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Diffstat (limited to 'drivers/squish/maths.cpp')
-rw-r--r-- | drivers/squish/maths.cpp | 227 |
1 files changed, 0 insertions, 227 deletions
diff --git a/drivers/squish/maths.cpp b/drivers/squish/maths.cpp deleted file mode 100644 index 59818a4d2b..0000000000 --- a/drivers/squish/maths.cpp +++ /dev/null @@ -1,227 +0,0 @@ -/* ----------------------------------------------------------------------------- - - Copyright (c) 2006 Simon Brown si@sjbrown.co.uk - - Permission is hereby granted, free of charge, to any person obtaining - a copy of this software and associated documentation files (the - "Software"), to deal in the Software without restriction, including - without limitation the rights to use, copy, modify, merge, publish, - distribute, sublicense, and/or sell copies of the Software, and to - permit persons to whom the Software is furnished to do so, subject to - the following conditions: - - The above copyright notice and this permission notice shall be included - in all copies or substantial portions of the Software. - - THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS - OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF - MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. - IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY - CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, - TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE - SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. - - -------------------------------------------------------------------------- */ - -/*! @file - - The symmetric eigensystem solver algorithm is from - http://www.geometrictools.com/Documentation/EigenSymmetric3x3.pdf -*/ - -#include "maths.h" -#include <cfloat> - -namespace squish { - -Sym3x3 ComputeWeightedCovariance( int n, Vec3 const* points, float const* weights ) -{ - // compute the centroid - float total = 0.0f; - Vec3 centroid( 0.0f ); - for( int i = 0; i < n; ++i ) - { - total += weights[i]; - centroid += weights[i]*points[i]; - } - centroid /= total; - - // accumulate the covariance matrix - Sym3x3 covariance( 0.0f ); - for( int i = 0; i < n; ++i ) - { - Vec3 a = points[i] - centroid; - Vec3 b = weights[i]*a; - - covariance[0] += a.X()*b.X(); - covariance[1] += a.X()*b.Y(); - covariance[2] += a.X()*b.Z(); - covariance[3] += a.Y()*b.Y(); - covariance[4] += a.Y()*b.Z(); - covariance[5] += a.Z()*b.Z(); - } - - // return it - return covariance; -} - -static Vec3 GetMultiplicity1Evector( Sym3x3 const& matrix, float evalue ) -{ - // compute M - Sym3x3 m; - m[0] = matrix[0] - evalue; - m[1] = matrix[1]; - m[2] = matrix[2]; - m[3] = matrix[3] - evalue; - m[4] = matrix[4]; - m[5] = matrix[5] - evalue; - - // compute U - Sym3x3 u; - u[0] = m[3]*m[5] - m[4]*m[4]; - u[1] = m[2]*m[4] - m[1]*m[5]; - u[2] = m[1]*m[4] - m[2]*m[3]; - u[3] = m[0]*m[5] - m[2]*m[2]; - u[4] = m[1]*m[2] - m[4]*m[0]; - u[5] = m[0]*m[3] - m[1]*m[1]; - - // find the largest component - float mc = std::fabs( u[0] ); - int mi = 0; - for( int i = 1; i < 6; ++i ) - { - float c = std::fabs( u[i] ); - if( c > mc ) - { - mc = c; - mi = i; - } - } - - // pick the column with this component - switch( mi ) - { - case 0: - return Vec3( u[0], u[1], u[2] ); - - case 1: - case 3: - return Vec3( u[1], u[3], u[4] ); - - default: - return Vec3( u[2], u[4], u[5] ); - } -} - -static Vec3 GetMultiplicity2Evector( Sym3x3 const& matrix, float evalue ) -{ - // compute M - Sym3x3 m; - m[0] = matrix[0] - evalue; - m[1] = matrix[1]; - m[2] = matrix[2]; - m[3] = matrix[3] - evalue; - m[4] = matrix[4]; - m[5] = matrix[5] - evalue; - - // find the largest component - float mc = std::fabs( m[0] ); - int mi = 0; - for( int i = 1; i < 6; ++i ) - { - float c = std::fabs( m[i] ); - if( c > mc ) - { - mc = c; - mi = i; - } - } - - // pick the first eigenvector based on this index - switch( mi ) - { - case 0: - case 1: - return Vec3( -m[1], m[0], 0.0f ); - - case 2: - return Vec3( m[2], 0.0f, -m[0] ); - - case 3: - case 4: - return Vec3( 0.0f, -m[4], m[3] ); - - default: - return Vec3( 0.0f, -m[5], m[4] ); - } -} - -Vec3 ComputePrincipleComponent( Sym3x3 const& matrix ) -{ - // compute the cubic coefficients - float c0 = matrix[0]*matrix[3]*matrix[5] - + 2.0f*matrix[1]*matrix[2]*matrix[4] - - matrix[0]*matrix[4]*matrix[4] - - matrix[3]*matrix[2]*matrix[2] - - matrix[5]*matrix[1]*matrix[1]; - float c1 = matrix[0]*matrix[3] + matrix[0]*matrix[5] + matrix[3]*matrix[5] - - matrix[1]*matrix[1] - matrix[2]*matrix[2] - matrix[4]*matrix[4]; - float c2 = matrix[0] + matrix[3] + matrix[5]; - - // compute the quadratic coefficients - float a = c1 - ( 1.0f/3.0f )*c2*c2; - float b = ( -2.0f/27.0f )*c2*c2*c2 + ( 1.0f/3.0f )*c1*c2 - c0; - - // compute the root count check - float Q = 0.25f*b*b + ( 1.0f/27.0f )*a*a*a; - - // test the multiplicity - if( FLT_EPSILON < Q ) - { - // only one root, which implies we have a multiple of the identity - return Vec3( 1.0f ); - } - else if( Q < -FLT_EPSILON ) - { - // three distinct roots - float theta = std::atan2( std::sqrt( -Q ), -0.5f*b ); - float rho = std::sqrt( 0.25f*b*b - Q ); - - float rt = std::pow( rho, 1.0f/3.0f ); - float ct = std::cos( theta/3.0f ); - float st = std::sin( theta/3.0f ); - - float l1 = ( 1.0f/3.0f )*c2 + 2.0f*rt*ct; - float l2 = ( 1.0f/3.0f )*c2 - rt*( ct + ( float )sqrt( 3.0f )*st ); - float l3 = ( 1.0f/3.0f )*c2 - rt*( ct - ( float )sqrt( 3.0f )*st ); - - // pick the larger - if( std::fabs( l2 ) > std::fabs( l1 ) ) - l1 = l2; - if( std::fabs( l3 ) > std::fabs( l1 ) ) - l1 = l3; - - // get the eigenvector - return GetMultiplicity1Evector( matrix, l1 ); - } - else // if( -FLT_EPSILON <= Q && Q <= FLT_EPSILON ) - { - // two roots - float rt; - if( b < 0.0f ) - rt = -std::pow( -0.5f*b, 1.0f/3.0f ); - else - rt = std::pow( 0.5f*b, 1.0f/3.0f ); - - float l1 = ( 1.0f/3.0f )*c2 + rt; // repeated - float l2 = ( 1.0f/3.0f )*c2 - 2.0f*rt; - - // get the eigenvector - if( std::fabs( l1 ) > std::fabs( l2 ) ) - return GetMultiplicity2Evector( matrix, l1 ); - else - return GetMultiplicity1Evector( matrix, l2 ); - } -} - -} // namespace squish |