mirror of
https://github.com/Relintai/pandemonium_engine_minimal.git
synced 2024-12-21 16:56:50 +01:00
260 lines
7.1 KiB
C++
260 lines
7.1 KiB
C++
/* -----------------------------------------------------------------------------
|
|
|
|
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 "simd.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];
|
|
}
|
|
if( total > FLT_EPSILON )
|
|
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;
|
|
}
|
|
|
|
#if 0
|
|
|
|
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 );
|
|
}
|
|
}
|
|
|
|
#else
|
|
|
|
#define POWER_ITERATION_COUNT 8
|
|
|
|
Vec3 ComputePrincipleComponent( Sym3x3 const& matrix )
|
|
{
|
|
Vec4 const row0( matrix[0], matrix[1], matrix[2], 0.0f );
|
|
Vec4 const row1( matrix[1], matrix[3], matrix[4], 0.0f );
|
|
Vec4 const row2( matrix[2], matrix[4], matrix[5], 0.0f );
|
|
Vec4 v = VEC4_CONST( 1.0f );
|
|
for( int i = 0; i < POWER_ITERATION_COUNT; ++i )
|
|
{
|
|
// matrix multiply
|
|
Vec4 w = row0*v.SplatX();
|
|
w = MultiplyAdd(row1, v.SplatY(), w);
|
|
w = MultiplyAdd(row2, v.SplatZ(), w);
|
|
|
|
// get max component from xyz in all channels
|
|
Vec4 a = Max(w.SplatX(), Max(w.SplatY(), w.SplatZ()));
|
|
|
|
// divide through and advance
|
|
v = w*Reciprocal(a);
|
|
}
|
|
return v.GetVec3();
|
|
}
|
|
|
|
#endif
|
|
|
|
} // namespace squish
|