From: Matthias Baas <mbaas@us...>  20060217 18:56:17

Update of /cvsroot/cgkit/cgkit2/cgkit In directory sc8prcvs1.sourceforge.net:/tmp/cvsserv20964/cgkit Added Files: hammersley.py Log Message: Added a module to create Hammersley and Halton points  NEW FILE: hammersley.py  ########################################################################### # cgkit  Python Computer Graphics Kit # Copyright (C) 2004 Matthias Baas (baas@...) # # This library is free software; you can redistribute it and/or # modify it under the terms of the GNU Lesser General Public # License as published by the Free Software Foundation; either # version 2.1 of the License, or (at your option) any later version. # # This library is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU # Lesser General Public License for more details. # # You should have received a copy of the GNU Lesser General Public # License along with this library; if not, write to the Free Software # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 021111307 USA # # cgkit homepage: http://cgkit.sourceforge.net ########################################################################### # $Id: hammersley.py,v 1.1 2006/02/17 18:56:09 mbaas Exp $ """ Hammersley & Halton point generation This module contains functions to generate points that are uniformly distributed and stochasticlooking on either a unit square or a unit sphere. The Hammersley point set is more uniform but is nonhierarchical, 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: TienTsin Wong, WaiShing Luk, PhengAnn Heng "Sampling with Hammersley and Halton points" Journal of Graphics Tools, Vol. 2, No. 2, 1997, pp. 924 http://www.acm.org/jgt/papers/WongLukHeng97/ http://www.cse.cuhk.edu.hk/~ttwong/papers/udpoint/udpoints.html The original C versions of these functions are distributed under the following license: (c) Copyright 1997, TienTsin 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, THE MATERIAL EMBODIED ON THIS SOFTWARE IS PROVIDED TO YOU "ASIS" AND WITHOUT WARRANTY OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL THE AUTHOR BE LIABLE TO YOU OR ANYONE ELSE FOR ANY DIRECT, SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER, INCLUDING WITHOUT LIMITATION, LOSS OF PROFIT, LOSS OF USE, SAVINGS OR REVENUE, OR THE CLAIMS OF THIRD PARTIES, WHETHER OR NOT THE AUTHOR HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH LOSS, HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH THE POSSESSION, USE OR PERFORMANCE OF THIS SOFTWARE. """ from math import pi, sqrt, cos, sin from cgtypes import * # planeHammersley def planeHammersley(n): """Yields n Hammersley points on the unit square in the xy plane. This function 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. """ for k in range(n): u = 0 p=0.5 kk = k while kk>0: if kk & 1: u += p p *= 0.5 kk >>= 1 v = (k+0.5)/n yield (u, v) # sphereHammersley def sphereHammersley(n): """Yields n Hammersley points on the unit sphere. 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. """ for k in range(n): t = 0 p = 0.5 kk = k while kk>0: if kk & 1: t += p p *= 0.5 kk >>= 1 t = 2.0*t  1.0 phi = (k+0.5)/n phirad = phi*2.0*pi st = sqrt(1.0t*t) yield vec3(st*cos(phirad), st*sin(phirad), t) # planeHalton def planeHalton(n=None, p2=3): """Yields a sequence of Halton points on the unit square in the xy plane. 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. """ k = 0 while k+1!=n: u = 0 p = 0.5 kk = k while kk>0: if kk & 1: u += p p *= 0.5 kk >>= 1 v = 0 ip = 1.0/p2 p = ip kk = k while kk>0: a = kk % p2 if a!=0: v += a*p p *= ip kk = int(kk/p2) yield (u,v) k += 1 # sphereHalton def sphereHalton(n=None, p2=3): """Yields a sequence of Halton points on the unit sphere. 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. """ k = 0 while k+1!=n: t = 0 p = 0.5 kk = k while kk>0: if kk & 1: t += p p *= 0.5 kk >>= 1 t = 2.0*t  1.0 st = sqrt(1.0t*t) phi = 0 ip = 1.0/p2 p = ip kk = k while kk>0: a = kk % p2 if a!=0: phi += a*p p *= ip kk = int(kk/p2) phirad = phi*4.0*pi yield vec3(st*cos(phirad), st*sin(phirad), t) k += 1 