import numpy as np import holoviews as hv from holoviews import opts from scipy.spatial import Delaunay hv.extension('bokeh')
TriMesh represents a mesh of triangles represented as the simplexes and vertices. The simplexes represent the indices into the vertex data, made up of three indices per triangle. The mesh therefore follows a datastructure very similar to a graph, with the abstract connectivity between nodes stored on the
TriMesh element itself, the node or vertex positions stored on a
Nodes element and the concrete
EdgePaths making up each triangle generated when required by accessing the edgepaths attribute.
Unlike a Graph each simplex is represented as the node indices of the three corners of each triangle rather than the usual source and target node.
We will begin with a simple random mesh, generated by sampling some random integers and then applying Delaunay triangulation, which is available in SciPy. We can then construct the
TriMesh by passing it the simplexes and the vertices (or nodes).
n_verts = 100 pts = np.random.randint(1, n_verts, (n_verts, 2)) tris = Delaunay(pts) trimesh = hv.TriMesh((tris.simplices, pts)) trimesh
To make this easier TriMesh also provides a convenient
from_vertices method, which will apply the Delaunay triangulation and construct the
TriMesh for us:
Just like the
Graph element we can access the
EdgePaths via the
.edgepaths attributes respectively.
trimesh.nodes + trimesh.edgepaths
Now let’s make a slightly more interesting example by generating a more complex geometry. Here we will compute a geometry, then apply Delaunay triangulation again and finally apply a mask to drop nodes in the center.
# First create the x and y coordinates of the points. n_angles = 36 n_radii = 8 min_radius = 0.25 radii = np.linspace(min_radius, 0.95, n_radii) angles = np.linspace(0, 2*np.pi, n_angles, endpoint=False) angles = np.repeat(angles[..., np.newaxis], n_radii, axis=1) angles[:, 1::2] += np.pi/n_angles x = (radii*np.cos(angles)).flatten() y = (radii*np.sin(angles)).flatten() z = (np.cos(radii)*np.cos(angles*3.0)).flatten() nodes = np.column_stack([x, y, z]) # Apply Delaunay triangulation delaunay = Delaunay(np.column_stack([x, y])) # Mask off unwanted triangles. xmid = x[delaunay.simplices].mean(axis=1) ymid = y[delaunay.simplices].mean(axis=1) mask = np.where(xmid*xmid + ymid*ymid < min_radius*min_radius, 1, 0) simplices = delaunay.simplices[np.logical_not(mask)]
Once again we can simply supply the simplices and nodes to the
nodes = hv.Points(nodes, vdims='z') hv.TriMesh((simplices, nodes))
We can also do something more interesting, e.g. by adding a value dimension to the vertices and coloring the edges by the vertex averaged value using the
edge_color plot option:
trimesh = hv.TriMesh((simplices, nodes)) trimesh.opts( opts.TriMesh(cmap='viridis', edge_color='z', filled=True, height=400, inspection_policy='edges', tools=['hover'], width=400))
For full documentation and the available style and plot options, use