Plot 3D curvature

This example shows how to plot curvature combs in 3D or how to color the spline based on the local curvature. Both options are illustrated in pyvista and matplotlib.

import matplotlib.pyplot as plt
import mpl_toolkits
import numpy as np
import pyvista
import splinebox

1. Construct as random spline

M = 4
spline = splinebox.Spline(M=M, basis_function=splinebox.B3(), closed=False)
np.random.seed(0)
spline.control_points = np.random.rand(M + 2, 3)

t = np.linspace(0, M - 1, M * 15)

vals = spline(t)

2. Curvature comb with pyvista

mesh = pyvista.MultipleLines(points=vals)

curvature = spline.curvature(t)

normals = spline.normal(t, frame="frenet")
normal = -normals[:, 0]

comb = vals + curvature[:, np.newaxis] / 100 * normal

comb_mesh_points = np.zeros((comb.shape[0] * 3 - 1, 3))
comb_mesh_points[0::3] = vals
comb_mesh_points[1::3] = comb
comb_mesh_points[2::3] = comb[1:]
comb_mesh = pyvista.MultipleLines(points=comb_mesh_points)

plotter = pyvista.Plotter()
plotter.add_mesh(mesh, color="blue")
plotter.add_mesh(comb_mesh, color="lightblue")
plotter.show()

Static Scene

Interactive Scene

3. Curvature comb with matplotlib

ax = plt.figure().add_subplot(projection="3d")
ax.plot(vals[:, 2], vals[:, 1], vals[:, 0], color="blue")
ax.plot(comb_mesh_points[:, 2], comb_mesh_points[:, 1], comb_mesh_points[:, 0], color="lightblue")
plt.show()

4. Colour with pyvista

We start with a simple line.

points, connectivity = spline.mesh(step_t=t[1] - t[0], radius=None)
connectivity = np.hstack((np.full((connectivity.shape[0], 1), 2), connectivity))
mesh = pyvista.PolyData(points, lines=connectivity)
mesh.cell_data["curvature"] = spline.curvature(t[:-1] + np.diff(t))
mesh.plot()

Static Scene

Interactive Scene

To control the thickness of the the line we can use a mesh

points, connectivity = spline.mesh(step_t=t[1] - t[0], radius=0.01)
connectivity = np.hstack((np.full((connectivity.shape[0], 1), 3), connectivity))
mesh = pyvista.PolyData(points, faces=connectivity)
segment_curvature = spline.curvature(t[:-1] + np.diff(t))
mesh.cell_data["curvature"] = np.repeat(segment_curvature, len(connectivity) / len(segment_curvature))
mesh.plot()

Static Scene

Interactive Scene

5. Colour with matplotlib

ax = plt.figure().add_subplot(projection="3d")
segments = np.stack([vals[:-1], vals[1:]], axis=1)
lc = mpl_toolkits.mplot3d.art3d.Line3DCollection(segments)
lc.set_array(segment_curvature)
ax.add_collection(lc)
plt.show()