# Calculate velocities by plate ID¶

This example calculates velocities at all points in geometries of a collection of features using the plate IDs of those features and a rotation model.

## Sample code¶

```
import pygplates
# Load one or more rotation files into a rotation model.
rotation_model = pygplates.RotationModel('rotations.rot')
# Load the features that contain the geometries we will calculate velocities at.
# Calling them 'domain' features since using them as input to velocities (but can be any type of feature).
domain_features = pygplates.FeatureCollection('features.gpml')
# Calculate velocities at 10Ma using a delta time interval of 1Ma.
reconstruction_time = 10
delta_time = 1
# All reconstructed geometry points and associated (magnitude, azimuth, inclination) velocities.
all_reconstructed_points = []
all_velocities = []
# Iterate over all geometries in all domain features and calculate velocities at each of their points.
for domain_feature in domain_features:
# We need the feature's plate ID to get the equivalent stage rotation of that tectonic plate.
domain_plate_id = domain_feature.get_reconstruction_plate_id()
# Get the rotation of plate 'domain_plate_id' from present day (0Ma) to 'reconstruction_time'.
equivalent_total_rotation = rotation_model.get_rotation(reconstruction_time, domain_plate_id)
# Get the rotation of plate 'domain_plate_id' from 'reconstruction_time + delta_time' to 'reconstruction_time'.
equivalent_stage_rotation = rotation_model.get_rotation(
reconstruction_time, domain_plate_id, reconstruction_time + delta_time)
# A feature usually has a single geometry but it could have more - iterate over them all.
for geometry in domain_feature.get_geometries():
# Reconstruct the geometry to 'reconstruction_time'.
reconstructed_geometry = equivalent_total_rotation * geometry
reconstructed_points = reconstructed_geometry.get_points()
# Calculate velocities at the reconstructed geometry points.
# This is from 'reconstruction_time + delta_time' to 'reconstruction_time' on plate 'domain_plate_id'.
velocity_vectors = pygplates.calculate_velocities(reconstructed_points, 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_magnitude_azimuth_inclination(
reconstructed_points, velocity_vectors)
# Append results for the current geometry to the final results.
all_reconstructed_points.extend(reconstructed_points)
all_velocities.extend(velocities)
```

## Details¶

The rotations are loaded from a rotation file into a `pygplates.RotationModel`

.

```
rotation_model = pygplates.RotationModel('rotations.rot')
```

The features to calculate velocities at are loaded into a `pygplates.FeatureCollection`

.
They can be any `type`

of feature as long as they have a
`reconstruction plate ID`

(and of course some `geometry`

).

```
domain_features = pygplates.FeatureCollection('features.gpml')
```

```
reconstruction_time = 10
delta_time = 1
```

`pygplates.RotationModel`

enables to calculate both the rotation from present day to 10Ma
of a particular tectonic plate relative to the anchor plate (defaults to zero):

```
equivalent_total_rotation = rotation_model.get_rotation(reconstruction_time, domain_plate_id)
```

…and the *stage* rotation from 11Ma to 10Ma:

```
equivalent_stage_rotation = rotation_model.get_rotation(
reconstruction_time, domain_plate_id, reconstruction_time + delta_time)
```

`pygplates.Feature`

usually contains a single geometry property but sometimes it contains more.`pygplates.Feature.get_geometries()`

instead of `pygplates.Feature.get_geometry()`

.`domain_feature.get_geometries()`

is just a convenient alternative to
`domain_feature.get_geometry(property_return=PropertyReturn.all)`

.```
for geometry in domain_feature.get_geometries():
```

The `geometries`

extracted from `features`

are in present day coordinates and need to be reconstructed to their 10Ma positions.

```
reconstructed_geometry = equivalent_total_rotation * geometry
```

`pygplates.PointOnSphere`

, `pygplates.MultiPointOnSphere`

,
`pygplates.PolylineOnSphere`

or `pygplates.PolygonOnSphere`

.`pygplates.PointOnSphere`

to calculate velocities at using
`pygplates.GeometryOnSphere.get_points()`

.```
reconstructed_points = reconstructed_geometry.get_points()
```

`calculated`

at the reconstructed geometry positions (10Ma) using the stage rotation.`pygplates.Vector3D`

(one global cartesian velocity vector per geometry point).```
velocity_vectors = pygplates.calculate_velocities(reconstructed_points, equivalent_stage_rotation, delta_time)
```

`pygplates.LocalCartesian.convert_from_geocentric_to_magnitude_azimuth_inclination()`

.`reconstructed_points`

determines a separate local coordinate system.
For example, the velocity *azimuth*is relative to North as viewed from a particular point position.

```
velocities = pygplates.LocalCartesian.convert_from_geocentric_to_magnitude_azimuth_inclination(
reconstructed_points, velocity_vectors)
```

*all*features.

```
all_reconstructed_points.extend(reconstructed_points)
all_velocities.extend(velocities)
```