First release
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/****************************************************************************
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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) 2006 \/)\/ *
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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 __VCGLIB_SPHERICAL_HARMONICS_H
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#define __VCGLIB_SPHERICAL_HARMONICS_H
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#include "vcg/math/base.h"
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#include "vcg/math/legendre.h"
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#include "vcg/math/factorial.h"
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namespace vcg{
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namespace math{
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/**
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* Although the Real Spherical Harmonic Function is correctly defined over any
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* positive l and any -l <= m <= l, the two internal functions computing the
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* imaginary and real parts of the Complex Spherical Harmonic Functions are defined
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* for positive m only.
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*/
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template <typename ScalarType>
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class SphericalHarmonics{
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private :
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inline static ScalarType scaling_factor(unsigned l, unsigned m)
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{
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return Sqrt( ( (2.0*l + 1.0) * Factorial<ScalarType>(l-m) ) / (4.0 * M_PI * Factorial<ScalarType>(l + m)) );;
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}
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inline static ScalarType complex_spherical_harmonic_re(unsigned l, unsigned m, ScalarType theta, ScalarType phi)
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{
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return scaling_factor(l, m) * Legendre<ScalarType>::AssociatedPolynomial(l, m, Cos(theta), Sin(theta)) * Cos(m * phi);
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}
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inline static ScalarType complex_spherical_harmonic_im(unsigned l, unsigned m, ScalarType theta, ScalarType phi)
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{
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return scaling_factor(l, m) * Legendre<ScalarType>::AssociatedPolynomial(l, m, Cos(theta), Sin(theta)) * Sin(m * phi);
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}
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ScalarType * coefficients;
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int max_band;
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public :
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/**
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* Returns the Real Spherical Harmonic Function
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*
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* l is any positive integer,
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* m is such that -l <= m <= l
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* theta is inside [0, PI]
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* phi is inside [0, 2*PI]
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*/
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static ScalarType Real(unsigned l, int m, ScalarType theta, ScalarType phi)
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{
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assert((int)-l <= m && m <= (int)l && theta >= 0 && theta <= M_PI && phi >= 0 && phi <= 2 * M_PI);
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if (m > 0) return SQRT_TWO * complex_spherical_harmonic_re(l, m, theta, phi);
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else if (m == 0) return scaling_factor(l, 0) * Legendre<ScalarType>::Polynomial(l, Cos(theta));
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else return SQRT_TWO * complex_spherical_harmonic_im(l, -m, theta, phi);
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}
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typedef ScalarType (*PolarFunction) (ScalarType theta, ScalarType phi);
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static SphericalHarmonics Project(PolarFunction fun, unsigned max_band, unsigned n_samples)
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{
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const ScalarType weight = 4 * M_PI;
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unsigned sqrt_n_samples = (unsigned int) Sqrt((int)n_samples);
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unsigned actual_n_samples = sqrt_n_samples * sqrt_n_samples;
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unsigned n_coeff = max_band * max_band;
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ScalarType one_over_n = 1.0/(ScalarType)sqrt_n_samples;
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RandomGenerator rand;
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SphericalHarmonics sph;
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sph.coefficients = new ScalarType[n_coeff];
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sph.max_band = max_band;
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int i = 0;
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for (unsigned k = 0; k < n_coeff; k++ ) sph.coefficients[k] = 0;
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for (unsigned a = 0; a < sqrt_n_samples; ++a )
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{
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for (unsigned b = 0; b < sqrt_n_samples; ++b)
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{
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ScalarType x = (a + rand(INT_MAX)/(ScalarType)INT_MAX) * one_over_n;
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ScalarType y = (b + rand(INT_MAX)/(ScalarType)INT_MAX) * one_over_n;
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ScalarType theta = 2.0 * Acos(Sqrt(1.0 - x));
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ScalarType phi = 2.0 * M_PI * y;
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for (int l = 0; l < (int)max_band; ++l)
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{
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for (int m = -l; m <= l; ++m)
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{
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int index = l * (l+1) + m;
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sph.coefficients[index] += fun(theta, phi) * Real(l, m, theta, phi);
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}
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}
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i++;
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}
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}
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ScalarType factor = weight / actual_n_samples;
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for(i = 0; i < (int)n_coeff; ++i)
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{
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sph.coefficients[i] *= factor;
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}
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return sph;
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}
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ScalarType operator()(ScalarType theta, ScalarType phi)
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{
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ScalarType f = 0;
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for (int l = 0; l < max_band; ++l)
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{
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for (int m = -l; m <= l; ++m)
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{
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int index = l * (l+1) + m;
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f += (coefficients[index] * Real(l, m, theta, phi));
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}
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}
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return f;
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}
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};
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}} //namespace vcg::math
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#endif
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