
segment.get_start_point().to_lat_lon()[0]
)
/ 1e3
)
# Note that the motion path coordinates come out starting with the oldest time and working forwards
# So, to match our 'times' array, we flip the order
Dist = np.flipud(Dist)
# Get rate of motion as distance per Myr
Rate = np.asarray(Dist) / TimeStep
# Manipulate arrays to get a step plot
StepRate = np.zeros(len(Rate) * 2)
StepRate[::2] = Rate
StepRate[1::2] = Rate
StepTime = np.zeros(len(Rate) * 2)
StepTime[::2] = time_array[:1]
StepTime[1::2] = time_array[1:]
# Append the nth point's step time and step rate coordinates to the ndarray
StepTimes[:, i] = StepTime
StepRates[:, i] = StepRate * 0.1 # cm/yr
# Obseleted by Lauren's changes above (though it is more efficient)
# multiply arc length of the motion path segment by a latitudedependent Earth radius
# use latitude of the segment start point
# distance.append( segment.get_arc_length() * _tools.geocentric_radius(segment.get_start_point().to_lat_lon()[0]) / 1e3)
# rate = np.asarray(distance)/np.diff(time_array)
# rates[:,i] = np.flipud(rate)
# rates *= 0.1 # cm/yr
if return_rate_of_motion is True:
return (
np.squeeze(rlons),
np.squeeze(rlats),
np.squeeze(StepTimes),
np.squeeze(StepRates),
)
else:
return np.squeeze(rlons), np.squeeze(rlats)
def create_flowline(
self,
lons,
lats,
time_array,
left_plate_ID,
right_plate_ID,
return_rate_of_motion=False,
):
"""Create a path of points to track plate motion away from
spreading ridges over time using halfstage rotations.
Parameters

lons : arr
An array of longitudes of points along spreading ridges.
lats : arr
An array of latitudes of points along spreading ridges.
time_array : arr
A list of times to obtain seed point locations at.
left_plate_ID : int
The plate ID of the polygon to the left of the spreading
ridge.
right_plate_ID : int
The plate ID of the polygon to the right of the spreading
ridge.
return_rate_of_motion : bool, default False
Choose whether to return a step time and step rate array
for a step plot of motion.
Returns

left_lon : ndarray
The longitudes of the __left__ flowline for n seed points.
There are n columns for n seed points, and m rows
for m time steps in `time_array`.
left_lat : ndarray
The latitudes of the __left__ flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in `time_array`.
right_lon : ndarray
The longitudes of the __right__ flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in `time_array`.
right_lat : ndarray
The latitudes of the __right__ flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in `time_array`.
Examples

To access the ith seed point's left and right latitudes and
longitudes:
for i in np.arange(0,len(seed_points)):
left_flowline_longitudes = left_lon[:,i]
left_flowline_latitudes = left_lat[:,i]
right_flowline_longitudes = right_lon[:,i]
right_flowline_latitudes = right_lat[:,i]
"""
lats = np.atleast_1d(lats)
lons = np.atleast_1d(lons)
time_array = np.atleast_1d(time_array)
seed_points = list(zip(lats, lons))
multi_point = pygplates.MultiPointOnSphere(seed_points)
start = 0
if time_array[0] != 0:
start = 1
time_array = np.hstack([[0], time_array])
# Create the flowline feature
flowline_feature = pygplates.Feature.create_flowline(
multi_point,
time_array.tolist(),
valid_time=(time_array.max(), time_array.min()),
left_plate=left_plate_ID,
right_plate=right_plate_ID,
)
# reconstruct the flowline in presentday coordinates
reconstructed_flowlines = self.reconstruct(
flowline_feature,
to_time=0,
reconstruct_type=pygplates.ReconstructType.flowline,
)
# Wrap things to the dateline, to avoid plotting artefacts.
date_line_wrapper = pygplates.DateLineWrapper()
# Create latlon ndarrays to store the left and right lats and lons of flowlines
left_lon = np.empty((len(time_array), len(lons)))
left_lat = np.empty((len(time_array), len(lons)))
right_lon = np.empty((len(time_array), len(lons)))
right_lat = np.empty((len(time_array), len(lons)))
StepTimes = np.empty(((len(time_array)  1) * 2, len(lons)))
StepRates = np.empty(((len(time_array)  1) * 2, len(lons)))
# Iterate over the reconstructed flowlines. Each seed point results in a 'left' and 'right' flowline
for i, reconstructed_flowline in enumerate(reconstructed_flowlines):
# Get the points for the left flowline only
left_latlon = reconstructed_flowline.get_left_flowline().to_lat_lon_array()
left_lon[:, i] = left_latlon[:, 1]
left_lat[:, i] = left_latlon[:, 0]
# Repeat for the right flowline points
right_latlon = (
reconstructed_flowline.get_right_flowline().to_lat_lon_array()
)
right_lon[:, i] = right_latlon[:, 1]
right_lat[:, i] = right_latlon[:, 0]
if return_rate_of_motion:
for i, reconstructed_motion_path in enumerate(reconstructed_flowlines):
distance = []
for (
segment
) in reconstructed_motion_path.get_left_flowline().get_segments():
distance.append(
segment.get_arc_length()
* _tools.geocentric_radius(
segment.get_start_point().to_lat_lon()[0]
)
/ 1e3
)
# Get rate of motion as distance per Myr
# Need to multiply rate by 2, since flowlines give us halfspreading rate
time_step = time_array[1]  time_array[0]
Rate = (
np.asarray(distance) / time_step
) * 2 # since we created the flowline at X increment
# Manipulate arrays to get a step plot
StepRate = np.zeros(len(Rate) * 2)
StepRate[::2] = Rate
StepRate[1::2] = Rate
StepTime = np.zeros(len(Rate) * 2)
StepTime[::2] = time_array[:1]
StepTime[1::2] = time_array[1:]
# Append the nth point's step time and step rate coordinates to the ndarray
StepTimes[:, i] = StepTime
StepRates[:, i] = StepRate * 0.1 # cm/yr
return (
left_lon[start:],
left_lat[start:],
right_lon[start:],
right_lat[start:],
StepTimes,
StepRates,
)
else:
return (
left_lon[start:],
left_lat[start:],
right_lon[start:],
right_lat[start:],
)
class Points(object):
"""`Points` contains methods to reconstruct and work with with geological point data. For example, the
locations and plate velocities of point data can be calculated at a specific geological `time`. The `Points`
object requires the `PlateReconstruction` object to work because it holds the `rotation_model` and `static_polygons`
needed to classify topological plates and quantify feature rotations through time.
Attributes

plate_reconstruction : object pointer
Allows for the accessibility of `PlateReconstruction` object attributes: `rotation_model`, `topology_featues`
and `static_polygons` for use in the `Points` object if called using “self.plate_reconstruction.X”,
where X is the attribute.
lons : float, or 1D array
A single float, or a 1D array containing the longitudes of point data.
lats : float 1D array
A single float, or a 1D array containing the latitudes of point data.
time : float, default=0
The specific geological time (Ma) at which to reconstruct the point data. By default, it is set to
the present day (0 Ma).
plate_id : int, default=None
The plate ID of a particular tectonic plate on which point data lies, if known. This is obtained in `init`
if not provided.
"""
def __init__(self, plate_reconstruction, lons, lats, time=0, plate_id=None):
self.lons = lons
self.lats = lats
self.time = time
self.attributes = dict()
self.plate_reconstruction = plate_reconstruction
self._update(lons, lats, time, plate_id)
def _update(self, lons, lats, time=0, plate_id=None):
# get Cartesian coordinates
self.x, self.y, self.z = _tools.lonlat2xyz(lons, lats, degrees=False)
# scale by average radius of the Earth
self.x *= _tools.EARTH_RADIUS
self.y *= _tools.EARTH_RADIUS
self.z *= _tools.EARTH_RADIUS
# store concatenated arrays
self.lonlat = np.c_[self.lons, self.lats]
self.xyz = np.c_[self.x, self.y, self.z]
rotation_model = self.plate_reconstruction.rotation_model
static_polygons = self.plate_reconstruction.static_polygons
features = _tools.points_to_features(lons, lats, plate_id)
if plate_id is not None:
plate_id = np.atleast_1d(plate_id)
self.features = features
else:
# partition using static polygons
# being careful to observe 'from time'
partitioned_features = pygplates.partition_into_plates(
static_polygons, rotation_model, features, reconstruction_time=time
)
self.features = partitioned_features
plate_id = np.empty(len(self.lons), dtype=int)
for i, feature in enumerate(partitioned_features):
plate_id[i] = feature.get_reconstruction_plate_id()
self.plate_id = plate_id
self.FeatureCollection = pygplates.FeatureCollection(self.features)
@property
def size(self):
"""Number of points"""
return len(self.lons)
def __getstate__(self):
filenames = self.plate_reconstruction.__getstate__()
# add important variables from Points object
filenames["lons"] = self.lons
filenames["lats"] = self.lats
filenames["time"] = self.time
filenames["plate_id"] = self.plate_id
for key in self.attributes:
filenames[key] = self.attributes[key]
return filenames
def __setstate__(self, state):
self.plate_reconstruction = PlateReconstruction(
state["rotation_model"],
state["topology_features"],
state["static_polygons"],
)
# reinstate unpicklable items
self.lons = state["lons"]
self.lats = state["lats"]
self.time = state["time"]
self.plate_id = state["plate_id"]
self.attributes = dict()
self._update(self.lons, self.lats, self.time, self.plate_id)
for key in state:
if key not in ["lons", "lats", "time", "plate_id"]:
self.attributes[key] = state[key]
def copy(self):
"""Returns a copy of the Points object
Returns

Points
A copy of the current Points object
"""
gpts = Points(
self.plate_reconstruction,
self.lons.copy(),
self.lats.copy(),
self.time,
self.plate_id.copy(),
)
gpts.add_attributes(**self.attributes.copy())
def add_attributes(self, **kwargs):
"""Adds the value of a feature attribute associated with a key.
Example

# Define latitudes and longitudes to set up a Points object
pt_lons = np.array([140., 150., 160.])
pt_lats = np.array([30., 40., 50.])
gpts = gplately.Points(model, pt_lons, pt_lats)
# Add the attributes a, b and c to the points in the Points object
gpts.add_attributes(
a=[10,2,2],
b=[2,3,3],
c=[30,0,0],
)
print(gpts.attributes)
The output would be:
{'a': [10, 2, 2], 'b': [2, 3, 3], 'c': [30, 0, 0]}
Parameters

**kwargs : sequence of key=item/s
A single key=value pair, or a sequence of key=value pairs denoting the name and
value of an attribute.
Notes

* An **assertion** is raised if the number of points in the Points object is not equal
to the number of values associated with an attribute key. For example, consider an instance
of the Points object with 3 points. If the points are ascribed an attribute `temperature`,
there must be one `temperature` value per point, i.e. `temperature = [20, 15, 17.5]`.
"""
keys = kwargs.keys()
for key in kwargs:
attribute = kwargs[key]
# make sure attribute is the same size as self.lons
if type(attribute) is int or type(attribute) is float:
array = np.full(self.lons.size, attribute)
attribute = array
elif isinstance(attribute, np.ndarray):
if attribute.size == 1:
array = np.full(self.lons.size, attribute, dtype=attribute.dtype)
attribute = array
assert (
len(attribute) == self.lons.size
), "Size mismatch, ensure attributes have the same number of entries as Points"
self.attributes[key] = attribute
if any(kwargs):
# add these to the FeatureCollection
for f, feature in enumerate(self.FeatureCollection):
for key in keys:
# extract value for each row in attribute
val = self.attributes[key][f]
# set this attribute on the feature
feature.set_shapefile_attribute(key, val)
def get_geopandas_dataframe(self):
"""Adds a shapely point `geometry` attribute to each point in the `gplately.Points` object.
pandas.DataFrame that has a column with geometry
Any existing point attributes are kept.
Returns

GeoDataFrame : instance of `geopandas.GeoDataFrame`
A pandas.DataFrame with rows equal to the number of points in the `gplately.Points` object,
and an additional column containing a shapely `geometry` attribute.
Example

pt_lons = np.array([140., 150., 160.])
pt_lats = np.array([30., 40., 50.])
gpts = gplately.Points(model, pt_lons, pt_lats)
# Add sample attributes a, b and c to the points in the Points object
gpts.add_attributes(
a=[10,2,2],
b=[2,3,3],
c=[30,0,0],
)
gpts.get_geopandas_dataframe()
...has the output:
a b c geometry
0 10 2 30 POINT (140.00000 30.00000)
1 2 3 0 POINT (150.00000 40.00000)
2 2 3 0 POINT (160.00000 50.00000)
"""
import geopandas as gpd
from shapely import geometry
# create shapely points
points = []
for lon, lat in zip(self.lons, self.lats):
points.append(geometry.Point(lon, lat))
attributes = self.attributes.copy()
attributes["geometry"] = points
return gpd.GeoDataFrame(attributes, geometry="geometry")
def get_geodataframe(self):
"""Returns the output of `Points.get_geopandas_dataframe()`.
Adds a shapely point `geometry` attribute to each point in the `gplately.Points` object.
pandas.DataFrame that has a column with geometry
Any existing point attributes are kept.
Returns

GeoDataFrame : instance of `geopandas.GeoDataFrame`
A pandas.DataFrame with rows equal to the number of points in the `gplately.Points` object,
and an additional column containing a shapely `geometry` attribute.
Example

pt_lons = np.array([140., 150., 160.])
pt_lats = np.array([30., 40., 50.])
gpts = gplately.Points(model, pt_lons, pt_lats)
# Add sample attributes a, b and c to the points in the Points object
gpts.add_attributes(
a=[10,2,2],
b=[2,3,3],
c=[30,0,0],
)
gpts.get_geopandas_dataframe()
...has the output:
a b c geometry
0 10 2 30 POINT (140.00000 30.00000)
1 2 3 0 POINT (150.00000 40.00000)
2 2 3 0 POINT (160.00000 50.00000)
"""
return self.get_geopandas_dataframe()
def reconstruct(self, time, anchor_plate_id=None, return_array=False, **kwargs):
"""Reconstructs regular geological features, motion paths or flowlines to a specific geological time and extracts
the latitudinal and longitudinal points of these features.
Note: this method accesses and uses the rotation model attribute from the PointReconstruction object, and reconstructs
the feature latlon point attributes of the Points object.
Parameters

time : float
The specific geological time (Ma) to reconstruct features to.
anchor_plate_id : int, default=None
Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made
with respect to the anchor_plate_ID specified in the `gplately.PlateReconstruction` object,
which is a default plate ID of 0 unless otherwise specified.
return_array : bool, default False
Return a `numpy.ndarray`, rather than a `Points` object.
**reconstruct_type : ReconstructType, default=ReconstructType.feature_geometry
The specific reconstruction type to generate based on input feature geometry type. Can be provided as
ReconstructType.feature_geometry to only reconstruct regular feature geometries, or ReconstructType.MotionPath to
only reconstruct motion path features, or ReconstructType.Flowline to only reconstruct flowline features. Generates
:class:`reconstructed feature geometries<ReconstructedFeatureGeometry>’, or :class:`reconstructed motion
paths<ReconstructedMotionPath>’, or :class:`reconstructed flowlines<ReconstructedFlowline>’ respectively.
**group_with_feature : bool, default=False
Used to group reconstructed geometries with their features. This can be useful when a feature has more than one
geometry and hence more than one reconstructed geometry. The output *reconstructed_geometries* then becomes a
list of tuples where each tuple contains a :class:`feature<Feature>` and a ``list`` of reconstructed geometries.
Note: this keyword argument only applies when *reconstructed_geometries* is a list because exported files are
always grouped with their features. This is applicable to all ReconstructType features.
**export_wrap_to_dateline : bool, default=True
Wrap/clip reconstructed geometries to the dateline (currently ignored).
Returns

rlons : list of float
A 1D numpy array enclosing all reconstructed point features' longitudes.
rlats : list of float
A 1D numpy array enclosing all reconstructed point features' latitudes.
Raises

NotImplementedError
if the starting time for reconstruction `from_time` is not equal to 0.0
"""
from_time = self.time
to_time = time
if not anchor_plate_id:
anchor_plate_id = self.plate_reconstruction.anchor_plate_id
reconstructed_features = self.plate_reconstruction.reconstruct(
self.features, to_time, from_time, anchor_plate_id=anchor_plate_id, **kwargs
)
rlons, rlats = _tools.extract_feature_lonlat(reconstructed_features)
if return_array:
return rlons, rlats
else:
gpts = Points(
self.plate_reconstruction,
rlons,
rlats,
time=to_time,
plate_id=self.plate_id,
)
gpts.add_attributes(**self.attributes.copy())
return gpts
def reconstruct_to_birth_age(self, ages, anchor_plate_id=None, **kwargs):
"""Reconstructs point features supplied to the `Points` object from the supplied initial time (`self.time`)
to a range of times. The number of supplied times must equal the number of point features supplied to the Points object.
Attributes

ages : array
Geological times to reconstruct features to. Must have the same length as the `Points `object's `self.features` attribute
(which holds all point features represented on a unit length sphere in 3D Cartesian coordinates).
anchor_plate_id : int, default=None
Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made
with respect to the anchor_plate_ID specified in the `gplately.PlateReconstruction` object,
which is a default plate ID of 0 unless otherwise specified.
**kwargs
Additional keyword arguments for the `gplately.PlateReconstruction.reconstruct` method.
Raises

ValueError
If the number of ages and number of point features supplied to the Points object are not identical.
Returns

rlons, rlats : float
The longitude and latitude coordinate lists of all point features reconstructed to all specified ages.
Examples

To reconstruct n seed points' locations to B Ma (for this example n=2, with (lon,lat) = (78,30) and (56,22) at time=0 Ma,
and we reconstruct to B=10 Ma):
# Longitude and latitude of n=2 seed points
pt_lon = np.array([78., 56])
pt_lat = np.array([30., 22])
# Call the Points object!
gpts = gplately.Points(model, pt_lon, pt_lat)
print(gpts.features[0].get_all_geometries()) # Confirms we have features represented as points on a sphere
ages = numpy.linspace(10,10, len(pt_lon))
rlons, rlats = gpts.reconstruct_to_birth_age(ages)
"""
from_time = self.time
if not anchor_plate_id:
anchor_plate_id = self.plate_reconstruction.anchor_plate_id
ages = np.array(ages)
if len(ages) != len(self.features):
raise ValueError("Number of points and ages must be identical")
unique_ages = np.unique(ages)
rlons = np.zeros(ages.shape)
rlats = np.zeros(ages.shape)
for age in unique_ages:
mask_age = ages == age
reconstructed_features = self.plate_reconstruction.reconstruct(
self.features, age, from_time, anchor_plate_id=anchor_plate_id, **kwargs
)
lons, lats = _tools.extract_feature_lonlat(reconstructed_features)
rlons[mask_age] = lons[mask_age]
rlats[mask_age] = lats[mask_age]
return rlons, rlats
def plate_velocity(self, time, delta_time=1):
"""Calculates the x and y components of tectonic plate velocities at a particular geological time.
This method accesses and uses the `rotation_model` attribute from the `PlateReconstruction` object and uses the `Points`
object's `self.features` attribute. Feature points are extracted and assigned plate IDs. These IDs are used to obtain the
equivalent stage rotations of identified tectonic plates over a time interval `delta_time`. Each feature point and its stage
rotation are used to calculate the point's plate velocity at a particular geological time. Obtained velocities for each domain
point are represented in the northeastdown coordinate system, and their x,y Cartesian coordinate components are extracted.
Parameters

time : float
The specific geological time (Ma) at which to calculate plate velocities.
delta_time : float, default=1.0
The time increment used for generating partitioning plate stage rotations. 1.0 Ma by default.
Returns

all_velocities.T : 2D numpy list
A transposed 2D numpy list with two rows and a number of columns equal to the number of x,y Cartesian velocity
components obtained (and thus the number of feature points extracted from a supplied feature). Each list column
stores one point’s x,y, velocity components along its two rows.
"""
time = float(time)
rotation_model = self.plate_reconstruction.rotation_model
all_velocities = np.empty((len(self.features), 2))
for i, feature in enumerate(self.features):
geometry = feature.get_geometry()
partitioning_plate_id = feature.get_reconstruction_plate_id()
equivalent_stage_rotation = rotation_model.get_rotation(
time, partitioning_plate_id, time + delta_time
)
velocity_vectors = pygplates.calculate_velocities(
[geometry],
equivalent_stage_rotation,
delta_time,
pygplates.VelocityUnits.cms_per_yr,
)
velocities = (
pygplates.LocalCartesian.convert_from_geocentric_to_north_east_down(
[geometry], velocity_vectors
)
)
all_velocities[i] = velocities[0].get_y(), velocities[0].get_x()
return list(all_velocities.T)
def motion_path(self, time_array, anchor_plate_id=0, return_rate_of_motion=False):
"""Create a path of points to mark the trajectory of a plate's motion
through geological time.
Parameters

time_array : arr
An array of reconstruction times at which to determine the trajectory
of a point on a plate. For example:
import numpy as np
min_time = 30
max_time = 100
time_step = 2.5
time_array = np.arange(min_time, max_time + time_step, time_step)
anchor_plate_id : int, default=0
The ID of the anchor plate.
return_rate_of_motion : bool, default=False
Choose whether to return the rate of plate motion through time for each
Returns

rlons : ndarray
An ndimensional array with columns containing the longitudes of
the seed points at each timestep in `time_array`. There are n
columns for n seed points.
rlats : ndarray
An ndimensional array with columns containing the latitudes of
the seed points at each timestep in `time_array`. There are n
columns for n seed points.
"""
time_array = np.atleast_1d(time_array)
# ndarrays to fill with reconstructed points and
# rates of motion (if requested)
rlons = np.empty((len(time_array), len(self.lons)))
rlats = np.empty((len(time_array), len(self.lons)))
for i, point_feature in enumerate(self.FeatureCollection):
# Create the motion path feature
motion_path_feature = pygplates.Feature.create_motion_path(
point_feature.get_geometry(),
time_array.tolist(),
valid_time=(time_array.max(), time_array.min()),
# relative_plate=int(self.plate_id[i]),
# reconstruction_plate_id=int(anchor_plate_id))
relative_plate=int(self.plate_id[i]),
reconstruction_plate_id=int(anchor_plate_id),
)
reconstructed_motion_paths = self.plate_reconstruction.reconstruct(
motion_path_feature,
to_time=0,
# from_time=0,
reconstruct_type=pygplates.ReconstructType.motion_path,
anchor_plate_id=int(anchor_plate_id),
)
# Turn motion paths in to latlon coordinates
for reconstructed_motion_path in reconstructed_motion_paths:
trail = reconstructed_motion_path.get_motion_path().to_lat_lon_array()
lon, lat = np.flipud(trail[:, 1]), np.flipud(trail[:, 0])
rlons[:, i] = lon
rlats[:, i] = lat
# Obtain stepplot coordinates for rate of motion
if return_rate_of_motion is True:
StepTimes = np.empty(((len(time_array)  1) * 2, len(self.lons)))
StepRates = np.empty(((len(time_array)  1) * 2, len(self.lons)))
# Get timestep
TimeStep = []
for j in range(len(time_array)  1):
diff = time_array[j + 1]  time_array[j]
TimeStep.append(diff)
# Iterate over each segment in the reconstructed motion path, get the distance travelled by the moving
# plate relative to the fixed plate in each time step
Dist = []
for reconstructed_motion_path in reconstructed_motion_paths:
for (
segment
) in reconstructed_motion_path.get_motion_path().get_segments():
Dist.append(
segment.get_arc_length()
* _tools.geocentric_radius(
segment.get_start_point().to_lat_lon()[0]
)
/ 1e3
)
# Note that the motion path coordinates come out starting with the oldest time and working forwards
# So, to match our 'times' array, we flip the order
Dist = np.flipud(Dist)
# Get rate of motion as distance per Myr
Rate = np.asarray(Dist) / TimeStep
# Manipulate arrays to get a step plot
StepRate = np.zeros(len(Rate) * 2)
StepRate[::2] = Rate
StepRate[1::2] = Rate
StepTime = np.zeros(len(Rate) * 2)
StepTime[::2] = time_array[:1]
StepTime[1::2] = time_array[1:]
# Append the nth point's step time and step rate coordinates to the ndarray
StepTimes[:, i] = StepTime
StepRates[:, i] = StepRate * 0.1 # cm/yr
if return_rate_of_motion is True:
return (
np.squeeze(rlons),
np.squeeze(rlats),
np.squeeze(StepTimes),
np.squeeze(StepRates),
)
else:
return np.squeeze(rlons), np.squeeze(rlats)
def flowline(
self, time_array, left_plate_ID, right_plate_ID, return_rate_of_motion=False
):
"""Create a path of points to track plate motion away from
spreading ridges over time using halfstage rotations.
Parameters

lons : arr
An array of longitudes of points along spreading ridges.
lats : arr
An array of latitudes of points along spreading ridges.
time_array : arr
A list of times to obtain seed point locations at.
left_plate_ID : int
The plate ID of the polygon to the left of the spreading
ridge.
right_plate_ID : int
The plate ID of the polygon to the right of the spreading
ridge.
return_rate_of_motion : bool, default False
Choose whether to return a step time and step rate array for
a stepplot of flowline motion.
Returns

left_lon : ndarray
The longitudes of the __left__ flowline for n seed points.
There are n columns for n seed points, and m rows
for m time steps in `time_array`.
left_lat : ndarray
The latitudes of the __left__ flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in `time_array`.
right_lon : ndarray
The longitudes of the __right__ flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in `time_array`.
right_lat : ndarray
The latitudes of the __right__ flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in `time_array`.
Examples

To access the ith seed point's left and right latitudes and
longitudes:
for i in np.arange(0,len(seed_points)):
left_flowline_longitudes = left_lon[:,i]
left_flowline_latitudes = left_lat[:,i]
right_flowline_longitudes = right_lon[:,i]
right_flowline_latitudes = right_lat[:,i]
"""
model = self.plate_reconstruction
return model.create_flowline(
self.lons,
self.lats,
time_array,
left_plate_ID,
right_plate_ID,
return_rate_of_motion,
)
def _get_dataframe(self):
import geopandas as gpd
data = dict()
data["Longitude"] = self.lons
data["Latitude"] = self.lats
data["Plate_ID"] = self.plate_id
for key in self.attributes:
data[key] = self.attributes[key]
return gpd.GeoDataFrame(data)
def save(self, filename):
"""Saves the feature collection used in the Points object under a given filename to the current directory.
The file format is determined from the filename extension.
Parameters

filename : string
Can be provided as a string including the filename and the file format needed.
Returns

Feature collection saved under given filename to current directory.
"""
filename = str(filename)
if filename.endswith((".csv", ".txt", ".dat")):
df = self._get_dataframe()
df.to_csv(filename, index=False)
elif filename.endswith((".xls", ".xlsx")):
df = self._get_dataframe()
df.to_excel(filename, index=False)
elif filename.endswith("xml"):
df = self._get_dataframe()
df.to_xml(filename, index=False)
elif filename.endswith(".gpml") or filename.endswith(".gpmlz"):
self.FeatureCollection.write(filename)
else:
raise ValueError(
"Cannot save to specified file type. Use csv, gpml, or xls file extension."
)
# FROM RECONSTRUCT_BY_TOPOLOGIES.PY
class _DefaultCollision(object):
"""
Default collision detection function class (the function is the '__call__' method).
"""
DEFAULT_GLOBAL_COLLISION_PARAMETERS = (7.0, 10.0)
"""
Default collision parameters for all feature types.
This is a 2tuple of (threshold velocity delta in kms/my, threshold distance to boundary per My in kms/my):
Here we default to the same constants used internally in GPlates 2.0 (ie, 7.0 and 10.0).
"""
def __init__(
self,
global_collision_parameters=DEFAULT_GLOBAL_COLLISION_PARAMETERS,
feature_specific_collision_parameters=None,
):
"""
global_collision_parameters: The collision parameters to use for any feature type not specified in 'feature_specific_collision_parameters'.
Should be a 2tuple of (threshold velocity delta in kms/my, threshold distance to boundary per My in kms/my).
The first threshold parameter means:
A point that transitions from one plate to another can disappear if the change in velocity exceeds this threshold.
The second threshold parameter means:
Only those transitioning points exceeding the threshold velocity delta and that are close enough to a plate boundary can disappear.
The distance is proportional to the relative velocity (change in velocity), plus a constant offset based on the threshold distance to boundary
to account for plate boundaries that change shape significantly from one time step to the next
(note that some boundaries are meant to do this and others are a result of digitisation).
The actual distance threshold used is (threshold_distance_to_boundary + relative_velocity) * time_interval
Defaults to parameters used in GPlates 2.0, if not specified.
feature_specific_collision_parameters: Optional sequence of collision parameters specific to feature types.
If specified then should be a sequence of 2tuples, with each 2tuple specifying (feature_type, collision_parameters).
And where each 'collision_parameters' is a 2tuple of (threshold velocity delta in kms/my, threshold distance to boundary per My in kms/my).
See 'global_collision_parameters' for details on these thresholds.
Any feature type not specified here defaults to using 'global_collision_parameters'.
"""
# Convert list of (feature_type, collision_parameters) tuples to a dictionary.
if feature_specific_collision_parameters:
self.feature_specific_collision_parameters = dict(
feature_specific_collision_parameters
)
else:
self.feature_specific_collision_parameters = dict()
# Fallback for any feature type not specified in the optional featurespecific list.
self.global_collision_parameters = global_collision_parameters
# Used to improve performance by caching velocity stage rotations in a dict (for a specific reconstruction time).
self.velocity_stage_rotation_dict = {}
self.velocity_stage_rotation_time = None
def __call__(
self,
rotation_model,
time,
reconstruction_time_interval,
prev_point,
curr_point,
prev_topology_plate_id,
prev_resolved_plate_boundary,
curr_topology_plate_id,
curr_resolved_plate_boundary,
):
"""
Returns True if a collision was detected.
If transitioning from a rigid plate to another rigid plate with a different plate ID then
calculate the difference in velocities and continue testing as follows
(otherwise, if there's no transition, then the point is still active)...
If the velocity difference is below a threshold then we assume the previous plate was split,
or two plates joined. In this case the point has not subducted (forward in time) or
been consumed by a midocean (backward in time) and hence is still active.
If the velocity difference is large enough then we see if the distance of the *previous* position
to the polygon boundary (of rigid plate containing it) exceeds a threshold.
If the distance exceeds the threshold then the point is far enough away from the boundary that it
cannot be subducted or consumed by it and hence the point is still active.
However if the point is close enough then we assume the point was subducted/consumed
(remember that the point switched plate IDs).
Also note that the threshold distance increases according to the velocity difference to account for fast
moving points (that would otherwise tunnel through the boundary and accrete onto the other plate).
The reason for testing the distance from the *previous* point, and not from the *current* point, is:
(i) A topological boundary may *appear* near the current point (such as a plate split at the current time)
and we don't want that split to consume the current point regardless of the velocity difference.
It won't get consumed because the *previous* point was not near a boundary (because before split happened).
If the velocity difference is large enough then it might cause the current point to transition to the
adjacent split plate in the *next* time step (and that's when it should get consumed, not in the current time step).
An example of this is a midocean ridge suddenly appearing (going forward in time).
(ii) A topological boundary may *disappear* near the current point (such as a plate merge at the current time)
and we want that merge to consume the current point if the velocity difference is large enough.
In this case the *previous* point is near a boundary (because before plate merged) and hence can be
consumed (provided velocity difference is large enough). And since the boundary existed in the previous
time step, it will affect position of the current point (and whether it gets consumed or not).
An example of this is a midocean ridge suddenly disappearing (going backward in time).
...note that items (i) and (ii) above apply both going forward and backward in time.
"""
# See if a collision occurred.
if (
curr_topology_plate_id != prev_topology_plate_id
and prev_topology_plate_id is not None
and curr_topology_plate_id is not None
):
#
# Speed up by caching velocity stage rotations in a dict.
#
if time != self.velocity_stage_rotation_time:
# We've just switched to a new time so clear the cache.
#
# We only cache stage rotations for a specific time.
# We only really need to cache different plate IDs at the same 'time', so this avoids caching for all times
# (which would also require including 'time' in the key) and using memory unnecessarily.
self.velocity_stage_rotation_dict.clear()
self.velocity_stage_rotation_time = time
prev_location_velocity_stage_rotation = (
self.velocity_stage_rotation_dict.get(prev_topology_plate_id)
)
if not prev_location_velocity_stage_rotation:
prev_location_velocity_stage_rotation = rotation_model.get_rotation(
time + 1, prev_topology_plate_id, time
)
self.velocity_stage_rotation_dict[
prev_topology_plate_id
] = prev_location_velocity_stage_rotation
curr_location_velocity_stage_rotation = (
self.velocity_stage_rotation_dict.get(curr_topology_plate_id)
)
if not curr_location_velocity_stage_rotation:
curr_location_velocity_stage_rotation = rotation_model.get_rotation(
time + 1, curr_topology_plate_id, time
)
self.velocity_stage_rotation_dict[
curr_topology_plate_id
] = curr_location_velocity_stage_rotation
# Note that even though the current point is not inside the previous boundary (because different plate ID), we can still
# calculate a velocity using its plate ID (because we really should use the same point in our velocity comparison).
prev_location_velocity = pygplates.calculate_velocities(
(curr_point,),
prev_location_velocity_stage_rotation,
1,
pygplates.VelocityUnits.kms_per_my,
)[0]
curr_location_velocity = pygplates.calculate_velocities(
(curr_point,),
curr_location_velocity_stage_rotation,
1,
pygplates.VelocityUnits.kms_per_my,
)[0]
delta_velocity = curr_location_velocity  prev_location_velocity
delta_velocity_magnitude = delta_velocity.get_magnitude()
# If we have featurespecific collision parameters then iterate over the boundary subsegments of the *previous* topological boundary
# and test proximity to each subsegment individually (with subsegment feature type specific collision parameters).
# Otherwise just test proximity to the entire boundary polygon using the global collision parameters.
if self.feature_specific_collision_parameters:
for (
prev_boundary_sub_segment
) in prev_resolved_plate_boundary.get_boundary_sub_segments():
# Use featurespecific collision parameters if found (falling back to global collision parameters).
(
threshold_velocity_delta,
threshold_distance_to_boundary_per_my,
) = self.feature_specific_collision_parameters.get(
prev_boundary_sub_segment.get_feature().get_feature_type(),
# Default to global collision parameters if no collision parameters specified for subsegment's feature type...
self.global_collision_parameters,
)
# Since each feature type could use different collision parameters we must use the current boundary subsegment instead of the boundary polygon.
if self._detect_collision_using_collision_parameters(
reconstruction_time_interval,
delta_velocity_magnitude,
prev_point,
prev_boundary_sub_segment.get_resolved_geometry(),
threshold_velocity_delta,
threshold_distance_to_boundary_per_my,
):
# Detected a collision.
return True
else:
# No featurespecific collision parameters so use global fallback.
(
threshold_velocity_delta,
threshold_distance_to_boundary_per_my,
) = self.global_collision_parameters
# Since all feature types use the same collision parameters we can use the boundary polygon instead of iterating over its subsegments.
if self._detect_collision_using_collision_parameters(
reconstruction_time_interval,
delta_velocity_magnitude,
prev_point,
prev_resolved_plate_boundary.get_resolved_boundary(),
threshold_velocity_delta,
threshold_distance_to_boundary_per_my,
):
# Detected a collision.
return True
return False
def _detect_collision_using_collision_parameters(
self,
reconstruction_time_interval,
delta_velocity_magnitude,
prev_point,
prev_boundary_geometry,
threshold_velocity_delta,
threshold_distance_to_boundary_per_my,
):
if delta_velocity_magnitude > threshold_velocity_delta:
# Add the minimum distance threshold to the delta velocity threshold.
# The delta velocity threshold only allows those points that are close enough to the boundary to reach
# it given their current relative velocity.
# The minimum distance threshold accounts for sudden changes in the shape of a plate boundary
# which are no supposed to represent a new or shifted boundary but are just a result of the topology
# builder/user digitising a new boundary line that differs noticeably from that of the previous time period.
distance_threshold_radians = (
(threshold_distance_to_boundary_per_my + delta_velocity_magnitude)
* reconstruction_time_interval
/ pygplates.Earth.equatorial_radius_in_kms
)
distance_threshold_radians = min(distance_threshold_radians, math.pi)
distance_threshold_radians = max(distance_threshold_radians, 0.0)
distance = pygplates.GeometryOnSphere.distance(
prev_point,
prev_boundary_geometry,
distance_threshold_radians=float(distance_threshold_radians),
)
if distance is not None:
# Detected a collision.
return True
return False
_DEFAULT_COLLISION = _DefaultCollision()
class _ContinentCollision(object):
"""
Continental collision detection function class (the function is the '__call__' method).
"""
def __init__(
self,
grd_output_dir,
chain_collision_detection=_DEFAULT_COLLISION,
verbose=False,
):
"""
grd_output_dir: The directory containing the continental grids.
chain_collision_detection: Another collision detection class/function to reference if we find no collision.
If None then no collision detection is chained. Defaults to the default collision detection.
verbose: Print progress messages
"""
self.grd_output_dir = grd_output_dir
self.chain_collision_detection = chain_collision_detection
self.verbose = verbose
# Load a new grid each time the reconstruction time changes.
self.grid_time = None
@property
def grid_time(self):
return self._grid_time
@grid_time.setter
def grid_time(self, time):
from .grids import read_netcdf_grid
if time is None:
self._grid_time = time
else:
filename = "{:s}".format(self.grd_output_dir.format(time))
if self.verbose:
print(
"Points masked against grid: {0}".format(os.path.basename(filename))
)
gridZ, gridX, gridY = read_netcdf_grid(filename, return_grids=True)
self.gridZ = gridZ
self.ni, self.nj = gridZ.shape
self.xmin = np.nanmin(gridX)
self.xmax = np.nanmax(gridX)
self.ymin = np.nanmin(gridY)
self.ymax = np.nanmax(gridY)
self._grid_time = float(time)
def __call__(
self,
rotation_model,
time,
reconstruction_time_interval,
prev_point,
curr_point,
prev_topology_plate_id,
prev_resolved_plate_boundary,
curr_topology_plate_id,
curr_resolved_plate_boundary,
):
"""
Returns True if a collision with a continent was detected, or returns result of
chained collision detection if 'self.chain_collision_detection' is not None.
"""
# Load the grid for the current time if encountering a new time.
if time != self.grid_time:
self.grid_time = time
self.continent_deletion_count = 0
# Sample mask grid, which is one over continents and zero over oceans.
point_lat, point_lon = curr_point.to_lat_lon()
point_i = (self.ni  1) * ((point_lat  self.ymin) / (self.ymax  self.ymin))
point_j = (self.nj  1) * ((point_lon  self.xmin) / (self.xmax  self.xmin))
point_i_uint = np.rint(point_i).astype(np.uint)
point_j_uint = np.rint(point_j).astype(np.uint)
try:
mask_value = self.gridZ[point_i_uint, point_j_uint]
except IndexError:
point_i = np.clip(np.rint(point_i), 0, self.ni  1).astype(np.int_)
point_j = np.clip(np.rint(point_j), 0, self.nj  1).astype(np.int_)
mask_value = self.gridZ[point_i, point_j]
if mask_value >= 0.5:
# Detected a collision.
self.continent_deletion_count += 1
return True
# We didn't find a collision, so ask the chained collision detection if it did (if we have anything chained).
if self.chain_collision_detection:
return self.chain_collision_detection(
rotation_model,
time,
reconstruction_time_interval,
prev_point,
curr_point,
prev_topology_plate_id,
prev_resolved_plate_boundary,
curr_topology_plate_id,
curr_resolved_plate_boundary,
)
return False
def reconstruct_points(
rotation_features_or_model,
topology_features,
reconstruction_begin_time,
reconstruction_end_time,
reconstruction_time_interval,
points,
point_begin_times=None,
point_end_times=None,
point_plate_ids=None,
detect_collisions=_DEFAULT_COLLISION,
):
"""
Function to reconstruct points using the ReconstructByTopologies class below.
For description of parameters see the ReconstructByTopologies class below.
"""
topology_reconstruction = _ReconstructByTopologies(
rotation_features_or_model,
topology_features,
reconstruction_begin_time,
reconstruction_end_time,
reconstruction_time_interval,
points,
point_begin_times,
point_end_times,
point_plate_ids,
detect_collisions,
)
return topology_reconstruction.reconstruct()
class _ReconstructByTopologies(object):
"""
Class to reconstruct geometries using topologies.
Currently only points are supported.
use_plate_partitioner: If True then use pygplates.PlatePartitioner to partition points,
otherwise use faster points_in_polygons.find_polygons().
"""
use_plate_partitioner = False
def __init__(
self,
rotation_features_or_model,
topology_features,
reconstruction_begin_time,
reconstruction_end_time,
reconstruction_time_interval,
points,
point_begin_times=None,
point_end_times=None,
point_plate_ids=None,
detect_collisions=_DEFAULT_COLLISION,
):
"""
rotation_features_or_model: Rotation model or feature collection(s), or list of features, or filename(s).
topology_features: Topology feature collection(s), or list of features, or filename(s) or any combination of those.
detect_collisions: Collision detection function, or None. Defaults to _DEFAULT_COLLISION.
"""
# Turn rotation data into a RotationModel (if not already).
if not isinstance(rotation_features_or_model, pygplates.RotationModel):
rotation_model = pygplates.RotationModel(rotation_features_or_model)
else:
rotation_model = rotation_features_or_model
self.rotation_model = rotation_model
# Turn topology data into a list of features (if not already).
self.topology_features = pygplates.FeaturesFunctionArgument(
topology_features
).get_features()
# Set up an array of reconstruction times covering the reconstruction time span.
self.reconstruction_begin_time = reconstruction_begin_time
self.reconstruction_end_time = reconstruction_end_time
if reconstruction_time_interval <= 0.0:
raise ValueError("'reconstruction_time_interval' must be positive.")
# Reconstruction can go forward or backward in time.
if self.reconstruction_begin_time > self.reconstruction_end_time:
self.reconstruction_time_step = reconstruction_time_interval
else:
self.reconstruction_time_step = reconstruction_time_interval
# Get number of times including end time if time span is a multiple of time step.
# The '1' is because, for example, 2 time intervals is 3 times.
# The '1e6' deals with limited floatingpoint precision, eg, we want (3.0  0.0) / 1.0 to be 3.0 and not 2.999999 (which gets truncated to 2).
self.num_times = 1 + int(
math.floor(
1e6
+ float(self.reconstruction_end_time  self.reconstruction_begin_time)
/ self.reconstruction_time_step
)
)
# It's possible the time step is larger than the time span, in which case we change it to equal the time span.
# This guarantees there'll be at least one time step (which has two times; one at either end of interval).
if self.num_times == 1:
self.num_times = 2
self.reconstruction_time_step = (
self.reconstruction_end_time  self.reconstruction_begin_time
)
self.reconstruction_time_interval = math.fabs(self.reconstruction_time_step)
self.last_time_index = self.num_times  1
self.points = points
self.num_points = len(points)
# Use the specified point begin times if provided (otherwise use 'inf').
self.point_begin_times = point_begin_times
if self.point_begin_times is None:
self.point_begin_times = [float("inf")] * self.num_points
elif len(self.point_begin_times) != self.num_points:
raise ValueError(
"Length of 'point_begin_times' must match length of 'points'."
)
# Use the specified point end times if provided (otherwise use 'inf').
self.point_end_times = point_end_times
if self.point_end_times is None:
self.point_end_times = [float("inf")] * self.num_points
elif len(self.point_end_times) != self.num_points:
raise ValueError(
"Length of 'point_end_times' must match length of 'points'."
)
# Use the specified point plate IDs if provided (otherwise use '0').
# These plate IDs are only used when a point falls outside all resolved topologies during a time step.
self.point_plate_ids = point_plate_ids
if self.point_plate_ids is None:
self.point_plate_ids = [0] * self.num_points
elif len(self.point_plate_ids) != self.num_points:
raise ValueError(
"Length of 'point_plate_ids' must match length of 'points'."
)
self.detect_collisions = detect_collisions
def reconstruct(self):
# Initialise the reconstruction.
self.begin_reconstruction()
# Loop over the reconstruction times until reached end of the reconstruction time span, or
# all points have entered their valid time range *and* either exited their time range or
# have been deactivated (subducted forward in time or consumed by MOR backward in time).
while self.reconstruct_to_next_time():
pass
return self.get_active_current_points()
def begin_reconstruction(self):
self.current_time_index = 0
# Set up point arrays.
# Store active and inactive points here (inactive points have None in corresponding entries).
self.prev_points = [None] * self.num_points
self.curr_points = [None] * self.num_points
self.next_points = [None] * self.num_points
# Each point can only get activated once (after deactivation it cannot be reactivated).
self.point_has_been_activated = [False] * self.num_points
self.num_activated_points = 0
# Set up topology arrays (corresponding to active/inactive points at same indices).
self.prev_topology_plate_ids = [None] * self.num_points
self.curr_topology_plate_ids = [None] * self.num_points
self.prev_resolved_plate_boundaries = [None] * self.num_points
self.curr_resolved_plate_boundaries = [None] * self.num_points
# Array to store indices of points found in continents
self.in_continent_indices = [None] * self.num_points
self.in_continent_points = [None] * self.num_points
self.deletedpoints = []
self._activate_deactivate_points()
self._find_resolved_topologies_containing_points()
def get_current_time(self):
return (
self.reconstruction_begin_time
+ self.current_time_index * self.reconstruction_time_step
)
def get_all_current_points(self):
return self.curr_points
def get_active_current_points(self):
# Return only the active points (the ones that are not None).
return [point for point in self.get_all_current_points() if point is not None]
def get_in_continent_indices(self):
return self.in_continent_points, self.in_continent_indices
def reconstruct_to_next_time(self):
# If we're at the last time then there is no next time to reconstruct to.
if self.current_time_index == self.last_time_index:
return False
# If all points have been previously activated, but none are currently active then we're finished.
# This means all points have entered their valid time range *and* either exited their time range or
# have been deactivated (subducted forward in time or consumed by MOR backward in time).
if self.num_activated_points == self.num_points and not any(self.curr_points):
return False
# Cache stage rotations by plate ID.
# Use different dicts since using different rotation models and time steps, etc.
reconstruct_stage_rotation_dict = {}
current_time = self.get_current_time()
# Iterate over all points to reconstruct them to the next time step.
for point_index in range(self.num_points):
curr_point = self.curr_points[point_index]
if curr_point is None:
# Current point is not currently active.
# So we cannot reconstruct to next time.
self.next_points[point_index] = None
continue
# Get plate ID of resolved topology containing current point
# (this was determined in last call to '_find_resolved_topologies_containing_points()').
curr_plate_id = self.curr_topology_plate_ids[point_index]
if curr_plate_id is None:
# Current point is currently active but it fell outside all resolved polygons.
# So instead we just reconstruct using its plate ID (that was manually assigned by the user/caller).
curr_plate_id = self.point_plate_ids[point_index]
continue
# Get the stage rotation that will move the point from where it is at the current time to its
# location at the next time step, based on the plate id that contains the point at the current time.
# Speed up by caching stage rotations in a dict.
stage_rotation = reconstruct_stage_rotation_dict.get(curr_plate_id)
if not stage_rotation:
stage_rotation = self.rotation_model.get_rotation(
# Positive/negative time step means reconstructing backward/forward in time.
current_time + self.reconstruction_time_step,
curr_plate_id,
current_time,
)
reconstruct_stage_rotation_dict[curr_plate_id] = stage_rotation
# Use the stage rotation to reconstruct the tracked point from position at current time
# to position at the next time step.
self.next_points[point_index] = stage_rotation * curr_point
#
# Set up for next loop iteration.
#
# Rotate previous, current and next point arrays.
# The new previous will be the old current.
# The new current will be the old next.
# The new next will be the old previous (but values are ignored and overridden in next time step; just reusing its memory).
self.prev_points, self.curr_points, self.next_points = (
self.curr_points,
self.next_points,
self.prev_points,
)
# Swap previous and current topology arrays.
# The new previous will be the old current.
# The new current will be the old previous (but values are ignored and overridden in next time step; just reusing its memory).
self.prev_topology_plate_ids, self.curr_topology_plate_ids = (
self.curr_topology_plate_ids,
self.prev_topology_plate_ids,
)
self.prev_resolved_plate_boundaries, self.curr_resolved_plate_boundaries = (
self.curr_resolved_plate_boundaries,
self.prev_resolved_plate_boundaries,
)
# Move the current time to the next time.
self.current_time_index += 1
current_time = self.get_current_time()
self._activate_deactivate_points()
self._find_resolved_topologies_containing_points()
# Iterate over all points to detect collisions.
if self.detect_collisions:
for point_index in range(self.num_points):
prev_point = self.prev_points[point_index]
curr_point = self.curr_points[point_index]
if prev_point is None or curr_point is None:
# If current point is not currently active then no need to detect a collision for it (to deactivate it).
# Also previous point might just have been activated now, at end of current time step, and hence
# not active at beginning of time step.
continue
# Get plate IDs of resolved topology containing previous and current point
# (this was determined in last call to '_find_resolved_topologies_containing_points()').
#
# Note that could be None, so the collision detection needs to handle that.
prev_plate_id = self.prev_topology_plate_ids[point_index]
curr_plate_id = self.curr_topology_plate_ids[point_index]
# Detect collisions at the end of the current time step since we need previous, and current, points and topologies.
# Deactivate point (in 'curr_points') if subducted (forward in time) or consumed back into MOR (backward in time).
if self.detect_collisions(
self.rotation_model,
current_time,
self.reconstruction_time_interval,
prev_point,
curr_point,
prev_plate_id,
self.prev_resolved_plate_boundaries[point_index],
curr_plate_id,
self.curr_resolved_plate_boundaries[point_index],
):
# An inactive point in 'curr_points' becomes None.
# It may have been reconstructed from the previous time step to a valid position
# but now we override that result as inactive.
self.curr_points[point_index] = None
# self.curr_points.remove(self.curr_points[point_index])
self.deletedpoints.append(point_index)
# We successfully reconstructed to the next time.
return True
def _activate_deactivate_points(self):
current_time = self.get_current_time()
# Iterate over all points and activate/deactivate as necessary depending on each point's valid time range.
for point_index in range(self.num_points):
if self.curr_points[point_index] is None:
if not self.point_has_been_activated[point_index]:
# Point is not active and has never been activated, so see if can activate it.
if (
current_time <= self.point_begin_times[point_index]
and current_time >= self.point_end_times[point_index]
):
# The initial point is assumed to be the position at the current time
# which is typically the point's begin time (approximately).
# But it could be the beginning of the reconstruction time span (specified in constructor)
# if that falls in the middle of the point's valid time range  in this case the
# initial point position is assumed to be in a position that is some time *after*
# it appeared (at its begin time)  and this can happen, for example, if you have a
# uniform grids of points at some intermediate time and want to see how they
# reconstruct to either a younger or older time (remembering that points can
# be subducted forward in time and consumed back into a midocean ridge going
# backward in time).
self.curr_points[point_index] = self.points[point_index]
self.point_has_been_activated[point_index] = True
self.num_activated_points += 1
else:
# Point is active, so see if can deactivate it.
if not (
current_time <= self.point_begin_times[point_index]
and current_time >= self.point_end_times[point_index]
):
self.curr_points[point_index] = None
def _find_resolved_topologies_containing_points(self):
from . import ptt as _ptt
current_time = self.get_current_time()
# Resolve the plate polygons for the current time.
resolved_topologies = []
pygplates.resolve_topologies(
self.topology_features,
self.rotation_model,
resolved_topologies,
current_time,
)
if _ReconstructByTopologies.use_plate_partitioner:
# Create a plate partitioner from the resolved polygons.
plate_partitioner = pygplates.PlatePartitioner(
resolved_topologies, self.rotation_model
)
else:
# Some of 'curr_points' will be None so 'curr_valid_points' contains only the valid (not None)
# points, and 'curr_valid_points_indices' is the same length as 'curr_points' but indexes into
# 'curr_valid_points' so we can quickly find which point (and hence which resolved topology)
# in 'curr_valid_points' is associated with the a particular point in 'curr_points'.
curr_valid_points = []
curr_valid_points_indices = [None] * self.num_points
for point_index, curr_point in enumerate(self.curr_points):
if curr_point is not None:
curr_valid_points_indices[point_index] = len(curr_valid_points)
curr_valid_points.append(curr_point)
# For each valid current point find the resolved topology containing it.
resolved_topologies_containing_curr_valid_points = (
_ptt.utils.points_in_polygons.find_polygons(
curr_valid_points,
[
resolved_topology.get_resolved_boundary()
for resolved_topology in resolved_topologies
],
resolved_topologies,
)
)
# Iterate over all points.
for point_index, curr_point in enumerate(self.curr_points):
if curr_point is None:
# Current point is not currently active  so skip it.
self.curr_topology_plate_ids[point_index] = None
self.curr_resolved_plate_boundaries[point_index] = None
continue
# Find the plate id of the polygon that contains 'curr_point'.
if _ReconstructByTopologies.use_plate_partitioner:
curr_polygon = plate_partitioner.partition_point(curr_point)
else:
curr_polygon = resolved_topologies_containing_curr_valid_points[
# Index back into 'curr_valid_points' and hence also into
# 'resolved_topologies_containing_curr_valid_points'.
curr_valid_points_indices[point_index]
]
self.curr_resolved_plate_boundaries[point_index] = curr_polygon
# If the polygon is None, that means (presumably) that it fell into a crack between
# topologies. So it will be skipped and thrown away from future iterations.
if curr_polygon is None:
self.curr_topology_plate_ids[point_index] = None
continue
# Set the plate ID of resolved topology containing current point.
self.curr_topology_plate_ids[
point_index
] = curr_polygon.get_feature().get_reconstruction_plate_id()
Functions
def reconstruct_points(rotation_features_or_model, topology_features, reconstruction_begin_time, reconstruction_end_time, reconstruction_time_interval, points, point_begin_times=None, point_end_times=None, point_plate_ids=None, detect_collisions=<gplately.reconstruction._DefaultCollision object>)

Function to reconstruct points using the ReconstructByTopologies class below.
For description of parameters see the ReconstructByTopologies class below.
Expand source code
def reconstruct_points( rotation_features_or_model, topology_features, reconstruction_begin_time, reconstruction_end_time, reconstruction_time_interval, points, point_begin_times=None, point_end_times=None, point_plate_ids=None, detect_collisions=_DEFAULT_COLLISION, ): """ Function to reconstruct points using the ReconstructByTopologies class below. For description of parameters see the ReconstructByTopologies class below. """ topology_reconstruction = _ReconstructByTopologies( rotation_features_or_model, topology_features, reconstruction_begin_time, reconstruction_end_time, reconstruction_time_interval, points, point_begin_times, point_end_times, point_plate_ids, detect_collisions, ) return topology_reconstruction.reconstruct()
Classes
class PlateReconstruction (rotation_model, topology_features=None, static_polygons=None, anchor_plate_id=0)

The
PlateReconstruction
class contains methods to reconstruct topology features to specific geological times given arotation_model
, a set oftopology_features
and a set ofstatic_polygons
. Topological plate velocity data at specific geological times can also be calculated from these reconstructed features.Attributes
rotation_model
:str,
orinstance
of<pygplates.FeatureCollection>,
or<pygplates.Feature>,
orsequence
of<pygplates.Feature>,
orinstance
of<pygplates.RotationModel>
, defaultNone
 A rotation model to query equivalent and/or relative topological plate rotations from a time in the past relative to another time in the past or to present day. Can be provided as a rotation filename, or rotation feature collection, or rotation feature, or sequence of rotation features, or a sequence (eg, a list or tuple) of any combination of those four types.
topology_features
:str,
ora sequence (eg,
listor
tuple)
ofinstances
of<pygplates.Feature>,
ora single instance
of<pygplates.Feature>,
oran instance
of<pygplates.FeatureCollection>
, defaultNone
 Reconstructable topological features like trenches, ridges and transforms. Can be provided as an optional topologyfeature filename, or sequence of features, or a single feature.
static_polygons
:str,
orinstance
of<pygplates.Feature>,
orsequence
of<pygplates.Feature>,or an instance
of<pygplates.FeatureCollection>
, defaultNone
 Presentday polygons whose shapes do not change through geological time. They are used to cookiecut dynamic polygons into identifiable topological plates (assigned an ID) according to their presentday locations. Can be provided as a static polygon feature collection, or optional filename, or a single feature, or a sequence of features.
Expand source code
class PlateReconstruction(object): """The `PlateReconstruction` class contains methods to reconstruct topology features to specific geological times given a `rotation_model`, a set of `topology_features` and a set of `static_polygons`. Topological plate velocity data at specific geological times can also be calculated from these reconstructed features. Attributes  rotation_model : str, or instance of <pygplates.FeatureCollection>, or <pygplates.Feature>, or sequence of <pygplates.Feature>, or instance of <pygplates.RotationModel>, default None A rotation model to query equivalent and/or relative topological plate rotations from a time in the past relative to another time in the past or to present day. Can be provided as a rotation filename, or rotation feature collection, or rotation feature, or sequence of rotation features, or a sequence (eg, a list or tuple) of any combination of those four types. topology_features : str, or a sequence (eg, `list` or `tuple`) of instances of <pygplates.Feature>, or a single instance of <pygplates.Feature>, or an instance of <pygplates.FeatureCollection>, default None Reconstructable topological features like trenches, ridges and transforms. Can be provided as an optional topologyfeature filename, or sequence of features, or a single feature. static_polygons : str, or instance of <pygplates.Feature>, or sequence of <pygplates.Feature>,or an instance of <pygplates.FeatureCollection>, default None Presentday polygons whose shapes do not change through geological time. They are used to cookiecut dynamic polygons into identifiable topological plates (assigned an ID) according to their presentday locations. Can be provided as a static polygon feature collection, or optional filename, or a single feature, or a sequence of features. """ def __init__( self, rotation_model, topology_features=None, static_polygons=None, anchor_plate_id=0, ): if hasattr(rotation_model, "reconstruction_identifier"): self.name = rotation_model.reconstruction_identifier else: self.name = None self.anchor_plate_id = int(anchor_plate_id) self.rotation_model = _RotationModel( rotation_model, default_anchor_plate_id=anchor_plate_id ) self.topology_features = _load_FeatureCollection(topology_features) self.static_polygons = _load_FeatureCollection(static_polygons) def __getstate__(self): filenames = {"rotation_model": self.rotation_model.filenames, "anchor_plate_id": self.anchor_plate_id} if self.topology_features: filenames["topology_features"] = self.topology_features.filenames if self.static_polygons: filenames["static_polygons"] = self.static_polygons.filenames # # remove unpicklable items # del self.rotation_model, self.topology_features, self.static_polygons # # really make sure they're gone # self.rotation_model = None # self.topology_features = None # self.static_polygons = None return filenames def __setstate__(self, state): # reinstate unpicklable items self.rotation_model = _RotationModel(state["rotation_model"], default_anchor_plate_id=state["anchor_plate_id"]) self.anchor_plate_id = state["anchor_plate_id"] self.topology_features = None self.static_polygons = None if "topology_features" in state: self.topology_features = _FeatureCollection() for topology in state["topology_features"]: self.topology_features.add(_FeatureCollection(topology)) if "static_polygons" in state: self.static_polygons = _FeatureCollection() for polygon in state["static_polygons"]: self.static_polygons.add(_FeatureCollection(polygon)) def tessellate_subduction_zones( self, time, tessellation_threshold_radians=0.001, ignore_warnings=False, return_geodataframe=False, **kwargs ): """Samples points along subduction zone trenches and obtains subduction data at a particular geological time. Resolves topologies at `time`, tessellates all resolved subducting features to within 'tessellation_threshold_radians' radians and obtains the following information for each sampled point along a trench: `tessellate_subduction_zones` returns a list of 10 verticallystacked tuples with the following data per sampled trench point: * Col. 0  longitude of sampled trench point * Col. 1  latitude of sampled trench point * Col. 2  subducting convergence (relative to trench) velocity magnitude (in cm/yr) * Col. 3  subducting convergence velocity obliquity angle (angle between trench normal vector and convergence velocity vector) * Col. 4  trench absolute (relative to anchor plate) velocity magnitude (in cm/yr) * Col. 5  trench absolute velocity obliquity angle (angle between trench normal vector and trench absolute velocity vector) * Col. 6  length of arc segment (in degrees) that current point is on * Col. 7  trench normal azimuth angle (clockwise starting at North, ie, 0 to 360 degrees) at current point * Col. 8  subducting plate ID * Col. 9  trench plate ID Parameters  time : float The reconstruction time (Ma) at which to query subduction convergence. tessellation_threshold_radians : float, default=0.001 The threshold sampling distance along the subducting trench (in radians). Returns  subduction_data : a list of verticallystacked tuples The results for all tessellated points sampled along the trench. The size of the returned list is equal to the number of tessellated points. Each tuple in the list corresponds to a tessellated point and has the following tuple items: * Col. 0  longitude of sampled trench point * Col. 1  latitude of sampled trench point * Col. 2  subducting convergence (relative to trench) velocity magnitude (in cm/yr) * Col. 3  subducting convergence velocity obliquity angle (angle between trench normal vector and convergence velocity vector) * Col. 4  trench absolute (relative to anchor plate) velocity magnitude (in cm/yr) * Col. 5  trench absolute velocity obliquity angle (angle between trench normal vector and trench absolute velocity vector) * Col. 6  length of arc segment (in degrees) that current point is on * Col. 7  trench normal azimuth angle (clockwise starting at North, ie, 0 to 360 degrees) at current point * Col. 8  subducting plate ID * Col. 9  trench plate ID Notes  Each sampled point in the output is the midpoint of a great circle arc between two adjacent points in the trench polyline. The trench normal vector used in the obliquity calculations is perpendicular to the great circle arc of each point (arc midpoint) and pointing towards the overriding plate (rather than away from it). Each trench is sampled at approximately uniform intervals along its length (specified via a threshold sampling distance). The sampling along the entire length of a trench is not exactly uniform. Each segment along a trench is sampled such that the samples have a uniform spacing that is less than or equal to the threshold sampling distance. However each segment in a trench might have a slightly different spacing distance (since segment lengths are not integer multiples of the threshold sampling distance). The trench normal (at each arc segment midpoint) always points *towards* the overriding plate. The obliquity angles are in the range (180 180). The range (0, 180) goes clockwise (when viewed from above the Earth) from the trench normal direction to the velocity vector. The range (0, 180) goes counterclockwise. You can change the range (180, 180) to the range (0, 360) by adding 360 to negative angles. The trench normal is perpendicular to the trench and pointing toward the overriding plate. Note that the convergence velocity magnitude is negative if the plates are diverging (if convergence obliquity angle is greater than 90 or less than 90). And note that the absolute velocity magnitude is negative if the trench (subduction zone) is moving towards the overriding plate (if absolute obliquity angle is less than 90 or greater than 90)  note that this ignores the kinematics of the subducting plate. The delta time interval used for velocity calculations is, by default, assumed to be 1Ma. """ from . import ptt as _ptt anchor_plate_id = kwargs.pop("anchor_plate_id", self.anchor_plate_id) if ignore_warnings: with warnings.catch_warnings(): warnings.simplefilter("ignore") subduction_data = _ptt.subduction_convergence.subduction_convergence( self.rotation_model, self.topology_features, tessellation_threshold_radians, float(time), anchor_plate_id=anchor_plate_id, **kwargs ) else: subduction_data = _ptt.subduction_convergence.subduction_convergence( self.rotation_model, self.topology_features, tessellation_threshold_radians, float(time), anchor_plate_id=anchor_plate_id, **kwargs ) subduction_data = np.vstack(subduction_data) if return_geodataframe: import geopandas as gpd from shapely import geometry coords = [ geometry.Point(lon, lat) for lon, lat in zip(subduction_data[:, 0], subduction_data[:, 1]) ] d = {"geometry": coords} labels = [ "convergence velocity (cm/yr)", "convergence obliquity angle (degrees)", "trench velocity (cm/yr)", "trench obliquity angle (degrees)", "length (degrees)", "trench normal angle (degrees)", "subducting plate ID", "overriding plate ID", ] for i, label in enumerate(labels): index = 2 + i d[label] = subduction_data[:, index] gdf = gpd.GeoDataFrame(d, geometry="geometry") return gdf else: return subduction_data def total_subduction_zone_length(self, time, use_ptt=False, ignore_warnings=False): """Calculates the total length of all midocean ridges (km) at the specified geological time (Ma). if `use_ptt` is True Uses Plate Tectonic Tools' `subduction_convergence` module to calculate trench segment lengths on a unit sphere. The aggregated total subduction zone length is scaled to kilometres using the geocentric radius. Otherwise Resolves topology features ascribed to the `PlateReconstruction` model and extracts their shared boundary sections. The lengths of each trench boundary section are appended to the total subduction zone length. The total length is scaled to kilometres using a latitudedependent (geocentric) Earth radius. Parameters  time : int The geological time at which to calculate total midocean ridge lengths. use_ptt : bool, default=False If set to `True`, the PTT method is used. ignore_warnings : bool, default=False Choose whether to ignore warning messages from PTT's `subduction_convergence` workflow. These warnings alert the user when certain subduction subsegments are ignored  this happens when the trench segments have unidentifiable subduction polarities and/or subducting plates. Raises  ValueError If neither `use_pygplates` or `use_ptt` have been set to `True`. Returns  total_subduction_zone_length_kms : float The total subduction zone length (in km) at the specified `time`. """ from . import ptt as _ptt if use_ptt: with warnings.catch_warnings(): warnings.simplefilter("ignore") subduction_data = self.tessellate_subduction_zones( time, ignore_warnings=ignore_warnings ) trench_arcseg = subduction_data[:, 6] trench_pt_lat = subduction_data[:, 1] total_subduction_zone_length_kms = 0 for i, segment in enumerate(trench_arcseg): earth_radius = _tools.geocentric_radius(trench_pt_lat[i]) / 1e3 total_subduction_zone_length_kms += np.deg2rad(segment) * earth_radius return total_subduction_zone_length_kms else: resolved_topologies = [] shared_boundary_sections = [] pygplates.resolve_topologies( self.topology_features, self.rotation_model, resolved_topologies, time, shared_boundary_sections, ) total_subduction_zone_length_kms = 0.0 for shared_boundary_section in shared_boundary_sections: if ( shared_boundary_section.get_feature().get_feature_type() != pygplates.FeatureType.gpml_subduction_zone ): continue for ( shared_sub_segment ) in shared_boundary_section.get_shared_sub_segments(): clat, clon = ( shared_sub_segment.get_resolved_geometry() .get_centroid() .to_lat_lon() ) earth_radius = _tools.geocentric_radius(clat) / 1e3 total_subduction_zone_length_kms += ( shared_sub_segment.get_resolved_geometry().get_arc_length() * earth_radius ) return total_subduction_zone_length_kms def total_continental_arc_length( self, time, continental_grid, trench_arc_distance, ignore_warnings=True, ): """Calculates the total length of all global continental arcs (km) at the specified geological time (Ma). Uses Plate Tectonic Tools' `subduction_convergence` workflow to sample a given plate model's trench features into point features and obtain their subduction polarities. The resolved points are projected out by the `trench_arc_distance` and their new locations are linearly interpolated onto the supplied `continental_grid`. If the projected trench points lie in the grid, they are considered continental arc points, and their arc segment lengths are appended to the total continental arc length for the specified `time`. The total length is scaled to kilometres using the geocentric Earth radius. Parameters  time : int The geological time at which to calculate total continental arc lengths. continental_grid: Raster, array_like, or str The continental grid used to identify continental arc points. Must be convertible to `Raster`. For an array, a global extent is assumed [180,180,90,90]. For a filename, the extent is obtained from the file. trench_arc_distance : float The trenchtoarc distance (in kilometres) to project sampled trench points out by in the direction of their subduction polarities. ignore_warnings : bool, default=True Choose whether to ignore warning messages from PTT's subduction_convergence workflow that alerts the user of subduction subsegments that are ignored due to unidentified polarities and/or subducting plates. Returns  total_continental_arc_length_kms : float The continental arc length (in km) at the specified time. """ from . import grids as _grids if isinstance(continental_grid, _grids.Raster): graster = continental_grid elif isinstance(continental_grid, str): # Process the continental grid directory graster = _grids.Raster( data=continental_grid, realign=True, time=float(time), ) else: # Process the masked continental grid try: continental_grid = np.array(continental_grid) graster = _grids.Raster( data=continental_grid, extent=[180, 180, 90, 90], time=float(time), ) except Exception as e: raise TypeError( "Invalid type for `continental_grid` (must be Raster," + " str, or array_like)" ) from e if (time != graster.time) and (not ignore_warnings): raise RuntimeWarning( "`continental_grid.time` ({}) ".format(graster.time) + "does not match `time` ({})".format(time) ) # Obtain trench data with Plate Tectonic Tools trench_data = self.tessellate_subduction_zones( time, ignore_warnings=ignore_warnings ) # Extract trench data trench_normal_azimuthal_angle = trench_data[:, 7] trench_arcseg = trench_data[:, 6] trench_pt_lon = trench_data[:, 0] trench_pt_lat = trench_data[:, 1] # Modify the trencharc distance using the geocentric radius arc_distance = trench_arc_distance / ( _tools.geocentric_radius(trench_pt_lat) / 1000 ) # Project trench points out along trencharc distance, and obtain their new latlon coordinates dlon = arc_distance * np.sin(np.radians(trench_normal_azimuthal_angle)) dlat = arc_distance * np.cos(np.radians(trench_normal_azimuthal_angle)) ilon = trench_pt_lon + np.degrees(dlon) ilat = trench_pt_lat + np.degrees(dlat) # Linearly interpolate projected points onto continental grids, and collect the indices of points that lie # within the grids. sampled_points = graster.interpolate( ilon, ilat, method="linear", return_indices=False, ) continental_indices = np.where(sampled_points > 0) point_lats = ilat[continental_indices] point_radii = _tools.geocentric_radius(point_lats) * 1.0e3 # km segment_arclens = np.deg2rad(trench_arcseg[continental_indices]) segment_lengths = point_radii * segment_arclens return np.sum(segment_lengths) def tessellate_mid_ocean_ridges( self, time, tessellation_threshold_radians=0.001, ignore_warnings=False, return_geodataframe=False, **kwargs ): """Samples points along resolved spreading features (e.g. midocean ridges) and calculates spreading rates and lengths of ridge segments at a particular geological time. Resolves topologies at `time`, tessellates all resolved spreading features to within 'tessellation_threshold_radians' radians. Returns a 4column vertically stacked tuple with the following data. * Col. 0  longitude of sampled ridge point * Col. 1  latitude of sampled ridge point * Col. 2  spreading velocity magnitude (in cm/yr) * Col. 3  length of arc segment (in degrees) that current point is on All spreading feature types are considered. The transform segments of spreading features are ignored. Note: by default, the function assumes that a segment can deviate 45 degrees from the stage pole before it is considered a transform segment. Parameters  time : float The reconstruction time (Ma) at which to query subduction convergence. tessellation_threshold_radians : float, default=0.001 The threshold sampling distance along the subducting trench (in radians). ignore_warnings : bool, default=False Choose to ignore warnings from Plate Tectonic Tools' ridge_spreading_rate workflow. Returns  ridge_data : a list of verticallystacked tuples The results for all tessellated points sampled along the trench. The size of the returned list is equal to the number of tessellated points. Each tuple in the list corresponds to a tessellated point and has the following tuple items: * longitude of sampled point * latitude of sampled point * spreading velocity magnitude (in cm/yr) * length of arc segment (in degrees) that current point is on """ from . import ptt as _ptt anchor_plate_id = kwargs.pop("anchor_plate_id", self.anchor_plate_id) if ignore_warnings: with warnings.catch_warnings(): warnings.simplefilter("ignore") spreading_feature_types = [pygplates.FeatureType.gpml_mid_ocean_ridge] ridge_data = _ptt.ridge_spreading_rate.spreading_rates( self.rotation_model, self.topology_features, float(time), tessellation_threshold_radians, spreading_feature_types, anchor_plate_id=anchor_plate_id, **kwargs ) else: spreading_feature_types = [pygplates.FeatureType.gpml_mid_ocean_ridge] ridge_data = _ptt.ridge_spreading_rate.spreading_rates( self.rotation_model, self.topology_features, float(time), tessellation_threshold_radians, spreading_feature_types, anchor_plate_id=anchor_plate_id, **kwargs ) if not ridge_data: # the _ptt.ridge_spreading_rate.spreading_rates might return None return ridge_data = np.vstack(ridge_data) if return_geodataframe: import geopandas as gpd from shapely import geometry points = [ geometry.Point(lon, lat) for lon, lat in zip(ridge_data[:, 0], ridge_data[:, 1]) ] gdf = gpd.GeoDataFrame( { "geometry": points, "velocity (cm/yr)": ridge_data[:, 2], "length (degrees)": ridge_data[:, 3], }, geometry="geometry", ) return gdf else: return ridge_data def total_ridge_length(self, time, use_ptt=False, ignore_warnings=False): """Calculates the total length of all midocean ridges (km) at the specified geological time (Ma). if `use_ptt` is True Uses Plate Tectonic Tools' `ridge_spreading_rate` workflow to calculate ridge segment lengths. Scales lengths to kilometres using the geocentric radius. Otherwise Resolves topology features of the PlateReconstruction model and extracts their shared boundary sections. The lengths of each GPML midocean ridge shared boundary section are appended to the total ridge length. Scales lengths to kilometres using the geocentric radius. Parameters  time : int The geological time at which to calculate total midocean ridge lengths. use_ptt : bool, default=False If set to `True`, the PTT method is used. ignore_warnings : bool, default=False Choose whether to ignore warning messages from PTT's `ridge_spreading_rate` workflow. Raises  ValueError If neither `use_pygplates` or `use_ptt` have been set to `True`. Returns  total_ridge_length_kms : float The total length of global midocean ridges (in kilometres) at the specified time. """ from . import ptt as _ptt if use_ptt is True: with warnings.catch_warnings(): warnings.simplefilter("ignore") ridge_data = self.tessellate_mid_ocean_ridges(time) ridge_arcseg = ridge_data[:, 3] ridge_pt_lat = ridge_data[:, 1] total_ridge_length_kms = 0 for i, segment in enumerate(ridge_arcseg): earth_radius = _tools.geocentric_radius(ridge_pt_lat[i]) / 1e3 total_ridge_length_kms += np.deg2rad(segment) * earth_radius return total_ridge_length_kms else: resolved_topologies = [] shared_boundary_sections = [] pygplates.resolve_topologies( self.topology_features, self.rotation_model, resolved_topologies, time, shared_boundary_sections, ) total_ridge_length_kms = 0.0 for shared_boundary_section in shared_boundary_sections: if ( shared_boundary_section.get_feature().get_feature_type() != pygplates.FeatureType.gpml_mid_ocean_ridge ): continue for ( shared_sub_segment ) in shared_boundary_section.get_shared_sub_segments(): clat, clon = ( shared_sub_segment.get_resolved_geometry() .get_centroid() .to_lat_lon() ) earth_radius = _tools.geocentric_radius(clat) / 1e3 total_ridge_length_kms += ( shared_sub_segment.get_resolved_geometry().get_arc_length() * earth_radius ) return total_ridge_length_kms def reconstruct(self, feature, to_time, from_time=0, anchor_plate_id=None, **kwargs): """Reconstructs regular geological features, motion paths or flowlines to a specific geological time. Parameters  feature : str, or instance of <pygplates.FeatureCollection>, or <pygplates.Feature>, or sequence of <pygplates.Feature> The geological features to reconstruct. Can be provided as a feature collection, or filename, or feature, or sequence of features, or a sequence (eg, a list or tuple) of any combination of those four types. to_time : float, or :class:`GeoTimeInstant` The specific geological time to reconstruct to. from_time : float, default=0 The specific geological time to reconstruct from. By default, this is set to present day. Raises `NotImplementedError` if `from_time` is not set to 0.0 Ma (present day). anchor_plate_id : int, default=None Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made with respect to the absolute reference frame (anchor_plate_id = 0), like a stationary object in the mantle, unless otherwise specified. **reconstruct_type : ReconstructType, default=ReconstructType.feature_geometry The specific reconstruction type to generate based on input feature geometry type. Can be provided as pygplates.ReconstructType.feature_geometry to only reconstruct regular feature geometries, or pygplates.ReconstructType.motion_path to only reconstruct motion path features, or pygplates.ReconstructType.flowline to only reconstruct flowline features. Generates :class:`reconstructed feature geometries<ReconstructedFeatureGeometry>’, or :class:`reconstructed motion paths<ReconstructedMotionPath>’, or :class:`reconstructed flowlines<ReconstructedFlowline>’ respectively. **group_with_feature : bool, default=False Used to group reconstructed geometries with their features. This can be useful when a feature has more than one geometry and hence more than one reconstructed geometry. The output *reconstructed_geometries* then becomes a list of tuples where each tuple contains a :class:`feature<Feature>` and a ``list`` of reconstructed geometries. Note: this keyword argument only applies when *reconstructed_geometries* is a list because exported files are always grouped with their features. This is applicable to all ReconstructType features. **export_wrap_to_dateline : bool, default=True Wrap/clip reconstructed geometries to the dateline. Returns  reconstructed_features : list Reconstructed geological features (generated by the reconstruction) are appended to the list. The reconstructed geometries are output in the same order as that of their respective input features (in the parameter “features”). The order across input feature collections is also retained. This happens regardless of whether *features* and *reconstructed_features* include files or not. Note: if keyword argument group_with_feature=True then the list contains tuples that group each :class:`feature<Feature>` with a list of its reconstructed geometries. Raises  NotImplementedError if the starting time for reconstruction `from_time` is not equal to 0.0. """ from_time, to_time = float(from_time), float(to_time) reconstructed_features = [] if not anchor_plate_id: anchor_plate_id = self.anchor_plate_id pygplates.reconstruct( feature, self.rotation_model, reconstructed_features, to_time, anchor_plate_id=anchor_plate_id, **kwargs ) return reconstructed_features def get_point_velocities(self, lons, lats, time, delta_time=1.0): """Generates a velocity domain feature collection, resolves them into points, and calculates the north and east components of the velocity vector for each point in the domain at a particular geological `time`. Notes  Velocity domain feature collections are MeshNodetype features. These are produced from `lons` and `lats` pairs represented as multipoint geometries (projections onto the surface of the unit length sphere). These features are resolved into domain points and assigned plate IDs which are used to obtain the equivalent stage rotations of identified tectonic plates over a time interval (`delta_time`). Each velocity domain point and its stage rotation are used to calculate the point's plate velocity at a particular `time`. Obtained velocities for each domain point are represented in the northeastdown coordinate system. Parameters  lons : array A 1D array of point data's longitudes. lats : array A 1D array of point data's latitudes. time : float The specific geological time (Ma) at which to calculate plate velocities. delta_time : float, default=1.0 The time increment used for generating partitioning plate stage rotations. 1.0Ma by default. Returns  all_velocities : 1D list of tuples For each velocity domain feature point, a tuple of (north, east, down) velocity components is generated and appended to a list of velocity data. The length of `all_velocities` is equivalent to the number of domain points resolved from the latlon array parameters. """ # Add points to a multipoint geometry time = float(time) multi_point = pygplates.MultiPointOnSphere( [(float(lat), float(lon)) for lat, lon in zip(lats, lons)] ) # Create a feature containing the multipoint feature, and defined as MeshNode type meshnode_feature = pygplates.Feature( pygplates.FeatureType.create_from_qualified_string("gpml:MeshNode") ) meshnode_feature.set_geometry(multi_point) meshnode_feature.set_name("Velocity Mesh Nodes from pygplates") velocity_domain_features = pygplates.FeatureCollection(meshnode_feature) # NB: at this point, the feature could be written to a file using # output_feature_collection.write('myfilename.gpmlz') # All domain points and associated (magnitude, azimuth, inclination) velocities for the current time. all_domain_points = [] all_velocities = [] # Partition our velocity domain features into our topological plate polygons at the current 'time'. plate_partitioner = pygplates.PlatePartitioner( self.topology_features, self.rotation_model, time ) for velocity_domain_feature in velocity_domain_features: # A velocity domain feature usually has a single geometry but we'll assume it can be any number. # Iterate over them all. for velocity_domain_geometry in velocity_domain_feature.get_geometries(): for velocity_domain_point in velocity_domain_geometry.get_points(): all_domain_points.append(velocity_domain_point) partitioning_plate = plate_partitioner.partition_point( velocity_domain_point ) if partitioning_plate: # We need the newly assigned plate ID # to get the equivalent stage rotation of that tectonic plate. partitioning_plate_id = ( partitioning_plate.get_feature().get_reconstruction_plate_id() ) # Get the stage rotation of partitioning plate from 'time + delta_time' to 'time'. equivalent_stage_rotation = self.rotation_model.get_rotation( time, partitioning_plate_id, time + delta_time ) # Calculate velocity at the velocity domain point. # This is from 'time + delta_time' to 'time' on the partitioning plate. velocity_vectors = pygplates.calculate_velocities( [velocity_domain_point], equivalent_stage_rotation, delta_time, ) # Convert global 3D velocity vectors to local (magnitude, azimuth, inclination) tuples # (one tuple per point). velocities = pygplates.LocalCartesian.convert_from_geocentric_to_north_east_down( [velocity_domain_point], velocity_vectors ) all_velocities.append( (velocities[0].get_x(), velocities[0].get_y()) ) else: all_velocities.append((0, 0)) return np.array(all_velocities) def create_motion_path( self, lons, lats, time_array, plate_id=None, anchor_plate_id=None, return_rate_of_motion=False, ): """Create a path of points to mark the trajectory of a plate's motion through geological time. Parameters  lons : arr An array containing the longitudes of seed points on a plate in motion. lats : arr An array containing the latitudes of seed points on a plate in motion. time_array : arr An array of reconstruction times at which to determine the trajectory of a point on a plate. For example: import numpy as np min_time = 30 max_time = 100 time_step = 2.5 time_array = np.arange(min_time, max_time + time_step, time_step) plate_id : int, default=None The ID of the moving plate. If this is not passed, the plate ID of the seed points are ascertained using pygplates' `PlatePartitioner`. anchor_plate_id : int, default=0 The ID of the anchor plate. return_rate_of_motion : bool, default=False Choose whether to return the rate of plate motion through time for each Returns  rlons : ndarray An ndimensional array with columns containing the longitudes of the seed points at each timestep in `time_array`. There are n columns for n seed points. rlats : ndarray An ndimensional array with columns containing the latitudes of the seed points at each timestep in `time_array`. There are n columns for n seed points. StepTimes StepRates Examples  To access the latitudes and longitudes of each seed point's motion path: for i in np.arange(0,len(seed_points)): current_lons = lon[:,i] current_lats = lat[:,i] """ lons = np.atleast_1d(lons) lats = np.atleast_1d(lats) time_array = np.atleast_1d(time_array) # ndarrays to fill with reconstructed points and # rates of motion (if requested) rlons = np.empty((len(time_array), len(lons))) rlats = np.empty((len(time_array), len(lons))) if plate_id is None: query_plate_id = True else: query_plate_id = False plate_ids = np.ones(len(lons), dtype=int) * plate_id if not anchor_plate_id: anchor_plate_id = self.anchor_plate_id seed_points = zip(lats, lons) for i, lat_lon in enumerate(seed_points): seed_points_at_digitisation_time = pygplates.PointOnSphere( pygplates.LatLonPoint(float(lat_lon[0]), float(lat_lon[1])) ) # Allocate the presentday plate ID to the PointOnSphere if # it was not given. if query_plate_id: plate_id = _tools.plate_partitioner_for_point( lat_lon, self.topology_features, self.rotation_model ) else: plate_id = plate_ids[i] # Create the motion path feature. enforce float and int for C++ signature. motion_path_feature = pygplates.Feature.create_motion_path( seed_points_at_digitisation_time, time_array, valid_time=(time_array.max(), time_array.min()), relative_plate=int(plate_id), reconstruction_plate_id=int(anchor_plate_id), ) reconstructed_motion_paths = self.reconstruct( motion_path_feature, to_time=0, reconstruct_type=pygplates.ReconstructType.motion_path, anchor_plate_id=int(plate_id), ) # Turn motion paths in to latlon coordinates for reconstructed_motion_path in reconstructed_motion_paths: trail = reconstructed_motion_path.get_motion_path().to_lat_lon_array() lon, lat = np.flipud(trail[:, 1]), np.flipud(trail[:, 0]) rlons[:, i] = lon rlats[:, i] = lat # Obtain stepplot coordinates for rate of motion if return_rate_of_motion is True: StepTimes = np.empty(((len(time_array)  1) * 2, len(lons))) StepRates = np.empty(((len(time_array)  1) * 2, len(lons))) # Get timestep TimeStep = [] for j in range(len(time_array)  1): diff = time_array[j + 1]  time_array[j] TimeStep.append(diff) # Iterate over each segment in the reconstructed motion path, get the distance travelled by the moving # plate relative to the fixed plate in each time step Dist = [] for reconstructed_motion_path in reconstructed_motion_paths: for ( segment ) in reconstructed_motion_path.get_motion_path().get_segments(): Dist.append( segment.get_arc_length() * _tools.geocentric_radius( segment.get_start_point().to_lat_lon()[0] ) / 1e3 ) # Note that the motion path coordinates come out starting with the oldest time and working forwards # So, to match our 'times' array, we flip the order Dist = np.flipud(Dist) # Get rate of motion as distance per Myr Rate = np.asarray(Dist) / TimeStep # Manipulate arrays to get a step plot StepRate = np.zeros(len(Rate) * 2) StepRate[::2] = Rate StepRate[1::2] = Rate StepTime = np.zeros(len(Rate) * 2) StepTime[::2] = time_array[:1] StepTime[1::2] = time_array[1:] # Append the nth point's step time and step rate coordinates to the ndarray StepTimes[:, i] = StepTime StepRates[:, i] = StepRate * 0.1 # cm/yr # Obseleted by Lauren's changes above (though it is more efficient) # multiply arc length of the motion path segment by a latitudedependent Earth radius # use latitude of the segment start point # distance.append( segment.get_arc_length() * _tools.geocentric_radius(segment.get_start_point().to_lat_lon()[0]) / 1e3) # rate = np.asarray(distance)/np.diff(time_array) # rates[:,i] = np.flipud(rate) # rates *= 0.1 # cm/yr if return_rate_of_motion is True: return ( np.squeeze(rlons), np.squeeze(rlats), np.squeeze(StepTimes), np.squeeze(StepRates), ) else: return np.squeeze(rlons), np.squeeze(rlats) def create_flowline( self, lons, lats, time_array, left_plate_ID, right_plate_ID, return_rate_of_motion=False, ): """Create a path of points to track plate motion away from spreading ridges over time using halfstage rotations. Parameters  lons : arr An array of longitudes of points along spreading ridges. lats : arr An array of latitudes of points along spreading ridges. time_array : arr A list of times to obtain seed point locations at. left_plate_ID : int The plate ID of the polygon to the left of the spreading ridge. right_plate_ID : int The plate ID of the polygon to the right of the spreading ridge. return_rate_of_motion : bool, default False Choose whether to return a step time and step rate array for a step plot of motion. Returns  left_lon : ndarray The longitudes of the __left__ flowline for n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. left_lat : ndarray The latitudes of the __left__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. right_lon : ndarray The longitudes of the __right__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. right_lat : ndarray The latitudes of the __right__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. Examples  To access the ith seed point's left and right latitudes and longitudes: for i in np.arange(0,len(seed_points)): left_flowline_longitudes = left_lon[:,i] left_flowline_latitudes = left_lat[:,i] right_flowline_longitudes = right_lon[:,i] right_flowline_latitudes = right_lat[:,i] """ lats = np.atleast_1d(lats) lons = np.atleast_1d(lons) time_array = np.atleast_1d(time_array) seed_points = list(zip(lats, lons)) multi_point = pygplates.MultiPointOnSphere(seed_points) start = 0 if time_array[0] != 0: start = 1 time_array = np.hstack([[0], time_array]) # Create the flowline feature flowline_feature = pygplates.Feature.create_flowline( multi_point, time_array.tolist(), valid_time=(time_array.max(), time_array.min()), left_plate=left_plate_ID, right_plate=right_plate_ID, ) # reconstruct the flowline in presentday coordinates reconstructed_flowlines = self.reconstruct( flowline_feature, to_time=0, reconstruct_type=pygplates.ReconstructType.flowline, ) # Wrap things to the dateline, to avoid plotting artefacts. date_line_wrapper = pygplates.DateLineWrapper() # Create latlon ndarrays to store the left and right lats and lons of flowlines left_lon = np.empty((len(time_array), len(lons))) left_lat = np.empty((len(time_array), len(lons))) right_lon = np.empty((len(time_array), len(lons))) right_lat = np.empty((len(time_array), len(lons))) StepTimes = np.empty(((len(time_array)  1) * 2, len(lons))) StepRates = np.empty(((len(time_array)  1) * 2, len(lons))) # Iterate over the reconstructed flowlines. Each seed point results in a 'left' and 'right' flowline for i, reconstructed_flowline in enumerate(reconstructed_flowlines): # Get the points for the left flowline only left_latlon = reconstructed_flowline.get_left_flowline().to_lat_lon_array() left_lon[:, i] = left_latlon[:, 1] left_lat[:, i] = left_latlon[:, 0] # Repeat for the right flowline points right_latlon = ( reconstructed_flowline.get_right_flowline().to_lat_lon_array() ) right_lon[:, i] = right_latlon[:, 1] right_lat[:, i] = right_latlon[:, 0] if return_rate_of_motion: for i, reconstructed_motion_path in enumerate(reconstructed_flowlines): distance = [] for ( segment ) in reconstructed_motion_path.get_left_flowline().get_segments(): distance.append( segment.get_arc_length() * _tools.geocentric_radius( segment.get_start_point().to_lat_lon()[0] ) / 1e3 ) # Get rate of motion as distance per Myr # Need to multiply rate by 2, since flowlines give us halfspreading rate time_step = time_array[1]  time_array[0] Rate = ( np.asarray(distance) / time_step ) * 2 # since we created the flowline at X increment # Manipulate arrays to get a step plot StepRate = np.zeros(len(Rate) * 2) StepRate[::2] = Rate StepRate[1::2] = Rate StepTime = np.zeros(len(Rate) * 2) StepTime[::2] = time_array[:1] StepTime[1::2] = time_array[1:] # Append the nth point's step time and step rate coordinates to the ndarray StepTimes[:, i] = StepTime StepRates[:, i] = StepRate * 0.1 # cm/yr return ( left_lon[start:], left_lat[start:], right_lon[start:], right_lat[start:], StepTimes, StepRates, ) else: return ( left_lon[start:], left_lat[start:], right_lon[start:], right_lat[start:], )
Methods
def create_flowline(self, lons, lats, time_array, left_plate_ID, right_plate_ID, return_rate_of_motion=False)

Create a path of points to track plate motion away from spreading ridges over time using halfstage rotations.
Parameters
lons
:arr
 An array of longitudes of points along spreading ridges.
lats
:arr
 An array of latitudes of points along spreading ridges.
time_array
:arr
 A list of times to obtain seed point locations at.
left_plate_ID
:int
 The plate ID of the polygon to the left of the spreading ridge.
right_plate_ID
:int
 The plate ID of the polygon to the right of the spreading ridge.
return_rate_of_motion
:bool
, defaultFalse
 Choose whether to return a step time and step rate array for a step plot of motion.
Returns
left_lon
:ndarray
 The longitudes of the left flowline for n seed points.
There are n columns for n seed points, and m rows
for m time steps in
time_array
. left_lat
:ndarray
 The latitudes of the left flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in
time_array
. right_lon
:ndarray
 The longitudes of the right flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in
time_array
. right_lat
:ndarray
 The latitudes of the right flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in
time_array
.
Examples
To access the ith seed point's left and right latitudes and longitudes:
for i in np.arange(0,len(seed_points)): left_flowline_longitudes = left_lon[:,i] left_flowline_latitudes = left_lat[:,i] right_flowline_longitudes = right_lon[:,i] right_flowline_latitudes = right_lat[:,i]
Expand source code
def create_flowline( self, lons, lats, time_array, left_plate_ID, right_plate_ID, return_rate_of_motion=False, ): """Create a path of points to track plate motion away from spreading ridges over time using halfstage rotations. Parameters  lons : arr An array of longitudes of points along spreading ridges. lats : arr An array of latitudes of points along spreading ridges. time_array : arr A list of times to obtain seed point locations at. left_plate_ID : int The plate ID of the polygon to the left of the spreading ridge. right_plate_ID : int The plate ID of the polygon to the right of the spreading ridge. return_rate_of_motion : bool, default False Choose whether to return a step time and step rate array for a step plot of motion. Returns  left_lon : ndarray The longitudes of the __left__ flowline for n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. left_lat : ndarray The latitudes of the __left__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. right_lon : ndarray The longitudes of the __right__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. right_lat : ndarray The latitudes of the __right__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. Examples  To access the ith seed point's left and right latitudes and longitudes: for i in np.arange(0,len(seed_points)): left_flowline_longitudes = left_lon[:,i] left_flowline_latitudes = left_lat[:,i] right_flowline_longitudes = right_lon[:,i] right_flowline_latitudes = right_lat[:,i] """ lats = np.atleast_1d(lats) lons = np.atleast_1d(lons) time_array = np.atleast_1d(time_array) seed_points = list(zip(lats, lons)) multi_point = pygplates.MultiPointOnSphere(seed_points) start = 0 if time_array[0] != 0: start = 1 time_array = np.hstack([[0], time_array]) # Create the flowline feature flowline_feature = pygplates.Feature.create_flowline( multi_point, time_array.tolist(), valid_time=(time_array.max(), time_array.min()), left_plate=left_plate_ID, right_plate=right_plate_ID, ) # reconstruct the flowline in presentday coordinates reconstructed_flowlines = self.reconstruct( flowline_feature, to_time=0, reconstruct_type=pygplates.ReconstructType.flowline, ) # Wrap things to the dateline, to avoid plotting artefacts. date_line_wrapper = pygplates.DateLineWrapper() # Create latlon ndarrays to store the left and right lats and lons of flowlines left_lon = np.empty((len(time_array), len(lons))) left_lat = np.empty((len(time_array), len(lons))) right_lon = np.empty((len(time_array), len(lons))) right_lat = np.empty((len(time_array), len(lons))) StepTimes = np.empty(((len(time_array)  1) * 2, len(lons))) StepRates = np.empty(((len(time_array)  1) * 2, len(lons))) # Iterate over the reconstructed flowlines. Each seed point results in a 'left' and 'right' flowline for i, reconstructed_flowline in enumerate(reconstructed_flowlines): # Get the points for the left flowline only left_latlon = reconstructed_flowline.get_left_flowline().to_lat_lon_array() left_lon[:, i] = left_latlon[:, 1] left_lat[:, i] = left_latlon[:, 0] # Repeat for the right flowline points right_latlon = ( reconstructed_flowline.get_right_flowline().to_lat_lon_array() ) right_lon[:, i] = right_latlon[:, 1] right_lat[:, i] = right_latlon[:, 0] if return_rate_of_motion: for i, reconstructed_motion_path in enumerate(reconstructed_flowlines): distance = [] for ( segment ) in reconstructed_motion_path.get_left_flowline().get_segments(): distance.append( segment.get_arc_length() * _tools.geocentric_radius( segment.get_start_point().to_lat_lon()[0] ) / 1e3 ) # Get rate of motion as distance per Myr # Need to multiply rate by 2, since flowlines give us halfspreading rate time_step = time_array[1]  time_array[0] Rate = ( np.asarray(distance) / time_step ) * 2 # since we created the flowline at X increment # Manipulate arrays to get a step plot StepRate = np.zeros(len(Rate) * 2) StepRate[::2] = Rate StepRate[1::2] = Rate StepTime = np.zeros(len(Rate) * 2) StepTime[::2] = time_array[:1] StepTime[1::2] = time_array[1:] # Append the nth point's step time and step rate coordinates to the ndarray StepTimes[:, i] = StepTime StepRates[:, i] = StepRate * 0.1 # cm/yr return ( left_lon[start:], left_lat[start:], right_lon[start:], right_lat[start:], StepTimes, StepRates, ) else: return ( left_lon[start:], left_lat[start:], right_lon[start:], right_lat[start:], )
def create_motion_path(self, lons, lats, time_array, plate_id=None, anchor_plate_id=None, return_rate_of_motion=False)

Create a path of points to mark the trajectory of a plate's motion through geological time.
Parameters
lons
:arr
 An array containing the longitudes of seed points on a plate in motion.
lats
:arr
 An array containing the latitudes of seed points on a plate in motion.
time_array
:arr
 An array of reconstruction times at which to determine the trajectory
of a point on a plate. For example:
import numpy as np min_time = 30 max_time = 100 time_step = 2.5 time_array = np.arange(min_time, max_time + time_step, time_step)
plate_id
:int
, default=None
 The ID of the moving plate. If this is not passed, the plate ID of the
seed points are ascertained using pygplates'
PlatePartitioner
. anchor_plate_id
:int
, default=0
 The ID of the anchor plate.
return_rate_of_motion
:bool
, default=False
 Choose whether to return the rate of plate motion through time for each
Returns
rlons
:ndarray
 An ndimensional array with columns containing the longitudes of
the seed points at each timestep in
time_array
. There are n columns for n seed points. rlats
:ndarray
 An ndimensional array with columns containing the latitudes of
the seed points at each timestep in
time_array
. There are n columns for n seed points. StepTimes
StepRates
Examples
To access the latitudes and longitudes of each seed point's motion path:
for i in np.arange(0,len(seed_points)): current_lons = lon[:,i] current_lats = lat[:,i]
Expand source code
def create_motion_path( self, lons, lats, time_array, plate_id=None, anchor_plate_id=None, return_rate_of_motion=False, ): """Create a path of points to mark the trajectory of a plate's motion through geological time. Parameters  lons : arr An array containing the longitudes of seed points on a plate in motion. lats : arr An array containing the latitudes of seed points on a plate in motion. time_array : arr An array of reconstruction times at which to determine the trajectory of a point on a plate. For example: import numpy as np min_time = 30 max_time = 100 time_step = 2.5 time_array = np.arange(min_time, max_time + time_step, time_step) plate_id : int, default=None The ID of the moving plate. If this is not passed, the plate ID of the seed points are ascertained using pygplates' `PlatePartitioner`. anchor_plate_id : int, default=0 The ID of the anchor plate. return_rate_of_motion : bool, default=False Choose whether to return the rate of plate motion through time for each Returns  rlons : ndarray An ndimensional array with columns containing the longitudes of the seed points at each timestep in `time_array`. There are n columns for n seed points. rlats : ndarray An ndimensional array with columns containing the latitudes of the seed points at each timestep in `time_array`. There are n columns for n seed points. StepTimes StepRates Examples  To access the latitudes and longitudes of each seed point's motion path: for i in np.arange(0,len(seed_points)): current_lons = lon[:,i] current_lats = lat[:,i] """ lons = np.atleast_1d(lons) lats = np.atleast_1d(lats) time_array = np.atleast_1d(time_array) # ndarrays to fill with reconstructed points and # rates of motion (if requested) rlons = np.empty((len(time_array), len(lons))) rlats = np.empty((len(time_array), len(lons))) if plate_id is None: query_plate_id = True else: query_plate_id = False plate_ids = np.ones(len(lons), dtype=int) * plate_id if not anchor_plate_id: anchor_plate_id = self.anchor_plate_id seed_points = zip(lats, lons) for i, lat_lon in enumerate(seed_points): seed_points_at_digitisation_time = pygplates.PointOnSphere( pygplates.LatLonPoint(float(lat_lon[0]), float(lat_lon[1])) ) # Allocate the presentday plate ID to the PointOnSphere if # it was not given. if query_plate_id: plate_id = _tools.plate_partitioner_for_point( lat_lon, self.topology_features, self.rotation_model ) else: plate_id = plate_ids[i] # Create the motion path feature. enforce float and int for C++ signature. motion_path_feature = pygplates.Feature.create_motion_path( seed_points_at_digitisation_time, time_array, valid_time=(time_array.max(), time_array.min()), relative_plate=int(plate_id), reconstruction_plate_id=int(anchor_plate_id), ) reconstructed_motion_paths = self.reconstruct( motion_path_feature, to_time=0, reconstruct_type=pygplates.ReconstructType.motion_path, anchor_plate_id=int(plate_id), ) # Turn motion paths in to latlon coordinates for reconstructed_motion_path in reconstructed_motion_paths: trail = reconstructed_motion_path.get_motion_path().to_lat_lon_array() lon, lat = np.flipud(trail[:, 1]), np.flipud(trail[:, 0]) rlons[:, i] = lon rlats[:, i] = lat # Obtain stepplot coordinates for rate of motion if return_rate_of_motion is True: StepTimes = np.empty(((len(time_array)  1) * 2, len(lons))) StepRates = np.empty(((len(time_array)  1) * 2, len(lons))) # Get timestep TimeStep = [] for j in range(len(time_array)  1): diff = time_array[j + 1]  time_array[j] TimeStep.append(diff) # Iterate over each segment in the reconstructed motion path, get the distance travelled by the moving # plate relative to the fixed plate in each time step Dist = [] for reconstructed_motion_path in reconstructed_motion_paths: for ( segment ) in reconstructed_motion_path.get_motion_path().get_segments(): Dist.append( segment.get_arc_length() * _tools.geocentric_radius( segment.get_start_point().to_lat_lon()[0] ) / 1e3 ) # Note that the motion path coordinates come out starting with the oldest time and working forwards # So, to match our 'times' array, we flip the order Dist = np.flipud(Dist) # Get rate of motion as distance per Myr Rate = np.asarray(Dist) / TimeStep # Manipulate arrays to get a step plot StepRate = np.zeros(len(Rate) * 2) StepRate[::2] = Rate StepRate[1::2] = Rate StepTime = np.zeros(len(Rate) * 2) StepTime[::2] = time_array[:1] StepTime[1::2] = time_array[1:] # Append the nth point's step time and step rate coordinates to the ndarray StepTimes[:, i] = StepTime StepRates[:, i] = StepRate * 0.1 # cm/yr # Obseleted by Lauren's changes above (though it is more efficient) # multiply arc length of the motion path segment by a latitudedependent Earth radius # use latitude of the segment start point # distance.append( segment.get_arc_length() * _tools.geocentric_radius(segment.get_start_point().to_lat_lon()[0]) / 1e3) # rate = np.asarray(distance)/np.diff(time_array) # rates[:,i] = np.flipud(rate) # rates *= 0.1 # cm/yr if return_rate_of_motion is True: return ( np.squeeze(rlons), np.squeeze(rlats), np.squeeze(StepTimes), np.squeeze(StepRates), ) else: return np.squeeze(rlons), np.squeeze(rlats)
def get_point_velocities(self, lons, lats, time, delta_time=1.0)

Generates a velocity domain feature collection, resolves them into points, and calculates the north and east components of the velocity vector for each point in the domain at a particular geological
time
.Notes
Velocity domain feature collections are MeshNodetype features. These are produced from
lons
andlats
pairs represented as multipoint geometries (projections onto the surface of the unit length sphere). These features are resolved into domain points and assigned plate IDs which are used to obtain the equivalent stage rotations of identified tectonic plates over a time interval (delta_time
). Each velocity domain point and its stage rotation are used to calculate the point's plate velocity at a particulartime
. Obtained velocities for each domain point are represented in the northeastdown coordinate system.Parameters
lons
:array
 A 1D array of point data's longitudes.
lats
:array
 A 1D array of point data's latitudes.
time
:float
 The specific geological time (Ma) at which to calculate plate velocities.
delta_time
:float
, default=1.0
 The time increment used for generating partitioning plate stage rotations. 1.0Ma by default.
Returns
all_velocities
:1D list
oftuples
 For each velocity domain feature point, a tuple of (north, east, down) velocity components is generated and
appended to a list of velocity data. The length of
all_velocities
is equivalent to the number of domain points resolved from the latlon array parameters.
Expand source code
def get_point_velocities(self, lons, lats, time, delta_time=1.0): """Generates a velocity domain feature collection, resolves them into points, and calculates the north and east components of the velocity vector for each point in the domain at a particular geological `time`. Notes  Velocity domain feature collections are MeshNodetype features. These are produced from `lons` and `lats` pairs represented as multipoint geometries (projections onto the surface of the unit length sphere). These features are resolved into domain points and assigned plate IDs which are used to obtain the equivalent stage rotations of identified tectonic plates over a time interval (`delta_time`). Each velocity domain point and its stage rotation are used to calculate the point's plate velocity at a particular `time`. Obtained velocities for each domain point are represented in the northeastdown coordinate system. Parameters  lons : array A 1D array of point data's longitudes. lats : array A 1D array of point data's latitudes. time : float The specific geological time (Ma) at which to calculate plate velocities. delta_time : float, default=1.0 The time increment used for generating partitioning plate stage rotations. 1.0Ma by default. Returns  all_velocities : 1D list of tuples For each velocity domain feature point, a tuple of (north, east, down) velocity components is generated and appended to a list of velocity data. The length of `all_velocities` is equivalent to the number of domain points resolved from the latlon array parameters. """ # Add points to a multipoint geometry time = float(time) multi_point = pygplates.MultiPointOnSphere( [(float(lat), float(lon)) for lat, lon in zip(lats, lons)] ) # Create a feature containing the multipoint feature, and defined as MeshNode type meshnode_feature = pygplates.Feature( pygplates.FeatureType.create_from_qualified_string("gpml:MeshNode") ) meshnode_feature.set_geometry(multi_point) meshnode_feature.set_name("Velocity Mesh Nodes from pygplates") velocity_domain_features = pygplates.FeatureCollection(meshnode_feature) # NB: at this point, the feature could be written to a file using # output_feature_collection.write('myfilename.gpmlz') # All domain points and associated (magnitude, azimuth, inclination) velocities for the current time. all_domain_points = [] all_velocities = [] # Partition our velocity domain features into our topological plate polygons at the current 'time'. plate_partitioner = pygplates.PlatePartitioner( self.topology_features, self.rotation_model, time ) for velocity_domain_feature in velocity_domain_features: # A velocity domain feature usually has a single geometry but we'll assume it can be any number. # Iterate over them all. for velocity_domain_geometry in velocity_domain_feature.get_geometries(): for velocity_domain_point in velocity_domain_geometry.get_points(): all_domain_points.append(velocity_domain_point) partitioning_plate = plate_partitioner.partition_point( velocity_domain_point ) if partitioning_plate: # We need the newly assigned plate ID # to get the equivalent stage rotation of that tectonic plate. partitioning_plate_id = ( partitioning_plate.get_feature().get_reconstruction_plate_id() ) # Get the stage rotation of partitioning plate from 'time + delta_time' to 'time'. equivalent_stage_rotation = self.rotation_model.get_rotation( time, partitioning_plate_id, time + delta_time ) # Calculate velocity at the velocity domain point. # This is from 'time + delta_time' to 'time' on the partitioning plate. velocity_vectors = pygplates.calculate_velocities( [velocity_domain_point], equivalent_stage_rotation, delta_time, ) # Convert global 3D velocity vectors to local (magnitude, azimuth, inclination) tuples # (one tuple per point). velocities = pygplates.LocalCartesian.convert_from_geocentric_to_north_east_down( [velocity_domain_point], velocity_vectors ) all_velocities.append( (velocities[0].get_x(), velocities[0].get_y()) ) else: all_velocities.append((0, 0)) return np.array(all_velocities)
def reconstruct(self, feature, to_time, from_time=0, anchor_plate_id=None, **kwargs)

Reconstructs regular geological features, motion paths or flowlines to a specific geological time.
Parameters
feature
:str,
orinstance
of<pygplates.FeatureCollection>,
or<pygplates.Feature>,
orsequence
of<pygplates.Feature>
 The geological features to reconstruct. Can be provided as a feature collection, or filename, or feature, or sequence of features, or a sequence (eg, a list or tuple) of any combination of those four types.
to_time
:float,
or:class:
GeoTimeInstant`` The specific geological time to reconstruct to.
from_time
:float
, default=0
 The specific geological time to reconstruct from. By default, this is set to present day. Raises
NotImplementedError
iffrom_time
is not set to 0.0 Ma (present day). anchor_plate_id
:int
, default=None
 Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made with respect to the absolute reference frame (anchor_plate_id = 0), like a stationary object in the mantle, unless otherwise specified.
**reconstruct_type
:ReconstructType
, default=ReconstructType.feature_geometry
 The specific reconstruction type to generate based on input feature geometry type. Can be provided as
pygplates.ReconstructType.feature_geometry to only reconstruct regular feature geometries, or
pygplates.ReconstructType.motion_path to only reconstruct motion path features, or
pygplates.ReconstructType.flowline to only reconstruct flowline features.
Generates :class:
reconstructed feature geometries<ReconstructedFeatureGeometry>’, or :class:
reconstructed motion paths’, or :class:`reconstructed flowlines ’ respectively. **group_with_feature
:bool
, default=False
 Used to group reconstructed geometries with their features. This can be useful when a feature has more than one
geometry and hence more than one reconstructed geometry. The output reconstructed_geometries then becomes a
list of tuples where each tuple contains a :class:
feature<Feature>
and alist
of reconstructed geometries. Note: this keyword argument only applies when reconstructed_geometries is a list because exported files are always grouped with their features. This is applicable to all ReconstructType features. **export_wrap_to_dateline
:bool
, default=True
 Wrap/clip reconstructed geometries to the dateline.
Returns
reconstructed_features
:list
 Reconstructed geological features (generated by the reconstruction) are appended to the list.
The reconstructed geometries are output in the same order as that of their respective input features (in the
parameter “features”). The order across input feature collections is also retained. This happens regardless
of whether features and reconstructed_features include files or not. Note: if keyword argument
group_with_feature=True then the list contains tuples that group each :class:
feature<Feature>
with a list of its reconstructed geometries.
Raises
NotImplementedError
 if the starting time for reconstruction
from_time
is not equal to 0.0.
Expand source code
def reconstruct(self, feature, to_time, from_time=0, anchor_plate_id=None, **kwargs): """Reconstructs regular geological features, motion paths or flowlines to a specific geological time. Parameters  feature : str, or instance of <pygplates.FeatureCollection>, or <pygplates.Feature>, or sequence of <pygplates.Feature> The geological features to reconstruct. Can be provided as a feature collection, or filename, or feature, or sequence of features, or a sequence (eg, a list or tuple) of any combination of those four types. to_time : float, or :class:`GeoTimeInstant` The specific geological time to reconstruct to. from_time : float, default=0 The specific geological time to reconstruct from. By default, this is set to present day. Raises `NotImplementedError` if `from_time` is not set to 0.0 Ma (present day). anchor_plate_id : int, default=None Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made with respect to the absolute reference frame (anchor_plate_id = 0), like a stationary object in the mantle, unless otherwise specified. **reconstruct_type : ReconstructType, default=ReconstructType.feature_geometry The specific reconstruction type to generate based on input feature geometry type. Can be provided as pygplates.ReconstructType.feature_geometry to only reconstruct regular feature geometries, or pygplates.ReconstructType.motion_path to only reconstruct motion path features, or pygplates.ReconstructType.flowline to only reconstruct flowline features. Generates :class:`reconstructed feature geometries<ReconstructedFeatureGeometry>’, or :class:`reconstructed motion paths<ReconstructedMotionPath>’, or :class:`reconstructed flowlines<ReconstructedFlowline>’ respectively. **group_with_feature : bool, default=False Used to group reconstructed geometries with their features. This can be useful when a feature has more than one geometry and hence more than one reconstructed geometry. The output *reconstructed_geometries* then becomes a list of tuples where each tuple contains a :class:`feature<Feature>` and a ``list`` of reconstructed geometries. Note: this keyword argument only applies when *reconstructed_geometries* is a list because exported files are always grouped with their features. This is applicable to all ReconstructType features. **export_wrap_to_dateline : bool, default=True Wrap/clip reconstructed geometries to the dateline. Returns  reconstructed_features : list Reconstructed geological features (generated by the reconstruction) are appended to the list. The reconstructed geometries are output in the same order as that of their respective input features (in the parameter “features”). The order across input feature collections is also retained. This happens regardless of whether *features* and *reconstructed_features* include files or not. Note: if keyword argument group_with_feature=True then the list contains tuples that group each :class:`feature<Feature>` with a list of its reconstructed geometries. Raises  NotImplementedError if the starting time for reconstruction `from_time` is not equal to 0.0. """ from_time, to_time = float(from_time), float(to_time) reconstructed_features = [] if not anchor_plate_id: anchor_plate_id = self.anchor_plate_id pygplates.reconstruct( feature, self.rotation_model, reconstructed_features, to_time, anchor_plate_id=anchor_plate_id, **kwargs ) return reconstructed_features
def tessellate_mid_ocean_ridges(self, time, tessellation_threshold_radians=0.001, ignore_warnings=False, return_geodataframe=False, **kwargs)

Samples points along resolved spreading features (e.g. midocean ridges) and calculates spreading rates and lengths of ridge segments at a particular geological time.
Resolves topologies at
time
, tessellates all resolved spreading features to within 'tessellation_threshold_radians' radians. Returns a 4column vertically stacked tuple with the following data. Col. 0  longitude of sampled ridge point
 Col. 1  latitude of sampled ridge point
 Col. 2  spreading velocity magnitude (in cm/yr)
 Col. 3  length of arc segment (in degrees) that current point is on
All spreading feature types are considered. The transform segments of spreading features are ignored. Note: by default, the function assumes that a segment can deviate 45 degrees from the stage pole before it is considered a transform segment.
Parameters
time
:float
 The reconstruction time (Ma) at which to query subduction convergence.
tessellation_threshold_radians
:float
, default=0.001
 The threshold sampling distance along the subducting trench (in radians).
ignore_warnings
:bool
, default=False
 Choose to ignore warnings from Plate Tectonic Tools' ridge_spreading_rate workflow.
Returns
ridge_data
:a list
ofverticallystacked tuples

The results for all tessellated points sampled along the trench. The size of the returned list is equal to the number of tessellated points. Each tuple in the list corresponds to a tessellated point and has the following tuple items:
 longitude of sampled point
 latitude of sampled point
 spreading velocity magnitude (in cm/yr)
 length of arc segment (in degrees) that current point is on
Expand source code
def tessellate_mid_ocean_ridges( self, time, tessellation_threshold_radians=0.001, ignore_warnings=False, return_geodataframe=False, **kwargs ): """Samples points along resolved spreading features (e.g. midocean ridges) and calculates spreading rates and lengths of ridge segments at a particular geological time. Resolves topologies at `time`, tessellates all resolved spreading features to within 'tessellation_threshold_radians' radians. Returns a 4column vertically stacked tuple with the following data. * Col. 0  longitude of sampled ridge point * Col. 1  latitude of sampled ridge point * Col. 2  spreading velocity magnitude (in cm/yr) * Col. 3  length of arc segment (in degrees) that current point is on All spreading feature types are considered. The transform segments of spreading features are ignored. Note: by default, the function assumes that a segment can deviate 45 degrees from the stage pole before it is considered a transform segment. Parameters  time : float The reconstruction time (Ma) at which to query subduction convergence. tessellation_threshold_radians : float, default=0.001 The threshold sampling distance along the subducting trench (in radians). ignore_warnings : bool, default=False Choose to ignore warnings from Plate Tectonic Tools' ridge_spreading_rate workflow. Returns  ridge_data : a list of verticallystacked tuples The results for all tessellated points sampled along the trench. The size of the returned list is equal to the number of tessellated points. Each tuple in the list corresponds to a tessellated point and has the following tuple items: * longitude of sampled point * latitude of sampled point * spreading velocity magnitude (in cm/yr) * length of arc segment (in degrees) that current point is on """ from . import ptt as _ptt anchor_plate_id = kwargs.pop("anchor_plate_id", self.anchor_plate_id) if ignore_warnings: with warnings.catch_warnings(): warnings.simplefilter("ignore") spreading_feature_types = [pygplates.FeatureType.gpml_mid_ocean_ridge] ridge_data = _ptt.ridge_spreading_rate.spreading_rates( self.rotation_model, self.topology_features, float(time), tessellation_threshold_radians, spreading_feature_types, anchor_plate_id=anchor_plate_id, **kwargs ) else: spreading_feature_types = [pygplates.FeatureType.gpml_mid_ocean_ridge] ridge_data = _ptt.ridge_spreading_rate.spreading_rates( self.rotation_model, self.topology_features, float(time), tessellation_threshold_radians, spreading_feature_types, anchor_plate_id=anchor_plate_id, **kwargs ) if not ridge_data: # the _ptt.ridge_spreading_rate.spreading_rates might return None return ridge_data = np.vstack(ridge_data) if return_geodataframe: import geopandas as gpd from shapely import geometry points = [ geometry.Point(lon, lat) for lon, lat in zip(ridge_data[:, 0], ridge_data[:, 1]) ] gdf = gpd.GeoDataFrame( { "geometry": points, "velocity (cm/yr)": ridge_data[:, 2], "length (degrees)": ridge_data[:, 3], }, geometry="geometry", ) return gdf else: return ridge_data
def tessellate_subduction_zones(self, time, tessellation_threshold_radians=0.001, ignore_warnings=False, return_geodataframe=False, **kwargs)

Samples points along subduction zone trenches and obtains subduction data at a particular geological time.
Resolves topologies at
time
, tessellates all resolved subducting features to within 'tessellation_threshold_radians' radians and obtains the following information for each sampled point along a trench:tessellate_subduction_zones
returns a list of 10 verticallystacked tuples with the following data per sampled trench point: Col. 0  longitude of sampled trench point
 Col. 1  latitude of sampled trench point
 Col. 2  subducting convergence (relative to trench) velocity magnitude (in cm/yr)
 Col. 3  subducting convergence velocity obliquity angle (angle between trench normal vector and convergence velocity vector)
 Col. 4  trench absolute (relative to anchor plate) velocity magnitude (in cm/yr)
 Col. 5  trench absolute velocity obliquity angle (angle between trench normal vector and trench absolute velocity vector)
 Col. 6  length of arc segment (in degrees) that current point is on
 Col. 7  trench normal azimuth angle (clockwise starting at North, ie, 0 to 360 degrees) at current point
 Col. 8  subducting plate ID
 Col. 9  trench plate ID
Parameters
time
:float
 The reconstruction time (Ma) at which to query subduction convergence.
tessellation_threshold_radians
:float
, default=0.001
 The threshold sampling distance along the subducting trench (in radians).
Returns
subduction_data
:a list
ofverticallystacked tuples

The results for all tessellated points sampled along the trench. The size of the returned list is equal to the number of tessellated points. Each tuple in the list corresponds to a tessellated point and has the following tuple items:
 Col. 0  longitude of sampled trench point
 Col. 1  latitude of sampled trench point
 Col. 2  subducting convergence (relative to trench) velocity magnitude (in cm/yr)
 Col. 3  subducting convergence velocity obliquity angle (angle between trench normal vector and convergence velocity vector)
 Col. 4  trench absolute (relative to anchor plate) velocity magnitude (in cm/yr)
 Col. 5  trench absolute velocity obliquity angle (angle between trench normal vector and trench absolute velocity vector)
 Col. 6  length of arc segment (in degrees) that current point is on
 Col. 7  trench normal azimuth angle (clockwise starting at North, ie, 0 to 360 degrees) at current point
 Col. 8  subducting plate ID
 Col. 9  trench plate ID
Notes
Each sampled point in the output is the midpoint of a great circle arc between two adjacent points in the trench polyline. The trench normal vector used in the obliquity calculations is perpendicular to the great circle arc of each point (arc midpoint) and pointing towards the overriding plate (rather than away from it).
Each trench is sampled at approximately uniform intervals along its length (specified via a threshold sampling distance). The sampling along the entire length of a trench is not exactly uniform. Each segment along a trench is sampled such that the samples have a uniform spacing that is less than or equal to the threshold sampling distance. However each segment in a trench might have a slightly different spacing distance (since segment lengths are not integer multiples of the threshold sampling distance).
The trench normal (at each arc segment midpoint) always points towards the overriding plate. The obliquity angles are in the range (180 180). The range (0, 180) goes clockwise (when viewed from above the Earth) from the trench normal direction to the velocity vector. The range (0, 180) goes counterclockwise. You can change the range (180, 180) to the range (0, 360) by adding 360 to negative angles. The trench normal is perpendicular to the trench and pointing toward the overriding plate.
Note that the convergence velocity magnitude is negative if the plates are diverging (if convergence obliquity angle is greater than 90 or less than 90). And note that the absolute velocity magnitude is negative if the trench (subduction zone) is moving towards the overriding plate (if absolute obliquity angle is less than 90 or greater than 90)  note that this ignores the kinematics of the subducting plate.
The delta time interval used for velocity calculations is, by default, assumed to be 1Ma.
Expand source code
def tessellate_subduction_zones( self, time, tessellation_threshold_radians=0.001, ignore_warnings=False, return_geodataframe=False, **kwargs ): """Samples points along subduction zone trenches and obtains subduction data at a particular geological time. Resolves topologies at `time`, tessellates all resolved subducting features to within 'tessellation_threshold_radians' radians and obtains the following information for each sampled point along a trench: `tessellate_subduction_zones` returns a list of 10 verticallystacked tuples with the following data per sampled trench point: * Col. 0  longitude of sampled trench point * Col. 1  latitude of sampled trench point * Col. 2  subducting convergence (relative to trench) velocity magnitude (in cm/yr) * Col. 3  subducting convergence velocity obliquity angle (angle between trench normal vector and convergence velocity vector) * Col. 4  trench absolute (relative to anchor plate) velocity magnitude (in cm/yr) * Col. 5  trench absolute velocity obliquity angle (angle between trench normal vector and trench absolute velocity vector) * Col. 6  length of arc segment (in degrees) that current point is on * Col. 7  trench normal azimuth angle (clockwise starting at North, ie, 0 to 360 degrees) at current point * Col. 8  subducting plate ID * Col. 9  trench plate ID Parameters  time : float The reconstruction time (Ma) at which to query subduction convergence. tessellation_threshold_radians : float, default=0.001 The threshold sampling distance along the subducting trench (in radians). Returns  subduction_data : a list of verticallystacked tuples The results for all tessellated points sampled along the trench. The size of the returned list is equal to the number of tessellated points. Each tuple in the list corresponds to a tessellated point and has the following tuple items: * Col. 0  longitude of sampled trench point * Col. 1  latitude of sampled trench point * Col. 2  subducting convergence (relative to trench) velocity magnitude (in cm/yr) * Col. 3  subducting convergence velocity obliquity angle (angle between trench normal vector and convergence velocity vector) * Col. 4  trench absolute (relative to anchor plate) velocity magnitude (in cm/yr) * Col. 5  trench absolute velocity obliquity angle (angle between trench normal vector and trench absolute velocity vector) * Col. 6  length of arc segment (in degrees) that current point is on * Col. 7  trench normal azimuth angle (clockwise starting at North, ie, 0 to 360 degrees) at current point * Col. 8  subducting plate ID * Col. 9  trench plate ID Notes  Each sampled point in the output is the midpoint of a great circle arc between two adjacent points in the trench polyline. The trench normal vector used in the obliquity calculations is perpendicular to the great circle arc of each point (arc midpoint) and pointing towards the overriding plate (rather than away from it). Each trench is sampled at approximately uniform intervals along its length (specified via a threshold sampling distance). The sampling along the entire length of a trench is not exactly uniform. Each segment along a trench is sampled such that the samples have a uniform spacing that is less than or equal to the threshold sampling distance. However each segment in a trench might have a slightly different spacing distance (since segment lengths are not integer multiples of the threshold sampling distance). The trench normal (at each arc segment midpoint) always points *towards* the overriding plate. The obliquity angles are in the range (180 180). The range (0, 180) goes clockwise (when viewed from above the Earth) from the trench normal direction to the velocity vector. The range (0, 180) goes counterclockwise. You can change the range (180, 180) to the range (0, 360) by adding 360 to negative angles. The trench normal is perpendicular to the trench and pointing toward the overriding plate. Note that the convergence velocity magnitude is negative if the plates are diverging (if convergence obliquity angle is greater than 90 or less than 90). And note that the absolute velocity magnitude is negative if the trench (subduction zone) is moving towards the overriding plate (if absolute obliquity angle is less than 90 or greater than 90)  note that this ignores the kinematics of the subducting plate. The delta time interval used for velocity calculations is, by default, assumed to be 1Ma. """ from . import ptt as _ptt anchor_plate_id = kwargs.pop("anchor_plate_id", self.anchor_plate_id) if ignore_warnings: with warnings.catch_warnings(): warnings.simplefilter("ignore") subduction_data = _ptt.subduction_convergence.subduction_convergence( self.rotation_model, self.topology_features, tessellation_threshold_radians, float(time), anchor_plate_id=anchor_plate_id, **kwargs ) else: subduction_data = _ptt.subduction_convergence.subduction_convergence( self.rotation_model, self.topology_features, tessellation_threshold_radians, float(time), anchor_plate_id=anchor_plate_id, **kwargs ) subduction_data = np.vstack(subduction_data) if return_geodataframe: import geopandas as gpd from shapely import geometry coords = [ geometry.Point(lon, lat) for lon, lat in zip(subduction_data[:, 0], subduction_data[:, 1]) ] d = {"geometry": coords} labels = [ "convergence velocity (cm/yr)", "convergence obliquity angle (degrees)", "trench velocity (cm/yr)", "trench obliquity angle (degrees)", "length (degrees)", "trench normal angle (degrees)", "subducting plate ID", "overriding plate ID", ] for i, label in enumerate(labels): index = 2 + i d[label] = subduction_data[:, index] gdf = gpd.GeoDataFrame(d, geometry="geometry") return gdf else: return subduction_data
def total_continental_arc_length(self, time, continental_grid, trench_arc_distance, ignore_warnings=True)

Calculates the total length of all global continental arcs (km) at the specified geological time (Ma).
Uses Plate Tectonic Tools'
subduction_convergence
workflow to sample a given plate model's trench features into point features and obtain their subduction polarities. The resolved points are projected out by thetrench_arc_distance
and their new locations are linearly interpolated onto the suppliedcontinental_grid
. If the projected trench points lie in the grid, they are considered continental arc points, and their arc segment lengths are appended to the total continental arc length for the specifiedtime
. The total length is scaled to kilometres using the geocentric Earth radius.Parameters
time
:int
 The geological time at which to calculate total continental arc lengths.
continental_grid
:Raster, array_like,
orstr
 The continental grid used to identify continental arc points. Must
be convertible to
Raster
. For an array, a global extent is assumed [180,180,90,90]. For a filename, the extent is obtained from the file. trench_arc_distance
:float
 The trenchtoarc distance (in kilometres) to project sampled trench points out by in the direction of their subduction polarities.
ignore_warnings
:bool
, default=True
 Choose whether to ignore warning messages from PTT's subduction_convergence workflow that alerts the user of subduction subsegments that are ignored due to unidentified polarities and/or subducting plates.
Returns
total_continental_arc_length_kms
:float
 The continental arc length (in km) at the specified time.
Expand source code
def total_continental_arc_length( self, time, continental_grid, trench_arc_distance, ignore_warnings=True, ): """Calculates the total length of all global continental arcs (km) at the specified geological time (Ma). Uses Plate Tectonic Tools' `subduction_convergence` workflow to sample a given plate model's trench features into point features and obtain their subduction polarities. The resolved points are projected out by the `trench_arc_distance` and their new locations are linearly interpolated onto the supplied `continental_grid`. If the projected trench points lie in the grid, they are considered continental arc points, and their arc segment lengths are appended to the total continental arc length for the specified `time`. The total length is scaled to kilometres using the geocentric Earth radius. Parameters  time : int The geological time at which to calculate total continental arc lengths. continental_grid: Raster, array_like, or str The continental grid used to identify continental arc points. Must be convertible to `Raster`. For an array, a global extent is assumed [180,180,90,90]. For a filename, the extent is obtained from the file. trench_arc_distance : float The trenchtoarc distance (in kilometres) to project sampled trench points out by in the direction of their subduction polarities. ignore_warnings : bool, default=True Choose whether to ignore warning messages from PTT's subduction_convergence workflow that alerts the user of subduction subsegments that are ignored due to unidentified polarities and/or subducting plates. Returns  total_continental_arc_length_kms : float The continental arc length (in km) at the specified time. """ from . import grids as _grids if isinstance(continental_grid, _grids.Raster): graster = continental_grid elif isinstance(continental_grid, str): # Process the continental grid directory graster = _grids.Raster( data=continental_grid, realign=True, time=float(time), ) else: # Process the masked continental grid try: continental_grid = np.array(continental_grid) graster = _grids.Raster( data=continental_grid, extent=[180, 180, 90, 90], time=float(time), ) except Exception as e: raise TypeError( "Invalid type for `continental_grid` (must be Raster," + " str, or array_like)" ) from e if (time != graster.time) and (not ignore_warnings): raise RuntimeWarning( "`continental_grid.time` ({}) ".format(graster.time) + "does not match `time` ({})".format(time) ) # Obtain trench data with Plate Tectonic Tools trench_data = self.tessellate_subduction_zones( time, ignore_warnings=ignore_warnings ) # Extract trench data trench_normal_azimuthal_angle = trench_data[:, 7] trench_arcseg = trench_data[:, 6] trench_pt_lon = trench_data[:, 0] trench_pt_lat = trench_data[:, 1] # Modify the trencharc distance using the geocentric radius arc_distance = trench_arc_distance / ( _tools.geocentric_radius(trench_pt_lat) / 1000 ) # Project trench points out along trencharc distance, and obtain their new latlon coordinates dlon = arc_distance * np.sin(np.radians(trench_normal_azimuthal_angle)) dlat = arc_distance * np.cos(np.radians(trench_normal_azimuthal_angle)) ilon = trench_pt_lon + np.degrees(dlon) ilat = trench_pt_lat + np.degrees(dlat) # Linearly interpolate projected points onto continental grids, and collect the indices of points that lie # within the grids. sampled_points = graster.interpolate( ilon, ilat, method="linear", return_indices=False, ) continental_indices = np.where(sampled_points > 0) point_lats = ilat[continental_indices] point_radii = _tools.geocentric_radius(point_lats) * 1.0e3 # km segment_arclens = np.deg2rad(trench_arcseg[continental_indices]) segment_lengths = point_radii * segment_arclens return np.sum(segment_lengths)
def total_ridge_length(self, time, use_ptt=False, ignore_warnings=False)

Calculates the total length of all midocean ridges (km) at the specified geological time (Ma).
if
use_ptt
is TrueUses Plate Tectonic Tools'
ridge_spreading_rate
workflow to calculate ridge segment lengths. Scales lengths to kilometres using the geocentric radius.Otherwise
Resolves topology features of the PlateReconstruction model and extracts their shared boundary sections. The lengths of each GPML midocean ridge shared boundary section are appended to the total ridge length. Scales lengths to kilometres using the geocentric radius.
Parameters
time
:int
 The geological time at which to calculate total midocean ridge lengths.
use_ptt
:bool
, default=False
 If set to
True
, the PTT method is used. ignore_warnings
:bool
, default=False
 Choose whether to ignore warning messages from PTT's
ridge_spreading_rate
workflow.
Raises
ValueError
 If neither
use_pygplates
oruse_ptt
have been set toTrue
.
Returns
total_ridge_length_kms
:float
 The total length of global midocean ridges (in kilometres) at the specified time.
Expand source code
def total_ridge_length(self, time, use_ptt=False, ignore_warnings=False): """Calculates the total length of all midocean ridges (km) at the specified geological time (Ma). if `use_ptt` is True Uses Plate Tectonic Tools' `ridge_spreading_rate` workflow to calculate ridge segment lengths. Scales lengths to kilometres using the geocentric radius. Otherwise Resolves topology features of the PlateReconstruction model and extracts their shared boundary sections. The lengths of each GPML midocean ridge shared boundary section are appended to the total ridge length. Scales lengths to kilometres using the geocentric radius. Parameters  time : int The geological time at which to calculate total midocean ridge lengths. use_ptt : bool, default=False If set to `True`, the PTT method is used. ignore_warnings : bool, default=False Choose whether to ignore warning messages from PTT's `ridge_spreading_rate` workflow. Raises  ValueError If neither `use_pygplates` or `use_ptt` have been set to `True`. Returns  total_ridge_length_kms : float The total length of global midocean ridges (in kilometres) at the specified time. """ from . import ptt as _ptt if use_ptt is True: with warnings.catch_warnings(): warnings.simplefilter("ignore") ridge_data = self.tessellate_mid_ocean_ridges(time) ridge_arcseg = ridge_data[:, 3] ridge_pt_lat = ridge_data[:, 1] total_ridge_length_kms = 0 for i, segment in enumerate(ridge_arcseg): earth_radius = _tools.geocentric_radius(ridge_pt_lat[i]) / 1e3 total_ridge_length_kms += np.deg2rad(segment) * earth_radius return total_ridge_length_kms else: resolved_topologies = [] shared_boundary_sections = [] pygplates.resolve_topologies( self.topology_features, self.rotation_model, resolved_topologies, time, shared_boundary_sections, ) total_ridge_length_kms = 0.0 for shared_boundary_section in shared_boundary_sections: if ( shared_boundary_section.get_feature().get_feature_type() != pygplates.FeatureType.gpml_mid_ocean_ridge ): continue for ( shared_sub_segment ) in shared_boundary_section.get_shared_sub_segments(): clat, clon = ( shared_sub_segment.get_resolved_geometry() .get_centroid() .to_lat_lon() ) earth_radius = _tools.geocentric_radius(clat) / 1e3 total_ridge_length_kms += ( shared_sub_segment.get_resolved_geometry().get_arc_length() * earth_radius ) return total_ridge_length_kms
def total_subduction_zone_length(self, time, use_ptt=False, ignore_warnings=False)

Calculates the total length of all midocean ridges (km) at the specified geological time (Ma).
if
use_ptt
is TrueUses Plate Tectonic Tools'
subduction_convergence
module to calculate trench segment lengths on a unit sphere. The aggregated total subduction zone length is scaled to kilometres using the geocentric radius.Otherwise
Resolves topology features ascribed to the
PlateReconstruction
model and extracts their shared boundary sections. The lengths of each trench boundary section are appended to the total subduction zone length. The total length is scaled to kilometres using a latitudedependent (geocentric) Earth radius.Parameters
time
:int
 The geological time at which to calculate total midocean ridge lengths.
use_ptt
:bool
, default=False
 If set to
True
, the PTT method is used. ignore_warnings
:bool
, default=False
 Choose whether to ignore warning messages from PTT's
subduction_convergence
workflow. These warnings alert the user when certain subduction subsegments are ignored  this happens when the trench segments have unidentifiable subduction polarities and/or subducting plates.
Raises
ValueError
 If neither
use_pygplates
oruse_ptt
have been set toTrue
.
Returns
total_subduction_zone_length_kms
:float
 The total subduction zone length (in km) at the specified
time
.
Expand source code
def total_subduction_zone_length(self, time, use_ptt=False, ignore_warnings=False): """Calculates the total length of all midocean ridges (km) at the specified geological time (Ma). if `use_ptt` is True Uses Plate Tectonic Tools' `subduction_convergence` module to calculate trench segment lengths on a unit sphere. The aggregated total subduction zone length is scaled to kilometres using the geocentric radius. Otherwise Resolves topology features ascribed to the `PlateReconstruction` model and extracts their shared boundary sections. The lengths of each trench boundary section are appended to the total subduction zone length. The total length is scaled to kilometres using a latitudedependent (geocentric) Earth radius. Parameters  time : int The geological time at which to calculate total midocean ridge lengths. use_ptt : bool, default=False If set to `True`, the PTT method is used. ignore_warnings : bool, default=False Choose whether to ignore warning messages from PTT's `subduction_convergence` workflow. These warnings alert the user when certain subduction subsegments are ignored  this happens when the trench segments have unidentifiable subduction polarities and/or subducting plates. Raises  ValueError If neither `use_pygplates` or `use_ptt` have been set to `True`. Returns  total_subduction_zone_length_kms : float The total subduction zone length (in km) at the specified `time`. """ from . import ptt as _ptt if use_ptt: with warnings.catch_warnings(): warnings.simplefilter("ignore") subduction_data = self.tessellate_subduction_zones( time, ignore_warnings=ignore_warnings ) trench_arcseg = subduction_data[:, 6] trench_pt_lat = subduction_data[:, 1] total_subduction_zone_length_kms = 0 for i, segment in enumerate(trench_arcseg): earth_radius = _tools.geocentric_radius(trench_pt_lat[i]) / 1e3 total_subduction_zone_length_kms += np.deg2rad(segment) * earth_radius return total_subduction_zone_length_kms else: resolved_topologies = [] shared_boundary_sections = [] pygplates.resolve_topologies( self.topology_features, self.rotation_model, resolved_topologies, time, shared_boundary_sections, ) total_subduction_zone_length_kms = 0.0 for shared_boundary_section in shared_boundary_sections: if ( shared_boundary_section.get_feature().get_feature_type() != pygplates.FeatureType.gpml_subduction_zone ): continue for ( shared_sub_segment ) in shared_boundary_section.get_shared_sub_segments(): clat, clon = ( shared_sub_segment.get_resolved_geometry() .get_centroid() .to_lat_lon() ) earth_radius = _tools.geocentric_radius(clat) / 1e3 total_subduction_zone_length_kms += ( shared_sub_segment.get_resolved_geometry().get_arc_length() * earth_radius ) return total_subduction_zone_length_kms
class Points (plate_reconstruction, lons, lats, time=0, plate_id=None)

Points
contains methods to reconstruct and work with with geological point data. For example, the locations and plate velocities of point data can be calculated at a specific geologicaltime
. ThePoints
object requires thePlateReconstruction
object to work because it holds therotation_model
andstatic_polygons
needed to classify topological plates and quantify feature rotations through time.Attributes
plate_reconstruction
:object pointer
 Allows for the accessibility of
PlateReconstruction
object attributes:rotation_model
,topology_featues
andstatic_polygons
for use in thePoints
object if called using “self.plate_reconstruction.X”, where X is the attribute. lons
:float,
or1D array
 A single float, or a 1D array containing the longitudes of point data.
lats
:float 1D array
 A single float, or a 1D array containing the latitudes of point data.
time
:float
, default=0
 The specific geological time (Ma) at which to reconstruct the point data. By default, it is set to the present day (0 Ma).
plate_id
:int
, default=None
 The plate ID of a particular tectonic plate on which point data lies, if known. This is obtained in
init
if not provided.
Expand source code
class Points(object): """`Points` contains methods to reconstruct and work with with geological point data. For example, the locations and plate velocities of point data can be calculated at a specific geological `time`. The `Points` object requires the `PlateReconstruction` object to work because it holds the `rotation_model` and `static_polygons` needed to classify topological plates and quantify feature rotations through time. Attributes  plate_reconstruction : object pointer Allows for the accessibility of `PlateReconstruction` object attributes: `rotation_model`, `topology_featues` and `static_polygons` for use in the `Points` object if called using “self.plate_reconstruction.X”, where X is the attribute. lons : float, or 1D array A single float, or a 1D array containing the longitudes of point data. lats : float 1D array A single float, or a 1D array containing the latitudes of point data. time : float, default=0 The specific geological time (Ma) at which to reconstruct the point data. By default, it is set to the present day (0 Ma). plate_id : int, default=None The plate ID of a particular tectonic plate on which point data lies, if known. This is obtained in `init` if not provided. """ def __init__(self, plate_reconstruction, lons, lats, time=0, plate_id=None): self.lons = lons self.lats = lats self.time = time self.attributes = dict() self.plate_reconstruction = plate_reconstruction self._update(lons, lats, time, plate_id) def _update(self, lons, lats, time=0, plate_id=None): # get Cartesian coordinates self.x, self.y, self.z = _tools.lonlat2xyz(lons, lats, degrees=False) # scale by average radius of the Earth self.x *= _tools.EARTH_RADIUS self.y *= _tools.EARTH_RADIUS self.z *= _tools.EARTH_RADIUS # store concatenated arrays self.lonlat = np.c_[self.lons, self.lats] self.xyz = np.c_[self.x, self.y, self.z] rotation_model = self.plate_reconstruction.rotation_model static_polygons = self.plate_reconstruction.static_polygons features = _tools.points_to_features(lons, lats, plate_id) if plate_id is not None: plate_id = np.atleast_1d(plate_id) self.features = features else: # partition using static polygons # being careful to observe 'from time' partitioned_features = pygplates.partition_into_plates( static_polygons, rotation_model, features, reconstruction_time=time ) self.features = partitioned_features plate_id = np.empty(len(self.lons), dtype=int) for i, feature in enumerate(partitioned_features): plate_id[i] = feature.get_reconstruction_plate_id() self.plate_id = plate_id self.FeatureCollection = pygplates.FeatureCollection(self.features) @property def size(self): """Number of points""" return len(self.lons) def __getstate__(self): filenames = self.plate_reconstruction.__getstate__() # add important variables from Points object filenames["lons"] = self.lons filenames["lats"] = self.lats filenames["time"] = self.time filenames["plate_id"] = self.plate_id for key in self.attributes: filenames[key] = self.attributes[key] return filenames def __setstate__(self, state): self.plate_reconstruction = PlateReconstruction( state["rotation_model"], state["topology_features"], state["static_polygons"], ) # reinstate unpicklable items self.lons = state["lons"] self.lats = state["lats"] self.time = state["time"] self.plate_id = state["plate_id"] self.attributes = dict() self._update(self.lons, self.lats, self.time, self.plate_id) for key in state: if key not in ["lons", "lats", "time", "plate_id"]: self.attributes[key] = state[key] def copy(self): """Returns a copy of the Points object Returns  Points A copy of the current Points object """ gpts = Points( self.plate_reconstruction, self.lons.copy(), self.lats.copy(), self.time, self.plate_id.copy(), ) gpts.add_attributes(**self.attributes.copy()) def add_attributes(self, **kwargs): """Adds the value of a feature attribute associated with a key. Example  # Define latitudes and longitudes to set up a Points object pt_lons = np.array([140., 150., 160.]) pt_lats = np.array([30., 40., 50.]) gpts = gplately.Points(model, pt_lons, pt_lats) # Add the attributes a, b and c to the points in the Points object gpts.add_attributes( a=[10,2,2], b=[2,3,3], c=[30,0,0], ) print(gpts.attributes) The output would be: {'a': [10, 2, 2], 'b': [2, 3, 3], 'c': [30, 0, 0]} Parameters  **kwargs : sequence of key=item/s A single key=value pair, or a sequence of key=value pairs denoting the name and value of an attribute. Notes  * An **assertion** is raised if the number of points in the Points object is not equal to the number of values associated with an attribute key. For example, consider an instance of the Points object with 3 points. If the points are ascribed an attribute `temperature`, there must be one `temperature` value per point, i.e. `temperature = [20, 15, 17.5]`. """ keys = kwargs.keys() for key in kwargs: attribute = kwargs[key] # make sure attribute is the same size as self.lons if type(attribute) is int or type(attribute) is float: array = np.full(self.lons.size, attribute) attribute = array elif isinstance(attribute, np.ndarray): if attribute.size == 1: array = np.full(self.lons.size, attribute, dtype=attribute.dtype) attribute = array assert ( len(attribute) == self.lons.size ), "Size mismatch, ensure attributes have the same number of entries as Points" self.attributes[key] = attribute if any(kwargs): # add these to the FeatureCollection for f, feature in enumerate(self.FeatureCollection): for key in keys: # extract value for each row in attribute val = self.attributes[key][f] # set this attribute on the feature feature.set_shapefile_attribute(key, val) def get_geopandas_dataframe(self): """Adds a shapely point `geometry` attribute to each point in the `gplately.Points` object. pandas.DataFrame that has a column with geometry Any existing point attributes are kept. Returns  GeoDataFrame : instance of `geopandas.GeoDataFrame` A pandas.DataFrame with rows equal to the number of points in the `gplately.Points` object, and an additional column containing a shapely `geometry` attribute. Example  pt_lons = np.array([140., 150., 160.]) pt_lats = np.array([30., 40., 50.]) gpts = gplately.Points(model, pt_lons, pt_lats) # Add sample attributes a, b and c to the points in the Points object gpts.add_attributes( a=[10,2,2], b=[2,3,3], c=[30,0,0], ) gpts.get_geopandas_dataframe() ...has the output: a b c geometry 0 10 2 30 POINT (140.00000 30.00000) 1 2 3 0 POINT (150.00000 40.00000) 2 2 3 0 POINT (160.00000 50.00000) """ import geopandas as gpd from shapely import geometry # create shapely points points = [] for lon, lat in zip(self.lons, self.lats): points.append(geometry.Point(lon, lat)) attributes = self.attributes.copy() attributes["geometry"] = points return gpd.GeoDataFrame(attributes, geometry="geometry") def get_geodataframe(self): """Returns the output of `Points.get_geopandas_dataframe()`. Adds a shapely point `geometry` attribute to each point in the `gplately.Points` object. pandas.DataFrame that has a column with geometry Any existing point attributes are kept. Returns  GeoDataFrame : instance of `geopandas.GeoDataFrame` A pandas.DataFrame with rows equal to the number of points in the `gplately.Points` object, and an additional column containing a shapely `geometry` attribute. Example  pt_lons = np.array([140., 150., 160.]) pt_lats = np.array([30., 40., 50.]) gpts = gplately.Points(model, pt_lons, pt_lats) # Add sample attributes a, b and c to the points in the Points object gpts.add_attributes( a=[10,2,2], b=[2,3,3], c=[30,0,0], ) gpts.get_geopandas_dataframe() ...has the output: a b c geometry 0 10 2 30 POINT (140.00000 30.00000) 1 2 3 0 POINT (150.00000 40.00000) 2 2 3 0 POINT (160.00000 50.00000) """ return self.get_geopandas_dataframe() def reconstruct(self, time, anchor_plate_id=None, return_array=False, **kwargs): """Reconstructs regular geological features, motion paths or flowlines to a specific geological time and extracts the latitudinal and longitudinal points of these features. Note: this method accesses and uses the rotation model attribute from the PointReconstruction object, and reconstructs the feature latlon point attributes of the Points object. Parameters  time : float The specific geological time (Ma) to reconstruct features to. anchor_plate_id : int, default=None Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made with respect to the anchor_plate_ID specified in the `gplately.PlateReconstruction` object, which is a default plate ID of 0 unless otherwise specified. return_array : bool, default False Return a `numpy.ndarray`, rather than a `Points` object. **reconstruct_type : ReconstructType, default=ReconstructType.feature_geometry The specific reconstruction type to generate based on input feature geometry type. Can be provided as ReconstructType.feature_geometry to only reconstruct regular feature geometries, or ReconstructType.MotionPath to only reconstruct motion path features, or ReconstructType.Flowline to only reconstruct flowline features. Generates :class:`reconstructed feature geometries<ReconstructedFeatureGeometry>’, or :class:`reconstructed motion paths<ReconstructedMotionPath>’, or :class:`reconstructed flowlines<ReconstructedFlowline>’ respectively. **group_with_feature : bool, default=False Used to group reconstructed geometries with their features. This can be useful when a feature has more than one geometry and hence more than one reconstructed geometry. The output *reconstructed_geometries* then becomes a list of tuples where each tuple contains a :class:`feature<Feature>` and a ``list`` of reconstructed geometries. Note: this keyword argument only applies when *reconstructed_geometries* is a list because exported files are always grouped with their features. This is applicable to all ReconstructType features. **export_wrap_to_dateline : bool, default=True Wrap/clip reconstructed geometries to the dateline (currently ignored). Returns  rlons : list of float A 1D numpy array enclosing all reconstructed point features' longitudes. rlats : list of float A 1D numpy array enclosing all reconstructed point features' latitudes. Raises  NotImplementedError if the starting time for reconstruction `from_time` is not equal to 0.0 """ from_time = self.time to_time = time if not anchor_plate_id: anchor_plate_id = self.plate_reconstruction.anchor_plate_id reconstructed_features = self.plate_reconstruction.reconstruct( self.features, to_time, from_time, anchor_plate_id=anchor_plate_id, **kwargs ) rlons, rlats = _tools.extract_feature_lonlat(reconstructed_features) if return_array: return rlons, rlats else: gpts = Points( self.plate_reconstruction, rlons, rlats, time=to_time, plate_id=self.plate_id, ) gpts.add_attributes(**self.attributes.copy()) return gpts def reconstruct_to_birth_age(self, ages, anchor_plate_id=None, **kwargs): """Reconstructs point features supplied to the `Points` object from the supplied initial time (`self.time`) to a range of times. The number of supplied times must equal the number of point features supplied to the Points object. Attributes  ages : array Geological times to reconstruct features to. Must have the same length as the `Points `object's `self.features` attribute (which holds all point features represented on a unit length sphere in 3D Cartesian coordinates). anchor_plate_id : int, default=None Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made with respect to the anchor_plate_ID specified in the `gplately.PlateReconstruction` object, which is a default plate ID of 0 unless otherwise specified. **kwargs Additional keyword arguments for the `gplately.PlateReconstruction.reconstruct` method. Raises  ValueError If the number of ages and number of point features supplied to the Points object are not identical. Returns  rlons, rlats : float The longitude and latitude coordinate lists of all point features reconstructed to all specified ages. Examples  To reconstruct n seed points' locations to B Ma (for this example n=2, with (lon,lat) = (78,30) and (56,22) at time=0 Ma, and we reconstruct to B=10 Ma): # Longitude and latitude of n=2 seed points pt_lon = np.array([78., 56]) pt_lat = np.array([30., 22]) # Call the Points object! gpts = gplately.Points(model, pt_lon, pt_lat) print(gpts.features[0].get_all_geometries()) # Confirms we have features represented as points on a sphere ages = numpy.linspace(10,10, len(pt_lon)) rlons, rlats = gpts.reconstruct_to_birth_age(ages) """ from_time = self.time if not anchor_plate_id: anchor_plate_id = self.plate_reconstruction.anchor_plate_id ages = np.array(ages) if len(ages) != len(self.features): raise ValueError("Number of points and ages must be identical") unique_ages = np.unique(ages) rlons = np.zeros(ages.shape) rlats = np.zeros(ages.shape) for age in unique_ages: mask_age = ages == age reconstructed_features = self.plate_reconstruction.reconstruct( self.features, age, from_time, anchor_plate_id=anchor_plate_id, **kwargs ) lons, lats = _tools.extract_feature_lonlat(reconstructed_features) rlons[mask_age] = lons[mask_age] rlats[mask_age] = lats[mask_age] return rlons, rlats def plate_velocity(self, time, delta_time=1): """Calculates the x and y components of tectonic plate velocities at a particular geological time. This method accesses and uses the `rotation_model` attribute from the `PlateReconstruction` object and uses the `Points` object's `self.features` attribute. Feature points are extracted and assigned plate IDs. These IDs are used to obtain the equivalent stage rotations of identified tectonic plates over a time interval `delta_time`. Each feature point and its stage rotation are used to calculate the point's plate velocity at a particular geological time. Obtained velocities for each domain point are represented in the northeastdown coordinate system, and their x,y Cartesian coordinate components are extracted. Parameters  time : float The specific geological time (Ma) at which to calculate plate velocities. delta_time : float, default=1.0 The time increment used for generating partitioning plate stage rotations. 1.0 Ma by default. Returns  all_velocities.T : 2D numpy list A transposed 2D numpy list with two rows and a number of columns equal to the number of x,y Cartesian velocity components obtained (and thus the number of feature points extracted from a supplied feature). Each list column stores one point’s x,y, velocity components along its two rows. """ time = float(time) rotation_model = self.plate_reconstruction.rotation_model all_velocities = np.empty((len(self.features), 2)) for i, feature in enumerate(self.features): geometry = feature.get_geometry() partitioning_plate_id = feature.get_reconstruction_plate_id() equivalent_stage_rotation = rotation_model.get_rotation( time, partitioning_plate_id, time + delta_time ) velocity_vectors = pygplates.calculate_velocities( [geometry], equivalent_stage_rotation, delta_time, pygplates.VelocityUnits.cms_per_yr, ) velocities = ( pygplates.LocalCartesian.convert_from_geocentric_to_north_east_down( [geometry], velocity_vectors ) ) all_velocities[i] = velocities[0].get_y(), velocities[0].get_x() return list(all_velocities.T) def motion_path(self, time_array, anchor_plate_id=0, return_rate_of_motion=False): """Create a path of points to mark the trajectory of a plate's motion through geological time. Parameters  time_array : arr An array of reconstruction times at which to determine the trajectory of a point on a plate. For example: import numpy as np min_time = 30 max_time = 100 time_step = 2.5 time_array = np.arange(min_time, max_time + time_step, time_step) anchor_plate_id : int, default=0 The ID of the anchor plate. return_rate_of_motion : bool, default=False Choose whether to return the rate of plate motion through time for each Returns  rlons : ndarray An ndimensional array with columns containing the longitudes of the seed points at each timestep in `time_array`. There are n columns for n seed points. rlats : ndarray An ndimensional array with columns containing the latitudes of the seed points at each timestep in `time_array`. There are n columns for n seed points. """ time_array = np.atleast_1d(time_array) # ndarrays to fill with reconstructed points and # rates of motion (if requested) rlons = np.empty((len(time_array), len(self.lons))) rlats = np.empty((len(time_array), len(self.lons))) for i, point_feature in enumerate(self.FeatureCollection): # Create the motion path feature motion_path_feature = pygplates.Feature.create_motion_path( point_feature.get_geometry(), time_array.tolist(), valid_time=(time_array.max(), time_array.min()), # relative_plate=int(self.plate_id[i]), # reconstruction_plate_id=int(anchor_plate_id)) relative_plate=int(self.plate_id[i]), reconstruction_plate_id=int(anchor_plate_id), ) reconstructed_motion_paths = self.plate_reconstruction.reconstruct( motion_path_feature, to_time=0, # from_time=0, reconstruct_type=pygplates.ReconstructType.motion_path, anchor_plate_id=int(anchor_plate_id), ) # Turn motion paths in to latlon coordinates for reconstructed_motion_path in reconstructed_motion_paths: trail = reconstructed_motion_path.get_motion_path().to_lat_lon_array() lon, lat = np.flipud(trail[:, 1]), np.flipud(trail[:, 0]) rlons[:, i] = lon rlats[:, i] = lat # Obtain stepplot coordinates for rate of motion if return_rate_of_motion is True: StepTimes = np.empty(((len(time_array)  1) * 2, len(self.lons))) StepRates = np.empty(((len(time_array)  1) * 2, len(self.lons))) # Get timestep TimeStep = [] for j in range(len(time_array)  1): diff = time_array[j + 1]  time_array[j] TimeStep.append(diff) # Iterate over each segment in the reconstructed motion path, get the distance travelled by the moving # plate relative to the fixed plate in each time step Dist = [] for reconstructed_motion_path in reconstructed_motion_paths: for ( segment ) in reconstructed_motion_path.get_motion_path().get_segments(): Dist.append( segment.get_arc_length() * _tools.geocentric_radius( segment.get_start_point().to_lat_lon()[0] ) / 1e3 ) # Note that the motion path coordinates come out starting with the oldest time and working forwards # So, to match our 'times' array, we flip the order Dist = np.flipud(Dist) # Get rate of motion as distance per Myr Rate = np.asarray(Dist) / TimeStep # Manipulate arrays to get a step plot StepRate = np.zeros(len(Rate) * 2) StepRate[::2] = Rate StepRate[1::2] = Rate StepTime = np.zeros(len(Rate) * 2) StepTime[::2] = time_array[:1] StepTime[1::2] = time_array[1:] # Append the nth point's step time and step rate coordinates to the ndarray StepTimes[:, i] = StepTime StepRates[:, i] = StepRate * 0.1 # cm/yr if return_rate_of_motion is True: return ( np.squeeze(rlons), np.squeeze(rlats), np.squeeze(StepTimes), np.squeeze(StepRates), ) else: return np.squeeze(rlons), np.squeeze(rlats) def flowline( self, time_array, left_plate_ID, right_plate_ID, return_rate_of_motion=False ): """Create a path of points to track plate motion away from spreading ridges over time using halfstage rotations. Parameters  lons : arr An array of longitudes of points along spreading ridges. lats : arr An array of latitudes of points along spreading ridges. time_array : arr A list of times to obtain seed point locations at. left_plate_ID : int The plate ID of the polygon to the left of the spreading ridge. right_plate_ID : int The plate ID of the polygon to the right of the spreading ridge. return_rate_of_motion : bool, default False Choose whether to return a step time and step rate array for a stepplot of flowline motion. Returns  left_lon : ndarray The longitudes of the __left__ flowline for n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. left_lat : ndarray The latitudes of the __left__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. right_lon : ndarray The longitudes of the __right__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. right_lat : ndarray The latitudes of the __right__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. Examples  To access the ith seed point's left and right latitudes and longitudes: for i in np.arange(0,len(seed_points)): left_flowline_longitudes = left_lon[:,i] left_flowline_latitudes = left_lat[:,i] right_flowline_longitudes = right_lon[:,i] right_flowline_latitudes = right_lat[:,i] """ model = self.plate_reconstruction return model.create_flowline( self.lons, self.lats, time_array, left_plate_ID, right_plate_ID, return_rate_of_motion, ) def _get_dataframe(self): import geopandas as gpd data = dict() data["Longitude"] = self.lons data["Latitude"] = self.lats data["Plate_ID"] = self.plate_id for key in self.attributes: data[key] = self.attributes[key] return gpd.GeoDataFrame(data) def save(self, filename): """Saves the feature collection used in the Points object under a given filename to the current directory. The file format is determined from the filename extension. Parameters  filename : string Can be provided as a string including the filename and the file format needed. Returns  Feature collection saved under given filename to current directory. """ filename = str(filename) if filename.endswith((".csv", ".txt", ".dat")): df = self._get_dataframe() df.to_csv(filename, index=False) elif filename.endswith((".xls", ".xlsx")): df = self._get_dataframe() df.to_excel(filename, index=False) elif filename.endswith("xml"): df = self._get_dataframe() df.to_xml(filename, index=False) elif filename.endswith(".gpml") or filename.endswith(".gpmlz"): self.FeatureCollection.write(filename) else: raise ValueError( "Cannot save to specified file type. Use csv, gpml, or xls file extension." )
Instance variables
var size

Number of points
Expand source code
@property def size(self): """Number of points""" return len(self.lons)
Methods
def add_attributes(self, **kwargs)

Adds the value of a feature attribute associated with a key.
Example
# Define latitudes and longitudes to set up a Points object pt_lons = np.array([140., 150., 160.]) pt_lats = np.array([30., 40., 50.]) gpts = gplately.Points(model, pt_lons, pt_lats) # Add the attributes a, b and c to the points in the Points object gpts.add_attributes( a=[10,2,2], b=[2,3,3], c=[30,0,0], ) print(gpts.attributes)
The output would be:
{'a': [10, 2, 2], 'b': [2, 3, 3], 'c': [30, 0, 0]}
Parameters
**kwargs
:sequence
ofkey=item/s
 A single key=value pair, or a sequence of key=value pairs denoting the name and value of an attribute.
Notes
 An assertion is raised if the number of points in the Points object is not equal
to the number of values associated with an attribute key. For example, consider an instance
of the Points object with 3 points. If the points are ascribed an attribute
temperature
, there must be onetemperature
value per point, i.e.temperature = [20, 15, 17.5]
.
Expand source code
def add_attributes(self, **kwargs): """Adds the value of a feature attribute associated with a key. Example  # Define latitudes and longitudes to set up a Points object pt_lons = np.array([140., 150., 160.]) pt_lats = np.array([30., 40., 50.]) gpts = gplately.Points(model, pt_lons, pt_lats) # Add the attributes a, b and c to the points in the Points object gpts.add_attributes( a=[10,2,2], b=[2,3,3], c=[30,0,0], ) print(gpts.attributes) The output would be: {'a': [10, 2, 2], 'b': [2, 3, 3], 'c': [30, 0, 0]} Parameters  **kwargs : sequence of key=item/s A single key=value pair, or a sequence of key=value pairs denoting the name and value of an attribute. Notes  * An **assertion** is raised if the number of points in the Points object is not equal to the number of values associated with an attribute key. For example, consider an instance of the Points object with 3 points. If the points are ascribed an attribute `temperature`, there must be one `temperature` value per point, i.e. `temperature = [20, 15, 17.5]`. """ keys = kwargs.keys() for key in kwargs: attribute = kwargs[key] # make sure attribute is the same size as self.lons if type(attribute) is int or type(attribute) is float: array = np.full(self.lons.size, attribute) attribute = array elif isinstance(attribute, np.ndarray): if attribute.size == 1: array = np.full(self.lons.size, attribute, dtype=attribute.dtype) attribute = array assert ( len(attribute) == self.lons.size ), "Size mismatch, ensure attributes have the same number of entries as Points" self.attributes[key] = attribute if any(kwargs): # add these to the FeatureCollection for f, feature in enumerate(self.FeatureCollection): for key in keys: # extract value for each row in attribute val = self.attributes[key][f] # set this attribute on the feature feature.set_shapefile_attribute(key, val)
def copy(self)

Expand source code
def copy(self): """Returns a copy of the Points object Returns  Points A copy of the current Points object """ gpts = Points( self.plate_reconstruction, self.lons.copy(), self.lats.copy(), self.time, self.plate_id.copy(), ) gpts.add_attributes(**self.attributes.copy())
def flowline(self, time_array, left_plate_ID, right_plate_ID, return_rate_of_motion=False)

Create a path of points to track plate motion away from spreading ridges over time using halfstage rotations.
Parameters
lons
:arr
 An array of longitudes of points along spreading ridges.
lats
:arr
 An array of latitudes of points along spreading ridges.
time_array
:arr
 A list of times to obtain seed point locations at.
left_plate_ID
:int
 The plate ID of the polygon to the left of the spreading ridge.
right_plate_ID
:int
 The plate ID of the polygon to the right of the spreading ridge.
return_rate_of_motion
:bool
, defaultFalse
 Choose whether to return a step time and step rate array for a stepplot of flowline motion.
Returns
left_lon
:ndarray
 The longitudes of the left flowline for n seed points.
There are n columns for n seed points, and m rows
for m time steps in
time_array
. left_lat
:ndarray
 The latitudes of the left flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in
time_array
. right_lon
:ndarray
 The longitudes of the right flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in
time_array
. right_lat
:ndarray
 The latitudes of the right flowline of n seed points.
There are n columns for n seed points, and m rows
for m time steps in
time_array
.
Examples
To access the ith seed point's left and right latitudes and longitudes:
for i in np.arange(0,len(seed_points)): left_flowline_longitudes = left_lon[:,i] left_flowline_latitudes = left_lat[:,i] right_flowline_longitudes = right_lon[:,i] right_flowline_latitudes = right_lat[:,i]
Expand source code
def flowline( self, time_array, left_plate_ID, right_plate_ID, return_rate_of_motion=False ): """Create a path of points to track plate motion away from spreading ridges over time using halfstage rotations. Parameters  lons : arr An array of longitudes of points along spreading ridges. lats : arr An array of latitudes of points along spreading ridges. time_array : arr A list of times to obtain seed point locations at. left_plate_ID : int The plate ID of the polygon to the left of the spreading ridge. right_plate_ID : int The plate ID of the polygon to the right of the spreading ridge. return_rate_of_motion : bool, default False Choose whether to return a step time and step rate array for a stepplot of flowline motion. Returns  left_lon : ndarray The longitudes of the __left__ flowline for n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. left_lat : ndarray The latitudes of the __left__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. right_lon : ndarray The longitudes of the __right__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. right_lat : ndarray The latitudes of the __right__ flowline of n seed points. There are n columns for n seed points, and m rows for m time steps in `time_array`. Examples  To access the ith seed point's left and right latitudes and longitudes: for i in np.arange(0,len(seed_points)): left_flowline_longitudes = left_lon[:,i] left_flowline_latitudes = left_lat[:,i] right_flowline_longitudes = right_lon[:,i] right_flowline_latitudes = right_lat[:,i] """ model = self.plate_reconstruction return model.create_flowline( self.lons, self.lats, time_array, left_plate_ID, right_plate_ID, return_rate_of_motion, )
def get_geodataframe(self)

Returns the output of
Points.get_geopandas_dataframe()
.Adds a shapely point
geometry
attribute to each point in thePoints
object. pandas.DataFrame that has a column with geometry Any existing point attributes are kept.Returns
GeoDataFrame
:instance
ofgeopandas.GeoDataFrame
 A pandas.DataFrame with rows equal to the number of points in the
Points
object, and an additional column containing a shapelygeometry
attribute.
Example
pt_lons = np.array([140., 150., 160.]) pt_lats = np.array([30., 40., 50.]) gpts = gplately.Points(model, pt_lons, pt_lats) # Add sample attributes a, b and c to the points in the Points object gpts.add_attributes( a=[10,2,2], b=[2,3,3], c=[30,0,0], ) gpts.get_geopandas_dataframe()
…has the output:
a b c geometry 0 10 2 30 POINT (140.00000 30.00000) 1 2 3 0 POINT (150.00000 40.00000) 2 2 3 0 POINT (160.00000 50.00000)
Expand source code
def get_geodataframe(self): """Returns the output of `Points.get_geopandas_dataframe()`. Adds a shapely point `geometry` attribute to each point in the `gplately.Points` object. pandas.DataFrame that has a column with geometry Any existing point attributes are kept. Returns  GeoDataFrame : instance of `geopandas.GeoDataFrame` A pandas.DataFrame with rows equal to the number of points in the `gplately.Points` object, and an additional column containing a shapely `geometry` attribute. Example  pt_lons = np.array([140., 150., 160.]) pt_lats = np.array([30., 40., 50.]) gpts = gplately.Points(model, pt_lons, pt_lats) # Add sample attributes a, b and c to the points in the Points object gpts.add_attributes( a=[10,2,2], b=[2,3,3], c=[30,0,0], ) gpts.get_geopandas_dataframe() ...has the output: a b c geometry 0 10 2 30 POINT (140.00000 30.00000) 1 2 3 0 POINT (150.00000 40.00000) 2 2 3 0 POINT (160.00000 50.00000) """ return self.get_geopandas_dataframe()
def get_geopandas_dataframe(self)

Adds a shapely point
geometry
attribute to each point in thePoints
object. pandas.DataFrame that has a column with geometry Any existing point attributes are kept.Returns
GeoDataFrame
:instance
ofgeopandas.GeoDataFrame
 A pandas.DataFrame with rows equal to the number of points in the
Points
object, and an additional column containing a shapelygeometry
attribute.
Example
pt_lons = np.array([140., 150., 160.]) pt_lats = np.array([30., 40., 50.]) gpts = gplately.Points(model, pt_lons, pt_lats) # Add sample attributes a, b and c to the points in the Points object gpts.add_attributes( a=[10,2,2], b=[2,3,3], c=[30,0,0], ) gpts.get_geopandas_dataframe()
…has the output:
a b c geometry 0 10 2 30 POINT (140.00000 30.00000) 1 2 3 0 POINT (150.00000 40.00000) 2 2 3 0 POINT (160.00000 50.00000)
Expand source code
def get_geopandas_dataframe(self): """Adds a shapely point `geometry` attribute to each point in the `gplately.Points` object. pandas.DataFrame that has a column with geometry Any existing point attributes are kept. Returns  GeoDataFrame : instance of `geopandas.GeoDataFrame` A pandas.DataFrame with rows equal to the number of points in the `gplately.Points` object, and an additional column containing a shapely `geometry` attribute. Example  pt_lons = np.array([140., 150., 160.]) pt_lats = np.array([30., 40., 50.]) gpts = gplately.Points(model, pt_lons, pt_lats) # Add sample attributes a, b and c to the points in the Points object gpts.add_attributes( a=[10,2,2], b=[2,3,3], c=[30,0,0], ) gpts.get_geopandas_dataframe() ...has the output: a b c geometry 0 10 2 30 POINT (140.00000 30.00000) 1 2 3 0 POINT (150.00000 40.00000) 2 2 3 0 POINT (160.00000 50.00000) """ import geopandas as gpd from shapely import geometry # create shapely points points = [] for lon, lat in zip(self.lons, self.lats): points.append(geometry.Point(lon, lat)) attributes = self.attributes.copy() attributes["geometry"] = points return gpd.GeoDataFrame(attributes, geometry="geometry")
def motion_path(self, time_array, anchor_plate_id=0, return_rate_of_motion=False)

Create a path of points to mark the trajectory of a plate's motion through geological time.
Parameters
time_array
:arr
 An array of reconstruction times at which to determine the trajectory
of a point on a plate. For example:
import numpy as np min_time = 30 max_time = 100 time_step = 2.5 time_array = np.arange(min_time, max_time + time_step, time_step)
anchor_plate_id
:int
, default=0
 The ID of the anchor plate.
return_rate_of_motion
:bool
, default=False
 Choose whether to return the rate of plate motion through time for each
Returns
rlons
:ndarray
 An ndimensional array with columns containing the longitudes of
the seed points at each timestep in
time_array
. There are n columns for n seed points. rlats
:ndarray
 An ndimensional array with columns containing the latitudes of
the seed points at each timestep in
time_array
. There are n columns for n seed points.
Expand source code
def motion_path(self, time_array, anchor_plate_id=0, return_rate_of_motion=False): """Create a path of points to mark the trajectory of a plate's motion through geological time. Parameters  time_array : arr An array of reconstruction times at which to determine the trajectory of a point on a plate. For example: import numpy as np min_time = 30 max_time = 100 time_step = 2.5 time_array = np.arange(min_time, max_time + time_step, time_step) anchor_plate_id : int, default=0 The ID of the anchor plate. return_rate_of_motion : bool, default=False Choose whether to return the rate of plate motion through time for each Returns  rlons : ndarray An ndimensional array with columns containing the longitudes of the seed points at each timestep in `time_array`. There are n columns for n seed points. rlats : ndarray An ndimensional array with columns containing the latitudes of the seed points at each timestep in `time_array`. There are n columns for n seed points. """ time_array = np.atleast_1d(time_array) # ndarrays to fill with reconstructed points and # rates of motion (if requested) rlons = np.empty((len(time_array), len(self.lons))) rlats = np.empty((len(time_array), len(self.lons))) for i, point_feature in enumerate(self.FeatureCollection): # Create the motion path feature motion_path_feature = pygplates.Feature.create_motion_path( point_feature.get_geometry(), time_array.tolist(), valid_time=(time_array.max(), time_array.min()), # relative_plate=int(self.plate_id[i]), # reconstruction_plate_id=int(anchor_plate_id)) relative_plate=int(self.plate_id[i]), reconstruction_plate_id=int(anchor_plate_id), ) reconstructed_motion_paths = self.plate_reconstruction.reconstruct( motion_path_feature, to_time=0, # from_time=0, reconstruct_type=pygplates.ReconstructType.motion_path, anchor_plate_id=int(anchor_plate_id), ) # Turn motion paths in to latlon coordinates for reconstructed_motion_path in reconstructed_motion_paths: trail = reconstructed_motion_path.get_motion_path().to_lat_lon_array() lon, lat = np.flipud(trail[:, 1]), np.flipud(trail[:, 0]) rlons[:, i] = lon rlats[:, i] = lat # Obtain stepplot coordinates for rate of motion if return_rate_of_motion is True: StepTimes = np.empty(((len(time_array)  1) * 2, len(self.lons))) StepRates = np.empty(((len(time_array)  1) * 2, len(self.lons))) # Get timestep TimeStep = [] for j in range(len(time_array)  1): diff = time_array[j + 1]  time_array[j] TimeStep.append(diff) # Iterate over each segment in the reconstructed motion path, get the distance travelled by the moving # plate relative to the fixed plate in each time step Dist = [] for reconstructed_motion_path in reconstructed_motion_paths: for ( segment ) in reconstructed_motion_path.get_motion_path().get_segments(): Dist.append( segment.get_arc_length() * _tools.geocentric_radius( segment.get_start_point().to_lat_lon()[0] ) / 1e3 ) # Note that the motion path coordinates come out starting with the oldest time and working forwards # So, to match our 'times' array, we flip the order Dist = np.flipud(Dist) # Get rate of motion as distance per Myr Rate = np.asarray(Dist) / TimeStep # Manipulate arrays to get a step plot StepRate = np.zeros(len(Rate) * 2) StepRate[::2] = Rate StepRate[1::2] = Rate StepTime = np.zeros(len(Rate) * 2) StepTime[::2] = time_array[:1] StepTime[1::2] = time_array[1:] # Append the nth point's step time and step rate coordinates to the ndarray StepTimes[:, i] = StepTime StepRates[:, i] = StepRate * 0.1 # cm/yr if return_rate_of_motion is True: return ( np.squeeze(rlons), np.squeeze(rlats), np.squeeze(StepTimes), np.squeeze(StepRates), ) else: return np.squeeze(rlons), np.squeeze(rlats)
def plate_velocity(self, time, delta_time=1)

Calculates the x and y components of tectonic plate velocities at a particular geological time.
This method accesses and uses the
rotation_model
attribute from thePlateReconstruction
object and uses thePoints
object'sself.features
attribute. Feature points are extracted and assigned plate IDs. These IDs are used to obtain the equivalent stage rotations of identified tectonic plates over a time intervaldelta_time
. Each feature point and its stage rotation are used to calculate the point's plate velocity at a particular geological time. Obtained velocities for each domain point are represented in the northeastdown coordinate system, and their x,y Cartesian coordinate components are extracted.Parameters
time
:float
 The specific geological time (Ma) at which to calculate plate velocities.
delta_time
:float
, default=1.0
 The time increment used for generating partitioning plate stage rotations. 1.0 Ma by default.
Returns
all_velocities.T : 2D numpy list
 A transposed 2D numpy list with two rows and a number of columns equal to the number of x,y Cartesian velocity components obtained (and thus the number of feature points extracted from a supplied feature). Each list column stores one point’s x,y, velocity components along its two rows.
Expand source code
def plate_velocity(self, time, delta_time=1): """Calculates the x and y components of tectonic plate velocities at a particular geological time. This method accesses and uses the `rotation_model` attribute from the `PlateReconstruction` object and uses the `Points` object's `self.features` attribute. Feature points are extracted and assigned plate IDs. These IDs are used to obtain the equivalent stage rotations of identified tectonic plates over a time interval `delta_time`. Each feature point and its stage rotation are used to calculate the point's plate velocity at a particular geological time. Obtained velocities for each domain point are represented in the northeastdown coordinate system, and their x,y Cartesian coordinate components are extracted. Parameters  time : float The specific geological time (Ma) at which to calculate plate velocities. delta_time : float, default=1.0 The time increment used for generating partitioning plate stage rotations. 1.0 Ma by default. Returns  all_velocities.T : 2D numpy list A transposed 2D numpy list with two rows and a number of columns equal to the number of x,y Cartesian velocity components obtained (and thus the number of feature points extracted from a supplied feature). Each list column stores one point’s x,y, velocity components along its two rows. """ time = float(time) rotation_model = self.plate_reconstruction.rotation_model all_velocities = np.empty((len(self.features), 2)) for i, feature in enumerate(self.features): geometry = feature.get_geometry() partitioning_plate_id = feature.get_reconstruction_plate_id() equivalent_stage_rotation = rotation_model.get_rotation( time, partitioning_plate_id, time + delta_time ) velocity_vectors = pygplates.calculate_velocities( [geometry], equivalent_stage_rotation, delta_time, pygplates.VelocityUnits.cms_per_yr, ) velocities = ( pygplates.LocalCartesian.convert_from_geocentric_to_north_east_down( [geometry], velocity_vectors ) ) all_velocities[i] = velocities[0].get_y(), velocities[0].get_x() return list(all_velocities.T)
def reconstruct(self, time, anchor_plate_id=None, return_array=False, **kwargs)

Reconstructs regular geological features, motion paths or flowlines to a specific geological time and extracts the latitudinal and longitudinal points of these features.
Note: this method accesses and uses the rotation model attribute from the PointReconstruction object, and reconstructs the feature latlon point attributes of the Points object.
Parameters
time
:float
 The specific geological time (Ma) to reconstruct features to.
anchor_plate_id
:int
, default=None
 Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made
with respect to the anchor_plate_ID specified in the
PlateReconstruction
object, which is a default plate ID of 0 unless otherwise specified. return_array
:bool
, defaultFalse
 Return a
numpy.ndarray
, rather than aPoints
object. **reconstruct_type
:ReconstructType
, default=ReconstructType.feature_geometry
 The specific reconstruction type to generate based on input feature geometry type. Can be provided as
ReconstructType.feature_geometry to only reconstruct regular feature geometries, or ReconstructType.MotionPath to
only reconstruct motion path features, or ReconstructType.Flowline to only reconstruct flowline features. Generates
:class:
reconstructed feature geometries<ReconstructedFeatureGeometry>’, or :class:
reconstructed motion paths’, or :class:`reconstructed flowlines ’ respectively. **group_with_feature
:bool
, default=False
 Used to group reconstructed geometries with their features. This can be useful when a feature has more than one
geometry and hence more than one reconstructed geometry. The output reconstructed_geometries then becomes a
list of tuples where each tuple contains a :class:
feature<Feature>
and alist
of reconstructed geometries. Note: this keyword argument only applies when reconstructed_geometries is a list because exported files are always grouped with their features. This is applicable to all ReconstructType features. **export_wrap_to_dateline
:bool
, default=True
 Wrap/clip reconstructed geometries to the dateline (currently ignored).
Returns
rlons
:list
offloat
 A 1D numpy array enclosing all reconstructed point features' longitudes.
rlats
:list
offloat
 A 1D numpy array enclosing all reconstructed point features' latitudes.
Raises
NotImplementedError
 if the starting time for reconstruction
from_time
is not equal to 0.0
Expand source code
def reconstruct(self, time, anchor_plate_id=None, return_array=False, **kwargs): """Reconstructs regular geological features, motion paths or flowlines to a specific geological time and extracts the latitudinal and longitudinal points of these features. Note: this method accesses and uses the rotation model attribute from the PointReconstruction object, and reconstructs the feature latlon point attributes of the Points object. Parameters  time : float The specific geological time (Ma) to reconstruct features to. anchor_plate_id : int, default=None Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made with respect to the anchor_plate_ID specified in the `gplately.PlateReconstruction` object, which is a default plate ID of 0 unless otherwise specified. return_array : bool, default False Return a `numpy.ndarray`, rather than a `Points` object. **reconstruct_type : ReconstructType, default=ReconstructType.feature_geometry The specific reconstruction type to generate based on input feature geometry type. Can be provided as ReconstructType.feature_geometry to only reconstruct regular feature geometries, or ReconstructType.MotionPath to only reconstruct motion path features, or ReconstructType.Flowline to only reconstruct flowline features. Generates :class:`reconstructed feature geometries<ReconstructedFeatureGeometry>’, or :class:`reconstructed motion paths<ReconstructedMotionPath>’, or :class:`reconstructed flowlines<ReconstructedFlowline>’ respectively. **group_with_feature : bool, default=False Used to group reconstructed geometries with their features. This can be useful when a feature has more than one geometry and hence more than one reconstructed geometry. The output *reconstructed_geometries* then becomes a list of tuples where each tuple contains a :class:`feature<Feature>` and a ``list`` of reconstructed geometries. Note: this keyword argument only applies when *reconstructed_geometries* is a list because exported files are always grouped with their features. This is applicable to all ReconstructType features. **export_wrap_to_dateline : bool, default=True Wrap/clip reconstructed geometries to the dateline (currently ignored). Returns  rlons : list of float A 1D numpy array enclosing all reconstructed point features' longitudes. rlats : list of float A 1D numpy array enclosing all reconstructed point features' latitudes. Raises  NotImplementedError if the starting time for reconstruction `from_time` is not equal to 0.0 """ from_time = self.time to_time = time if not anchor_plate_id: anchor_plate_id = self.plate_reconstruction.anchor_plate_id reconstructed_features = self.plate_reconstruction.reconstruct( self.features, to_time, from_time, anchor_plate_id=anchor_plate_id, **kwargs ) rlons, rlats = _tools.extract_feature_lonlat(reconstructed_features) if return_array: return rlons, rlats else: gpts = Points( self.plate_reconstruction, rlons, rlats, time=to_time, plate_id=self.plate_id, ) gpts.add_attributes(**self.attributes.copy()) return gpts
def reconstruct_to_birth_age(self, ages, anchor_plate_id=None, **kwargs)

Reconstructs point features supplied to the
Points
object from the supplied initial time (self.time
) to a range of times. The number of supplied times must equal the number of point features supplied to the Points object.Attributes
ages
:array
 Geological times to reconstruct features to. Must have the same length as the
Points
object'sself.features
attribute (which holds all point features represented on a unit length sphere in 3D Cartesian coordinates). anchor_plate_id
:int
, default=None
 Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made
with respect to the anchor_plate_ID specified in the
PlateReconstruction
object, which is a default plate ID of 0 unless otherwise specified. **kwargs
 Additional keyword arguments for the
PlateReconstruction.reconstruct()
method.
Raises
ValueError
 If the number of ages and number of point features supplied to the Points object are not identical.
Returns
rlons
,rlats
:float
 The longitude and latitude coordinate lists of all point features reconstructed to all specified ages.
Examples
To reconstruct n seed points' locations to B Ma (for this example n=2, with (lon,lat) = (78,30) and (56,22) at time=0 Ma, and we reconstruct to B=10 Ma):
# Longitude and latitude of n=2 seed points pt_lon = np.array([78., 56]) pt_lat = np.array([30., 22]) # Call the Points object! gpts = gplately.Points(model, pt_lon, pt_lat) print(gpts.features[0].get_all_geometries()) # Confirms we have features represented as points on a sphere ages = numpy.linspace(10,10, len(pt_lon)) rlons, rlats = gpts.reconstruct_to_birth_age(ages)
Expand source code
def reconstruct_to_birth_age(self, ages, anchor_plate_id=None, **kwargs): """Reconstructs point features supplied to the `Points` object from the supplied initial time (`self.time`) to a range of times. The number of supplied times must equal the number of point features supplied to the Points object. Attributes  ages : array Geological times to reconstruct features to. Must have the same length as the `Points `object's `self.features` attribute (which holds all point features represented on a unit length sphere in 3D Cartesian coordinates). anchor_plate_id : int, default=None Reconstruct features with respect to a certain anchor plate. By default, reconstructions are made with respect to the anchor_plate_ID specified in the `gplately.PlateReconstruction` object, which is a default plate ID of 0 unless otherwise specified. **kwargs Additional keyword arguments for the `gplately.PlateReconstruction.reconstruct` method. Raises  ValueError If the number of ages and number of point features supplied to the Points object are not identical. Returns  rlons, rlats : float The longitude and latitude coordinate lists of all point features reconstructed to all specified ages. Examples  To reconstruct n seed points' locations to B Ma (for this example n=2, with (lon,lat) = (78,30) and (56,22) at time=0 Ma, and we reconstruct to B=10 Ma): # Longitude and latitude of n=2 seed points pt_lon = np.array([78., 56]) pt_lat = np.array([30., 22]) # Call the Points object! gpts = gplately.Points(model, pt_lon, pt_lat) print(gpts.features[0].get_all_geometries()) # Confirms we have features represented as points on a sphere ages = numpy.linspace(10,10, len(pt_lon)) rlons, rlats = gpts.reconstruct_to_birth_age(ages) """ from_time = self.time if not anchor_plate_id: anchor_plate_id = self.plate_reconstruction.anchor_plate_id ages = np.array(ages) if len(ages) != len(self.features): raise ValueError("Number of points and ages must be identical") unique_ages = np.unique(ages) rlons = np.zeros(ages.shape) rlats = np.zeros(ages.shape) for age in unique_ages: mask_age = ages == age reconstructed_features = self.plate_reconstruction.reconstruct( self.features, age, from_time, anchor_plate_id=anchor_plate_id, **kwargs ) lons, lats = _tools.extract_feature_lonlat(reconstructed_features) rlons[mask_age] = lons[mask_age] rlats[mask_age] = lats[mask_age] return rlons, rlats
def save(self, filename)

Saves the feature collection used in the Points object under a given filename to the current directory.
The file format is determined from the filename extension.
Parameters
filename
:string
 Can be provided as a string including the filename and the file format needed.
Returns
Feature collection saved under given filename to current directory.
Expand source code
def save(self, filename): """Saves the feature collection used in the Points object under a given filename to the current directory. The file format is determined from the filename extension. Parameters  filename : string Can be provided as a string including the filename and the file format needed. Returns  Feature collection saved under given filename to current directory. """ filename = str(filename) if filename.endswith((".csv", ".txt", ".dat")): df = self._get_dataframe() df.to_csv(filename, index=False) elif filename.endswith((".xls", ".xlsx")): df = self._get_dataframe() df.to_excel(filename, index=False) elif filename.endswith("xml"): df = self._get_dataframe() df.to_xml(filename, index=False) elif filename.endswith(".gpml") or filename.endswith(".gpmlz"): self.FeatureCollection.write(filename) else: raise ValueError( "Cannot save to specified file type. Use csv, gpml, or xls file extension." )