scipy - python split 3D spline curve to equally spaced (euclidean) points

Question

I have a set of points that represent a 3D curve. And I have a number of links/segments (n) and their length (L).

I want to split the 3D curve (starting from the first point of the curve) into n segments, so the euclidean distance between them is L. The curve is longer than n segments, so the last point of the segments is not at the end of the curve.

I currently have a solution for that but it's not optimized and takes a lot of time to compute (~110ms), using Python3.6

This my current solution:

1. I'm using scipy.interpolate.splprep to create the 3D curve
2. Starting from parameter u=0, I am using the Bisection method to find the next u value that will give me a 3D point which is at a distance of L from the first points
3. repeating these steps until all the n segments are found

This is the function that I wrote to do it:

• self.epsilon - The allowed error for the distance between the points
• self.link_N = Number of segments/links
• self.link_L - The length of the segments/links

def split_curve(self, curve):
    joint_pos = curve[:, 0].reshape(3, 1)
    tck, u = sc.splprep(curve, k=2, s=0)
    a = 0
    prev_pos = joint_pos
    for i in range(self.link_N-1):
        iter_count = 0
        b = 1
        error = self.epsilon + 1
        while np.abs(error) > self.epsilon and iter_count < self.iter_max:
            iter_count += 1
            c = (a+b)/2
            temp_pos = np.asarray([sc.splev(c, tck)]).T
            error = self.link_L - np.linalg.norm(temp_pos - prev_pos)
            if error > 0:
                a = c
            else:
                b = c
        u = c
        joint_pos = np.hstack((joint_pos, temp_pos))
        prev_pos = temp_pos
    return joint_pos

My curve is changing fast (about 100-150hz) and this function (which takes about 100ms to compute) slows me down. Is there a better solution for that problem rather than using the Bisection method?

question from:https://stackoverflow.com/questions/65864253/python-split-3d-spline-curve-to-equally-spaced-euclidean-points

Answer 1

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