如何在SciPy中沿着3D样条曲线找到点？

Question

I want to make a curve like this:

A 3D curve, with 3 points in space defining the end and middle points, which the curve passes through, but also 2 points in space that the curve bends towards without touching.

Similar to defining curves using points in 2D in Inkscape:

Additionally, I want to calculate the points along this curve equally spaced along the x dimension of the space. (Not equally spaced along the t variable that defines the spline, and not equally spaced along the curve length. The curve will not backtrack along the x dimension.)

I've tried reading the documentation , but I'm confused. It either shows the curve going through all the points:

or none of them:

Answer 1

Here is a code using the bezier python package to obtain points along a Bezier curve .

To obtain points "along this curve equally spaced along the x dimension" a linear interpolation is performed using numpy.interp . For each coordinate x wanted, the corresponding curvilinear coordinate t is interpolated. Then, the coordinates of the point at t is obtain using curve.evaluate_multi again.

The example is in 2D but should be working in 3D by defining 3D nodes coordinates.

%matplotlib inline
import matplotlib.pylab as plt

import bezier
import numpy as np

# Define the Bezier curve
nodes = np.array([
        [0.0, 0.2, 1.0, 2.0],
        [0.0, 1.8, 0.3, 0.5] ])

curve = bezier.Curve(nodes, degree=3)

t_fine = np.linspace(0, 1, 60) # Curvilinear coordinate
points_fine = curve.evaluate_multi(t_fine)
points_fine.shape  # (2, 60)

# Interpolation on regular x coordinates
x_xregular = np.linspace(0, 2, 7)

t_xregular = np.interp(x_xregular, points_fine[0], t_fine)
points_xregular = curve.evaluate_multi(t_xregular)

# Plot
plt.plot(*nodes, '-o', label='definition nodes');
plt.plot(*points_fine, label='Bezier curve');
plt.plot(*points_xregular, 'ok', label='regularly spaced along x');
plt.xlabel('x'); plt.ylabel('y'); plt.legend();