Interpolating a hemispherical shape leads to ZeroDivisionError about nurbs-python

[chvillanuevap]

I tried the solution in #132. I no longer get the ZeroDivisionError, but I now get a closed surface as the interpolation.

(Red is data points, blue is evaluation points). Here is the code I use:

from geomdl import fitting, linalg
from geomdl.visualization import VisMPL as vis

import numpy as np
import matplotlib.pyplot as plt
import math
import h5py

np.set_printoptions(threshold=np.inf, linewidth=np.inf)

# From Github #132 
def my_compute_params(points, centripetal=False):
    if not isinstance(points, (list, tuple)):
        raise TypeError("Data points must be a list or a tuple")

    # Length of the points array
    num_points = len(points)

    # Calculate chord lengths
    cds = [0.0 for _ in range(num_points + 1)]
    cds[-1] = 1.0
    for i in range(1, num_points):
        distance = linalg.point_distance(points[i], points[i - 1])
        cds[i] = math.sqrt(distance) if centripetal else distance

    # Find the total chord length
    d = sum(cds[1:-1])

    # Divide individual chord lengths by the total chord length
    uk = [0.0 for _ in range(num_points)]
    for i in range(num_points):
        s = sum(cds[0:i + 1])
        if s == 0:
            uk[i] = i / (num_points - 1)
        else:
            try:
                uk[i] = s / d
            except ZeroDivisionError:
                uk[i] = 0

    return uk

theta = np.linspace(0, np.pi/2, num=50)
phi = np.linspace(0, 2*np.pi, num=100)
theta, phi = np.meshgrid(theta, phi)
x = np.sin(theta) * np.cos(phi)
y = np.sin(theta) * np.sin(phi)
z = np.cos(theta)
points = np.column_stack((x.ravel(), y.ravel(), z.ravel()))

# Set interpolation parameters
size_u = 50
size_v = 100
degree_u = 3
degree_v = 3

fitting.compute_params_curve = my_compute_params

# Perform surface interpolation
surf = fitting.interpolate_surface(points, size_u, size_v, degree_u, degree_v,centripetal=False)

surf.sample_size_u = 50
surf.sample_size_v = 100

# Evaluate the surface at the new resolution
surf.evaluate()

[orbingol]

The implemented algorithms, as they are, may not be able to handle surfaces like the hemisphere. Depending on how you generate the surface, you could play with the knot vectors or modify the fitting algorithm to use custom knot vectors. I am not sure custom knot vectors would be successful, but it might be worth a try.

[orbingol]

Just as a future reference to ZeroDivisionError: #168 (comment)