equidistant sampling on a spline

equidistant_spline.py

import numpy as np
import napari
from scipy.interpolate import splprep, splev

n = 10
w = np.linspace(0, 8*np.pi, num=n)
x = [0, 1,  1, 1,]
y = [0,  0, 10, 10]
z = [0, 0, 0, 100]
xyz = np.stack((x, y, z), axis=-1)

# calculate spline representation of curve
tck, _ = splprep([*xyz.T], s=0, k=3)

# sample points on spline
n_points_spline = 100
u = np.linspace(0, 1, n_points_spline)
sampled_points = splev(u, tck)
sampled_points = np.stack(sampled_points, axis=-1)
inter_point_differences = np.diff(sampled_points, axis=0)
inter_point_distances = np.linalg.norm(inter_point_differences, axis=-1)
cumulative_distance = np.cumsum(inter_point_distances)
cumulative_distance /= cumulative_distance[-1]

# compute spline coefficients for normalised cumulative distance
tck_prime, _ = splprep([np.linspace(0, 1, num=len(cumulative_distance))], u=cumulative_distance, s=0, k=3)

equidistant_u = splev(u, tck_prime)
equidistant_point_samples = splev(equidistant_u, tck)
equidistant_point_samples = np.stack(equidistant_point_samples, axis=-1).squeeze(axis=0)

viewer = napari.Viewer(ndisplay=3)
viewer.add_points(xyz)
viewer.add_points(sampled_points)
viewer.add_points(equidistant_point_samples)
napari.run()