microstructpy.geometry.n_sphere.NSphere¶

class microstructpy.geometry.n_sphere.NSphere(**kwargs)[source]

Bases: object

An N-dimensional sphere.

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

If multiple size or position keywords are given, there is no guarantee whhich keywords are used to create the geometry.

Parameters: r (float) – (optional) The radius of the n-sphere. Defaults to 1. center (list) – (optional) The coordinates of the center. Defaults to []. radius – Alias for r. d – Alias for 2*r. diameter – Alias for 2*r. size – Alias for 2*r. position – Alias for center.
approximate()[source]

Approximate the n-sphere with itself

Other geometries can be approximated by a set of circles or spheres. For the n-sphere, this approximation is exact.

Returns: A list containing [(x, y, z, …, r)] list
classmethod best_fit(points)[source]

Find n-sphere of best fit for set of points.

This function takes a list of points and computes an n-sphere of best fit, in an algebraic sense. This method was developed using the a published writeup, which was extended from 2D to ND. [1]

Parameters: points (list, numpy.ndarray) – List of points to fit. An instance of the class that fits the points. NSphere
 [1] Circle fitting writup by Randy Bullock, https://dtcenter.org/met/users/docs/write_ups/circle_fit.pdf
reflect(points)[source]

Reflect points across surface.

This function reflects a point or set of points across the surface of the n-sphere. Points at the center of the n-sphere are not reflected.

Parameters: points (list or numpy.ndarray) – Points to reflect. Reflected points. numpy.ndarray
within(points)[source]

Test if points are within n-sphere.

This function tests whether a point or set of points are within the n-sphere. For the set of points, a list of booleans is returned to indicate which points are within the n-sphere.

Parameters: points (list or numpy.ndarray) – Point or list of points. Set to True for points in geometry. bool or numpy.ndarray
bound_max

maximum bounding n-sphere

Type: tuple
bound_min

minimum interior n-sphere

Type: tuple
d

diameter of n-sphere.

Type: float
diameter

diameter of n-sphere.

Type: float
limits

list of (lower, upper) bounds for the bounding box

Type: list
position

position of n-sphere.

Type: list
radius

sample_limits
size`