microstructpy.geometry.sphere module

Sphere

This module contains the Sphere class.

class microstructpy.geometry.sphere.Sphere(**kwargs)[source]

Bases: microstructpy.geometry.n_sphere.NSphere

A 3D sphere.

This class represents a three-dimensional circle. It is defined by a center point and size parameter, which can be either radius or diameter.

Parameters:
  • r (float, optional) – The radius of the n-sphere.
  • radius (float, optional) – The radius of the n-sphere.
  • d (float, optional) – The diameter of the n-sphere.
  • diameter (float, optional) – The diameter of the n-sphere.
  • size (float, optional) – The size of the n-sphere.
  • center (list, float, numpy.ndarray) – The coordinates of the center.
  • position (list, float, numpy.ndarray) – The coordinates of the center.
plot(**kwargs)[source]

Plot the sphere.

This function uses the Axes3D.plot_surface method to add the sphere to the current axes. The keyword arguments are passed through to plot_surface.

Parameters:**kwargs (dict) – Keyword arguments for plot_surface.
classmethod volume_expectation(**kwargs)[source]

Expected value of volume.

This function computes the expected value for the volume of a sphere. The keyword arguments are identical to the __init__ function. The values for these keywords can be either constants or scip.stats distributions.

The expected value is computed by the following formula:

\[\begin{split}\begin{align} \mathbb{E}[V] &= \mathbb{E}[\frac{4}{3}\pi R^3] \\ &= \frac{4}{3}\pi \mathbb{E}[R^3] \\ &= \frac{4}{3}\pi (\mu_R^3 + 3 \mu_R \sigma_R^2 + \gamma_{1, R} \sigma_R^3) \end{align}\end{split}\]
Parameters:**kwargs – Keyword arguments, see microstructpy.geometry.Sphere.
Returns:Expected value of the volume of the sphere.
Return type:float
n_dim

number of dimensions, 3

Type:int
volume

volume of sphere

Type:float