This module contains functions to generate points that are uniformly distributed and stochastic-looking on either a unit square or a unit sphere. The Hammersley point set is more uniform but is non-hierarchical, i.e. for different n arguments you get an entirely new sequence. If you need hierarchical behavior you can use the Halton point set.
This is a Python version of the implementation provided in:
Tien-Tsin Wong, Wai-Shing Luk, Pheng-Ann HengSampling with Hammersley and Halton pointsJournal of Graphics Tools, Vol. 2, No. 2, 1997, pp. 9-24
Yields a sequence of n tuples (x, y) which represent a point on the unit square. The sequence of points for a particular n is always the same. When n changes an entirely new sequence will be generated.
This function uses a base of 2.
This function yields n vec3 objects representing points on the unit sphere. The sequence of points for a particular n is always the same. When n changes an entirely new sequence will be generated.
This function uses a base of 2.
This function yields a sequence of two floats (x, y) which represent a point on the unit square. The number of points to generate is given by n. If n is set to None, an infinite number of points is generated and the caller has to make sure the loop stops by checking some other critera. The sequence of generated points is always the same, no matter what n is (i.e. the first n elements generated by the sequence planeHalton(n+1) is identical to the sequence planeHalton(n)).
This function uses 2 as its first prime base whereas the second prime p2 (which must be a prime number) can be provided by the user.
This function yields a sequence of vec3 objects representing points on the unit sphere. The number of points to generate is given by n. If n is set to None, an infinite number of points is generated and the caller has to make sure the loop stops by checking some other critera. The sequence of generated points is always the same, no matter what n is (i.e. the first n elements generated by the sequence sphereHalton(n+1) is identical to the sequence sphereHalton(n)).
This function uses 2 as its first prime base whereas the second base p2 (which must be a prime number) can be provided by the user.
Note
The original C versions of these functions are distributed under the following license:
(c) Copyright 1997, Tien-Tsin Wong — ALL RIGHTS RESERVED — Permission to use, copy, modify, and distribute this software for any purpose and without fee is hereby granted, provided that the above copyright notice appear in all copies and that both the copyright notice and this permission notice appear in supporting documentation,
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