Spatial analysis

import movekit as mkit
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.spatial import Voronoi, voronoi_plot_2d, convex_hull_plot_2d, delaunay_plot_2d

path = "datasets/fish-5-cleaned.csv"
data = mkit.read_data(path)
data = mkit.extract_features(data)
data.head()

Extracting all absolute features: 100%|██████████| 100.0/100 [00:01<00:00, 81.44it/s]

	time	animal_id	x	y	distance	direction	turning	average_speed	average_acceleration	stopped
0	1	312	405.29	417.76	0.0	(0.0, 0.0)	0.0	0.210217	-0.006079	1
1	1	511	369.99	428.78	0.0	(0.0, 0.0)	0.0	0.020944	0.000041	1
2	1	607	390.33	405.89	0.0	(0.0, 0.0)	0.0	0.070235	0.000344	1
3	1	811	445.15	411.94	0.0	(0.0, 0.0)	0.0	0.370500	0.007092	1
4	1	905	366.06	451.76	0.0	(0.0, 0.0)	0.0	0.118000	-0.003975	1

Spatial Objects

The function below produces three types of spatial objects: Voronoi-Diagrams, Convex Hulls and Delaunay Triangles. Optionally, one may obtain only group-specific outputs - one object per time-capture. These spatial objects may be used for a set of attributes, which are described below in detail. To get the full functionality of all attributes, please go to https://docs.scipy.org/doc/scipy-0.14.0/reference/tutorial/spatial.html.

spatial_obj = mkit.get_spatial_objects(data, group_output = True)
spatial_obj.head()

Calculating spatial objects: 100%|██████████| 1000/1000 [00:15<00:00, 63.51it/s]

	time	convex_hull_object	voronoi_object	delaunay_object	convex_hull_volume	voronoi_volume
0	1	<scipy.spatial.qhull.ConvexHull object at 0x7f...	<scipy.spatial.qhull.Voronoi object at 0x7ff88...	<scipy.spatial.qhull.Delaunay object at 0x7ff8...	1519.44120	inf
1	2	<scipy.spatial.qhull.ConvexHull object at 0x7f...	<scipy.spatial.qhull.Voronoi object at 0x7ff88...	<scipy.spatial.qhull.Delaunay object at 0x7ff8...	1528.95525	inf
2	3	<scipy.spatial.qhull.ConvexHull object at 0x7f...	<scipy.spatial.qhull.Voronoi object at 0x7ff88...	<scipy.spatial.qhull.Delaunay object at 0x7ff8...	1539.23800	inf
3	4	<scipy.spatial.qhull.ConvexHull object at 0x7f...	<scipy.spatial.qhull.Voronoi object at 0x7ff88...	<scipy.spatial.qhull.Delaunay object at 0x7ff8...	1549.61380	inf
4	5	<scipy.spatial.qhull.ConvexHull object at 0x7f...	<scipy.spatial.qhull.Voronoi object at 0x7ff88...	<scipy.spatial.qhull.Delaunay object at 0x7ff8...	1560.33905	inf

Producing a voronoi diagram

Each timestep gets a voronoi object as well as the area of the voronoi - shape. Infinity, if respective animal is outmost in swarm.

Voronoi object contains the following attributes:

• points Coordinates of input points.

• vertices Coordinates of the Voronoi vertices.

• ridge_points Indices of the points between which each Voronoi ridge lies.

• ridge_vertices Indices of the Voronoi vertices forming each Voronoi ridge.

• regions Indices of the Voronoi vertices forming each Voronoi region. -1 indicates vertex outside the Voronoi diagram.

• point_region Index of the Voronoi region for each input point. If qhull option “Qc” was not specified, the list will contain -1 for points that are not associated with a Voronoi region.

• furthest_site True if this was a furthest site triangulation and False if not.

Producing a convex hull

Similar to voronoi-diagram, also the convex hull is of interest for movement-related data. Additionally, a set of attributes may be attached to the convex hull objects. Examples are:

• points (array of ints) Coordinates of input points

• vertices (array of ints ) Point indices forming the veritces of the convex hull

• area Area of the convex hull.

• volume Volume of the convex hull.

Producing Delaunay-triangles

Examples for attributes of interest consist of:

• transform Affine transform from x to the barycentric coordinates c.

• vertex_to_simplex Lookup array, from a vertex, to some simplex which it is a part of.

• convex_hull Vertices of facets forming the convex hull of the point set.

• vertex_neighbor_vertices Neighboring vertices of vertices.

• points (ndarray of double, shape (npoints, ndim)) Coordinates of input points.

• simplices (ndarray of ints, shape (nsimplex, ndim+1)) Indices of the points forming the simplices in the triangulation. For 2-D, the points are oriented counterclockwise.

• neighbors (ndarray of ints, shape (nsimplex, ndim+1)) Indices of neighbor simplices for each simplex. The kth neighbor is opposite to the kth vertex. For simplices at the boundary, -1 denotes no neighbor.

Plotting all spatial objects at the 3rd timestep.

# Plot all scipy - spatial objects of a given timestamp
voronoi_plot_2d(spatial_obj.voronoi_object[2])
convex_hull_plot_2d(spatial_obj.convex_hull_object[2])
delaunay_plot_2d(spatial_obj.delaunay_object[2])
plt.show()