Sphere.py

import mathutils
import numpy as np

from src.main.Provider import Provider


class Sphere(Provider):
    """ Samples a point from the surface or from the interior of solid sphere

        Example 1: Sample a point from the surface of the solid sphere of a defined radius and center location.

        {
          "provider":"sampler.Sphere",
          "center":[0, 0, 0],
          "radius": 2,
          "mode": "SURFACE"
        }

    **Configuration**:

    .. csv-table::
        :header: "Parameter", "Description"

        "center", "Location of the center of the sphere. Type: mathutils.Vector."
        "radius", "The radius of the sphere. Type: float."
        "mode", "Mode of sampling. Determines the geometrical structure used for sampling. Type: string. "
                "Available: SURFACE (sampling from the 2-sphere), INTERIOR (sampling from the 3-ball)."
    """

    def __init__(self, config):
        Provider.__init__(self, config)

    # https://math.stackexchange.com/a/87238
    # https://math.stackexchange.com/a/1585996
    def run(self):
        """
        :param config: A configuration object containing the parameters necessary to sample.
        :return: A random point lying inside or on the surface of a solid sphere. Type: mathutils vector
        """
        # Center of the sphere.
        center = np.array(self.config.get_list("center"))
        # Radius of the sphere.
        radius = self.config.get_float("radius")
        # Mode of operation.
        mode = self.config.get_string("mode")

        return Sphere.sample(center, radius, mode)

    @staticmethod
    def sample(center, radius, mode):
        """
        Samples a point according to the mode, the center and the radius.

       :param center, A list of three values, describing the x, y and z coordinate of the center of the sphere. Type: mathutils.Vector
       :param radius, The radius of the sphere. Type: float
       :param mode, Mode of sampling. SURFACE - sampling from the 2-sphere, INTERIOR - sampling from the 3-ball. Type: str
        """
        # Sample
        direction = np.random.normal(size=3)
        
        if np.count_nonzero(direction) == 0:  # Check no division by zero
            direction[0] = 1e-5

        # For normalization
        norm = np.sqrt(direction.dot(direction))

        # If sampling from the surface set magnitude to radius of the sphere
        if mode == "SURFACE":
            magnitude = radius
        # If sampling from the interior set it to scaled radius
        elif mode == "INTERIOR":
            magnitude = radius * np.cbrt(np.random.uniform())
        else:
            raise Exception("Unknown sampling mode: " + mode)
        
        # Normalize
        sampled_point = list(map(lambda x: magnitude*x/norm, direction))
        
        # Add center
        location = mathutils.Vector(np.array(sampled_point) + center)

        return location