500 lines
15 KiB
C++
500 lines
15 KiB
C++
/****************************************************************************
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* VCGLib o o *
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* Visual and Computer Graphics Library o o *
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* _ O _ *
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* Copyright(C) 2004-2016 \/)\/ *
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* Visual Computing Lab /\/| *
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* ISTI - Italian National Research Council | *
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* \ *
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* All rights reserved. *
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* *
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* This program is free software; you can redistribute it and/or modify *
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* it under the terms of the GNU General Public License as published by *
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* the Free Software Foundation; either version 2 of the License, or *
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* (at your option) any later version. *
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* *
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* This program is distributed in the hope that it will be useful, *
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* but WITHOUT ANY WARRANTY; without even the implied warranty of *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
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* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
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* for more details. *
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* *
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****************************************************************************/
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#ifndef __VCG_RandomGenerator
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#define __VCG_RandomGenerator
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#include <vcg/math/base.h>
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namespace vcg {
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namespace math {
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/**
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* Common interface for random generation (with uniform distribution).
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*
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* Two RNGs are available: Subtractive Ring and an improved Marsenne-Twister.
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*/
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class RandomGenerator
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{
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// construction
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public:
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RandomGenerator(){}
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virtual ~RandomGenerator()
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{}
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// public methods
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public:
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/// (Re-)initialize with a given seed.
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virtual void initialize(unsigned int seed)=0;
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/// Return a random number in the given range (note that not all the RNG can handle a given limit).
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virtual unsigned int generate(unsigned int limit)=0;
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/// Return a random number in the [0,1) real interval.
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virtual double generate01()=0;
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/// Returns a random number in the [0,1] real interval.
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virtual double generate01closed()=0;
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/// Generates a random number in the (0,1) real interval.
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virtual double generate01open()=0;
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virtual double generateRange(double minV, double maxV) { return minV+(maxV-minV)*generate01(); }
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};
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/// \brief Generate the barycentric coords of a random point over a single face,
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/// with a uniform distribution over the triangle.
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/// It uses the parallelogram folding trick.
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template <class ScalarType, class GeneratorType>
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vcg::Point3<ScalarType> GenerateBarycentricUniform(GeneratorType &rnd)
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{
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vcg::Point3<ScalarType> interp;
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interp[1] = rnd.generate01();
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interp[2] = rnd.generate01();
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if(interp[1] + interp[2] > 1.0)
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{
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interp[1] = 1.0 - interp[1];
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interp[2] = 1.0 - interp[2];
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}
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assert(interp[1] + interp[2] <= 1.0);
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interp[0]=1.0-(interp[1] + interp[2]);
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return interp;
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}
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/// \brief Generate a random point insidie a box with uniform distribution
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template <class ScalarType, class GeneratorType>
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vcg::Point3<ScalarType> GeneratePointInBox3Uniform(GeneratorType &rnd, const Box3<ScalarType> &bb)
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{
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return Point3<ScalarType>(
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(ScalarType) rnd.generateRange(double(bb.min[0]),double(bb.max[0])),
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(ScalarType) rnd.generateRange(double(bb.min[1]),double(bb.max[1])),
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(ScalarType) rnd.generateRange(double(bb.min[2]),double(bb.max[2]))
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);
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}
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/** \brief Generate a point over the surface of a unit sphere with uniform distribution
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* This is the algorithm proposed by George Marsaglia [1]
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* to generate a point over a unit sphere
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* Independently generate V1 and V2, taken from a uniform distribution on (-1,1) such that
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* S=(V1^2+V2^2)<1
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*
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* The random vector is then :
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* (2V1 sqrt(1-S), 2V2 sqrt(1-S),1-2S)
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*
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* Marsaglia, G. "Choosing a Point from the Surface of a Sphere." Ann. Math. Stat. 43, 645-646, 1972.
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*/
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template <class ScalarType, class GeneratorType>
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vcg::Point3<ScalarType> GeneratePointOnUnitSphereUniform(GeneratorType &rnd)
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{
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vcg::Point3<ScalarType> p;
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double x,y,s;
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do
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{
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x = 2.0*rnd.generate01()-1.0;
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y = 2.0*rnd.generate01()-1.0;
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s = x*x+y*y;
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} while (s>1);
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p[0]= ScalarType(2 * x * sqrt(1-s));
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p[1]= ScalarType(2 * y * sqrt(1-s));
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p[2]= ScalarType(1-2*s);
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return p;
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}
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/// \brief generate a point inside a unit sphere with uniform distribution
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template <class ScalarType, class GeneratorType>
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vcg::Point3<ScalarType> GeneratePointInUnitBallUniform(GeneratorType &rnd)
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{
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vcg::Point3<ScalarType> p;
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while(1)
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{
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p.Import(Point3d(0.5-rnd.generate01(),0.5-rnd.generate01(),0.5-rnd.generate01()));
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if(SquaredNorm(p)<=0.25){
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p*=2;
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return p;
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}
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}
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}
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/**
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* Uniform RNG derived from a STL extension of sgi.
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*
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* It is based on the Subtractive Ring method.
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* This implementation assumes that int is 32 bits.
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*
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* References
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*
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* D. E. Knuth, The Art of Computer Programming. Volume 2: Seminumerical Algorithms, 2nd Edition. Addison-Wesley, 1981.
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* (section 3.6 of Knuth for an implementation of the subtractive method in FORTRAN)
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* (section 3.2.2 of Knuth analyzes this class of algorithms)
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*/
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class SubtractiveRingRNG : public RandomGenerator
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{
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// private data member
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private:
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// Subtractive Ring RNG status variables
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unsigned int _M_table[55];
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size_t _M_index1;
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size_t _M_index2;
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// construction
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public:
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// ctor
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SubtractiveRingRNG(int default_seed=161803398u)
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{
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initialize(default_seed);
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}
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virtual ~SubtractiveRingRNG()
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{}
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// public methods
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public:
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/// (Re-)initialize with a given seed.
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void initialize(unsigned int seed)
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{
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unsigned int __k = 1;
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_M_table[54] = seed;
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size_t __i;
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for (__i = 0; __i < 54; __i++)
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{
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size_t __ii = (21 * (__i + 1) % 55) - 1;
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_M_table[__ii] = __k;
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__k = seed - __k;
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seed = _M_table[__ii];
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}
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for (int __loop = 0; __loop < 4; __loop++)
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{
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for (__i = 0; __i < 55; __i++)
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_M_table[__i] = _M_table[__i] - _M_table[(1 + __i + 30) % 55];
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}
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_M_index1 = 0;
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_M_index2 = 31;
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}
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/// Return a random number in the given range (limit) using the Subtractive Ring method.
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unsigned int generate(unsigned int limit= 0xffffffffu)
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{
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_M_index1 = (_M_index1 + 1) % 55;
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_M_index2 = (_M_index2 + 1) % 55;
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_M_table[_M_index1] = _M_table[_M_index1] - _M_table[_M_index2];
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return _M_table[_M_index1] % limit;
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}
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/// Return a random number in the [0,1) real interval using the Subtractive Ring method.
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double generate01()
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{
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const unsigned int lmt = 0xffffffffu;
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unsigned int number = generate(lmt);
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return static_cast<double>(number) / static_cast<double>(lmt);
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}
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/// Returns a random number in the [0,1] real interval using the Subtractive Ring method.
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double generate01closed()
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{
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const unsigned int lmt = 0xffffffffu;
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unsigned int number = generate(lmt);
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return static_cast<double>(number) / static_cast<double>(0xfffffffEu);
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}
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/// Generates a random number in the (0,1) real interval using the Subtractive Ring method.
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double generate01open()
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{
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const unsigned int lmt = 0xffffffffu;
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unsigned int number = generate(lmt);
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return (static_cast<double>(number) + 0.5) * (1.0/static_cast<double>(lmt));
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}
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};
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/**
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* The second one is an improved Marsenne-Twister algorithm (MT19937)
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* Coded by Takuji Nishimura and Makoto Matsumoto (see copyright note below)
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* and successively modified to be a C++ class by Daniel Dunbar.
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*
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*
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* References for improved Marsenne-Twister:
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*
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* http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
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*
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*/
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class MarsenneTwisterRNG : public RandomGenerator
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{
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// definitions
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private:
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static const int N = 624;
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static const int M = 397;
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static const unsigned int MATRIX_A = 0x9908b0dfu; // constant vector a
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static const unsigned int UPPER_MASK = 0x80000000u; // most significant w-r bits
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static const unsigned int LOWER_MASK = 0x7fffffffu; // least significant r bits
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// private data member
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private:
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// Improved Marsenne-Twister RNG status variables
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unsigned int mt[N]; // the array for the state vector
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int mti;
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// construction
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public:
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// ctor
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MarsenneTwisterRNG()
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{
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initialize(5489u);
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}
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MarsenneTwisterRNG(unsigned int seed)
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{
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initialize(seed);
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}
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virtual ~MarsenneTwisterRNG()
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{}
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// public methods
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public:
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/// (Re-)initialize with the given seed.
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void initialize(unsigned int seed)
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{
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mt[0]= seed & 0xffffffffu;
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for (mti=1; mti<N; mti++)
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{
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mt[mti] = (1812433253u * (mt[mti-1] ^ (mt[mti-1] >> 30)) + mti);
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/* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
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/* In the previous versions, MSBs of the seed affect */
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/* only MSBs of the array mt[]. */
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/* 2002/01/09 modified by Makoto Matsumoto */
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mt[mti] &= 0xffffffffu;
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/* for >32 bit machines */
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}
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}
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/**
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* Initialize by an array with array-length.
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*
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* init_key is the array for initializing keys
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* key_length is its length
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*/
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void initializeByArray(unsigned int init_key[], int key_length)
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{
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int i, j, k;
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initialize(19650218u);
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i=1; j=0;
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k = (N>key_length ? N : key_length);
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for (; k; k--)
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{
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mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1664525u)) + init_key[j] + j; /* non linear */
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mt[i] &= 0xffffffffu; /* for WORDSIZE > 32 machines */
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i++; j++;
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if (i>=N)
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{
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mt[0] = mt[N-1];
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i=1;
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}
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if (j>=key_length) j=0;
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}
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for (k=N-1; k; k--)
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{
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mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941u)) - i; /* non linear */
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mt[i] &= 0xffffffffu; /* for WORDSIZE > 32 machines */
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i++;
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if (i>=N)
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{
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mt[0] = mt[N-1];
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i=1;
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}
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}
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mt[0] = 0x80000000u; /* MSB is 1; assuring non-zero initial array */
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}
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unsigned int generate(unsigned int limit)
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{
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return generate()%limit;
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}
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/**
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* Return a random number in the [0,0xffffffff] interval using the improved Marsenne Twister algorithm.
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*
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* NOTE: Limit is not considered, the interval is fixed.
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*/
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unsigned int generate()
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{
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unsigned int y;
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static unsigned int mag01[2]={0x0u, MATRIX_A};
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/* mag01[x] = x * MATRIX_A for x=0,1 */
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if (mti >= N) // generate N words at one time
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{
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int kk;
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for (kk=0;kk<N-M;kk++)
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{
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y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
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mt[kk] = mt[kk+M] ^ (y >> 1) ^ mag01[y & 0x1u];
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}
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for (;kk<N-1;kk++)
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{
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y = (mt[kk]&UPPER_MASK)|(mt[kk+1]&LOWER_MASK);
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mt[kk] = mt[kk+(M-N)] ^ (y >> 1) ^ mag01[y & 0x1u];
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}
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y = (mt[N-1]&UPPER_MASK)|(mt[0]&LOWER_MASK);
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mt[N-1] = mt[M-1] ^ (y >> 1) ^ mag01[y & 0x1u];
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mti = 0;
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}
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y = mt[mti++];
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/* Tempering */
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y ^= (y >> 11);
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y ^= (y << 7) & 0x9d2c5680u;
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y ^= (y << 15) & 0xefc60000u;
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y ^= (y >> 18);
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return y;
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}
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/// Returns a random number in the [0,1] real interval using the improved Marsenne-Twister.
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double generate01closed()
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{
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return generate()*(1.0/4294967295.0);
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}
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/// Returns a random number in the [0,1) real interval using the improved Marsenne-Twister.
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double generate01()
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{
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return generate()*(1.0/4294967296.0);
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}
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/// Generates a random number in the (0,1) real interval using the improved Marsenne-Twister.
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double generate01open()
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{
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return (((double)generate()) + 0.5)*(1.0/4294967296.0);
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}
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/// Generate a random triple of baricentric coords
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template <class PointType>
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void generateBarycentric(PointType &p){
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p[1] = this->generate01();
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p[2] = this->generate01();
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if(p[1] + p[2] > 1.0){
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p[1] = 1.0 - p[1];
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p[2] = 1.0 - p[2];
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}
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p[0]=1.0-(p[1] + p[2]);
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}
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}; // end class MarsenneTwisterRNG
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/* Returns a value with normal distribution with mean m, standard deviation s
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*
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* It implements the Polar form of the Box-Muller Transformation
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* A transformation which transforms from a two-dimensional continuous uniform distribution
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* to a two-dimensional bivariate normal distribution
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* with mean m, standard deviation s
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*/
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inline double box_muller(RandomGenerator &generator, double m, double s) /* normal random variate generator */
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{ /* */
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double x1, x2, w, y1;
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static double y2;
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static int use_last = 0;
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static RandomGenerator *last_generator = 0;
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if(last_generator != &generator)
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use_last = 0;
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last_generator = &generator;
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if (use_last){ /* use value from previous call */
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y1 = y2;
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use_last = 0;
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} else {
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do {
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x1 = 2.0 * generator.generate01closed() - 1.0;
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x2 = 2.0 * generator.generate01closed() - 1.0;
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w = x1 * x1 + x2 * x2;
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} while ( w >= 1.0 );
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w = sqrt( (-2.0 * log( w ) ) / w );
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y1 = x1 * w;
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y2 = x2 * w;
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use_last = 1;
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}
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return( m + y1 * s );
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}
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} // end namespace math
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} // end namespace vcg
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/*
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Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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1. Redistributions of source code must retain the above copyright
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notice, this list of conditions and the following disclaimer.
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2. Redistributions in binary form must reproduce the above copyright
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notice, this list of conditions and the following disclaimer in the
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documentation and/or other materials provided with the distribution.
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3. The names of its contributors may not be used to endorse or promote
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products derived from this software without specific prior written
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permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
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CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
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LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
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NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#endif /* __VCG_RandomGenerator */
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