Returns N points spread over a torus. Returns normals, handle self-intersections.

README.md

Golden dot spiral on a torus

This code sample demonstrates how to generates a set of points that covers a torus, for any number of points. The trick is to use a spiral and the golden angle.

42 points	256 points	999 points

Such points sets are useful for anything that requires sampling a torus.

spiral-torus.py

import numpy

def norm2(X):
    return numpy.sqrt(numpy.sum(X ** 2, axis = -1))

golden_angle = numpy.pi * (3 - numpy.sqrt(5))

def get_spiral_torus(r_major, r_minor, N, return_normals = False):
    # Generate the surface samples
    theta = golden_angle * numpy.arange(N)
    alpha = numpy.linspace(0., 2 * numpy.pi, N)
    
    cos_theta, sin_theta = numpy.cos(theta), numpy.sin(theta)
    cos_alpha, sin_alpha = numpy.cos(alpha), numpy.sin(alpha)

    Q = r_major + r_minor * cos_theta
    XYZ = numpy.stack([Q * cos_alpha, Q * sin_alpha, r_minor * sin_theta], axis = 1)

    if return_normals:
        UVW = numpy.stack([cos_alpha * cos_theta, sin_alpha * cos_theta, sin_theta], axis = 1)
       
    # Handle self-intersecting torus case
    if r_major < r_minor:
        outside = (norm2(XYZ[:, :2]) - r_major) ** 2 + XYZ[:, 2] ** 2 >= r_minor ** 2
        XYZ = XYZ[outside].copy()
        if returns_normals:
            UVW = UVW[outside].copy()
        
    # Job done
    if return_normals:
        return XYZ, UVW
    else:
        return XYZ