392 lines
14 KiB
C++
392 lines
14 KiB
C++
/* -----------------------------------------------------------------------------
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Copyright (c) 2006 Simon Brown si@sjbrown.co.uk
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Copyright (c) 2007 Ignacio Castano icastano@nvidia.com
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Permission is hereby granted, free of charge, to any person obtaining
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a copy of this software and associated documentation files (the
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"Software"), to deal in the Software without restriction, including
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without limitation the rights to use, copy, modify, merge, publish,
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distribute, sublicense, and/or sell copies of the Software, and to
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permit persons to whom the Software is furnished to do so, subject to
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the following conditions:
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The above copyright notice and this permission notice shall be included
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in all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
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IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
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CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
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TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
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SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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-------------------------------------------------------------------------- */
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#include "clusterfit.h"
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#include "colourset.h"
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#include "colourblock.h"
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#include <cfloat>
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namespace squish {
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ClusterFit::ClusterFit( ColourSet const* colours, int flags, float* metric )
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: ColourFit( colours, flags )
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{
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// set the iteration count
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m_iterationCount = ( m_flags & kColourIterativeClusterFit ) ? kMaxIterations : 1;
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// initialise the metric (old perceptual = 0.2126f, 0.7152f, 0.0722f)
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if( metric )
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m_metric = Vec4( metric[0], metric[1], metric[2], 1.0f );
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else
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m_metric = VEC4_CONST( 1.0f );
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// initialise the best error
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m_besterror = VEC4_CONST( FLT_MAX );
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// cache some values
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int const count = m_colours->GetCount();
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Vec3 const* values = m_colours->GetPoints();
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// get the covariance matrix
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Sym3x3 covariance = ComputeWeightedCovariance( count, values, m_colours->GetWeights() );
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// compute the principle component
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m_principle = ComputePrincipleComponent( covariance );
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}
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bool ClusterFit::ConstructOrdering( Vec3 const& axis, int iteration )
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{
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// cache some values
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int const count = m_colours->GetCount();
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Vec3 const* values = m_colours->GetPoints();
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// build the list of dot products
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float dps[16];
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u8* order = ( u8* )m_order + 16*iteration;
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for( int i = 0; i < count; ++i )
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{
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dps[i] = Dot( values[i], axis );
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order[i] = ( u8 )i;
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}
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// stable sort using them
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for( int i = 0; i < count; ++i )
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{
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for( int j = i; j > 0 && dps[j] < dps[j - 1]; --j )
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{
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std::swap( dps[j], dps[j - 1] );
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std::swap( order[j], order[j - 1] );
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}
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}
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// check this ordering is unique
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for( int it = 0; it < iteration; ++it )
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{
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u8 const* prev = ( u8* )m_order + 16*it;
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bool same = true;
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for( int i = 0; i < count; ++i )
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{
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if( order[i] != prev[i] )
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{
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same = false;
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break;
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}
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}
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if( same )
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return false;
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}
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// copy the ordering and weight all the points
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Vec3 const* unweighted = m_colours->GetPoints();
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float const* weights = m_colours->GetWeights();
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m_xsum_wsum = VEC4_CONST( 0.0f );
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for( int i = 0; i < count; ++i )
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{
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int j = order[i];
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Vec4 p( unweighted[j].X(), unweighted[j].Y(), unweighted[j].Z(), 1.0f );
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Vec4 w( weights[j] );
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Vec4 x = p*w;
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m_points_weights[i] = x;
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m_xsum_wsum += x;
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}
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return true;
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}
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void ClusterFit::Compress3( void* block )
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{
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// declare variables
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int const count = m_colours->GetCount();
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Vec4 const two = VEC4_CONST( 2.0 );
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Vec4 const one = VEC4_CONST( 1.0f );
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Vec4 const half_half2( 0.5f, 0.5f, 0.5f, 0.25f );
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Vec4 const zero = VEC4_CONST( 0.0f );
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Vec4 const half = VEC4_CONST( 0.5f );
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Vec4 const grid( 31.0f, 63.0f, 31.0f, 0.0f );
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Vec4 const gridrcp( 1.0f/31.0f, 1.0f/63.0f, 1.0f/31.0f, 0.0f );
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// prepare an ordering using the principle axis
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ConstructOrdering( m_principle, 0 );
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// check all possible clusters and iterate on the total order
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Vec4 beststart = VEC4_CONST( 0.0f );
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Vec4 bestend = VEC4_CONST( 0.0f );
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Vec4 besterror = m_besterror;
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u8 bestindices[16];
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int bestiteration = 0;
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int besti = 0, bestj = 0;
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// loop over iterations (we avoid the case that all points in first or last cluster)
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for( int iterationIndex = 0;; )
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{
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// first cluster [0,i) is at the start
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Vec4 part0 = VEC4_CONST( 0.0f );
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for( int i = 0; i < count; ++i )
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{
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// second cluster [i,j) is half along
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Vec4 part1 = ( i == 0 ) ? m_points_weights[0] : VEC4_CONST( 0.0f );
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int jmin = ( i == 0 ) ? 1 : i;
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for( int j = jmin;; )
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{
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// last cluster [j,count) is at the end
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Vec4 part2 = m_xsum_wsum - part1 - part0;
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// compute least squares terms directly
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Vec4 alphax_sum = MultiplyAdd( part1, half_half2, part0 );
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Vec4 alpha2_sum = alphax_sum.SplatW();
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Vec4 betax_sum = MultiplyAdd( part1, half_half2, part2 );
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Vec4 beta2_sum = betax_sum.SplatW();
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Vec4 alphabeta_sum = ( part1*half_half2 ).SplatW();
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// compute the least-squares optimal points
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Vec4 factor = Reciprocal( NegativeMultiplySubtract( alphabeta_sum, alphabeta_sum, alpha2_sum*beta2_sum ) );
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Vec4 a = NegativeMultiplySubtract( betax_sum, alphabeta_sum, alphax_sum*beta2_sum )*factor;
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Vec4 b = NegativeMultiplySubtract( alphax_sum, alphabeta_sum, betax_sum*alpha2_sum )*factor;
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// clamp to the grid
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a = Min( one, Max( zero, a ) );
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b = Min( one, Max( zero, b ) );
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a = Truncate( MultiplyAdd( grid, a, half ) )*gridrcp;
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b = Truncate( MultiplyAdd( grid, b, half ) )*gridrcp;
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// compute the error (we skip the constant xxsum)
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Vec4 e1 = MultiplyAdd( a*a, alpha2_sum, b*b*beta2_sum );
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Vec4 e2 = NegativeMultiplySubtract( a, alphax_sum, a*b*alphabeta_sum );
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Vec4 e3 = NegativeMultiplySubtract( b, betax_sum, e2 );
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Vec4 e4 = MultiplyAdd( two, e3, e1 );
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// apply the metric to the error term
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Vec4 e5 = e4*m_metric;
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Vec4 error = e5.SplatX() + e5.SplatY() + e5.SplatZ();
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// keep the solution if it wins
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if( CompareAnyLessThan( error, besterror ) )
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{
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beststart = a;
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bestend = b;
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besti = i;
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bestj = j;
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besterror = error;
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bestiteration = iterationIndex;
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}
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// advance
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if( j == count )
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break;
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part1 += m_points_weights[j];
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++j;
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}
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// advance
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part0 += m_points_weights[i];
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}
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// stop if we didn't improve in this iteration
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if( bestiteration != iterationIndex )
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break;
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// advance if possible
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++iterationIndex;
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if( iterationIndex == m_iterationCount )
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break;
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// stop if a new iteration is an ordering that has already been tried
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Vec3 axis = ( bestend - beststart ).GetVec3();
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if( !ConstructOrdering( axis, iterationIndex ) )
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break;
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}
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// save the block if necessary
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if( CompareAnyLessThan( besterror, m_besterror ) )
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{
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// remap the indices
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u8 const* order = ( u8* )m_order + 16*bestiteration;
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u8 unordered[16];
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for( int m = 0; m < besti; ++m )
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unordered[order[m]] = 0;
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for( int m = besti; m < bestj; ++m )
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unordered[order[m]] = 2;
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for( int m = bestj; m < count; ++m )
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unordered[order[m]] = 1;
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m_colours->RemapIndices( unordered, bestindices );
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// save the block
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WriteColourBlock3( beststart.GetVec3(), bestend.GetVec3(), bestindices, block );
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// save the error
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m_besterror = besterror;
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}
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}
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void ClusterFit::Compress4( void* block )
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{
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// declare variables
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int const count = m_colours->GetCount();
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Vec4 const two = VEC4_CONST( 2.0f );
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Vec4 const one = VEC4_CONST( 1.0f );
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Vec4 const onethird_onethird2( 1.0f/3.0f, 1.0f/3.0f, 1.0f/3.0f, 1.0f/9.0f );
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Vec4 const twothirds_twothirds2( 2.0f/3.0f, 2.0f/3.0f, 2.0f/3.0f, 4.0f/9.0f );
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Vec4 const twonineths = VEC4_CONST( 2.0f/9.0f );
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Vec4 const zero = VEC4_CONST( 0.0f );
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Vec4 const half = VEC4_CONST( 0.5f );
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Vec4 const grid( 31.0f, 63.0f, 31.0f, 0.0f );
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Vec4 const gridrcp( 1.0f/31.0f, 1.0f/63.0f, 1.0f/31.0f, 0.0f );
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// prepare an ordering using the principle axis
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ConstructOrdering( m_principle, 0 );
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// check all possible clusters and iterate on the total order
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Vec4 beststart = VEC4_CONST( 0.0f );
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Vec4 bestend = VEC4_CONST( 0.0f );
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Vec4 besterror = m_besterror;
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u8 bestindices[16];
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int bestiteration = 0;
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int besti = 0, bestj = 0, bestk = 0;
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// loop over iterations (we avoid the case that all points in first or last cluster)
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for( int iterationIndex = 0;; )
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{
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// first cluster [0,i) is at the start
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Vec4 part0 = VEC4_CONST( 0.0f );
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for( int i = 0; i < count; ++i )
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{
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// second cluster [i,j) is one third along
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Vec4 part1 = VEC4_CONST( 0.0f );
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for( int j = i;; )
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{
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// third cluster [j,k) is two thirds along
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Vec4 part2 = ( j == 0 ) ? m_points_weights[0] : VEC4_CONST( 0.0f );
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int kmin = ( j == 0 ) ? 1 : j;
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for( int k = kmin;; )
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{
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// last cluster [k,count) is at the end
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Vec4 part3 = m_xsum_wsum - part2 - part1 - part0;
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// compute least squares terms directly
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Vec4 const alphax_sum = MultiplyAdd( part2, onethird_onethird2, MultiplyAdd( part1, twothirds_twothirds2, part0 ) );
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Vec4 const alpha2_sum = alphax_sum.SplatW();
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Vec4 const betax_sum = MultiplyAdd( part1, onethird_onethird2, MultiplyAdd( part2, twothirds_twothirds2, part3 ) );
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Vec4 const beta2_sum = betax_sum.SplatW();
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Vec4 const alphabeta_sum = twonineths*( part1 + part2 ).SplatW();
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// compute the least-squares optimal points
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Vec4 factor = Reciprocal( NegativeMultiplySubtract( alphabeta_sum, alphabeta_sum, alpha2_sum*beta2_sum ) );
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Vec4 a = NegativeMultiplySubtract( betax_sum, alphabeta_sum, alphax_sum*beta2_sum )*factor;
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Vec4 b = NegativeMultiplySubtract( alphax_sum, alphabeta_sum, betax_sum*alpha2_sum )*factor;
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// clamp to the grid
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a = Min( one, Max( zero, a ) );
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b = Min( one, Max( zero, b ) );
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a = Truncate( MultiplyAdd( grid, a, half ) )*gridrcp;
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b = Truncate( MultiplyAdd( grid, b, half ) )*gridrcp;
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// compute the error (we skip the constant xxsum)
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Vec4 e1 = MultiplyAdd( a*a, alpha2_sum, b*b*beta2_sum );
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Vec4 e2 = NegativeMultiplySubtract( a, alphax_sum, a*b*alphabeta_sum );
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Vec4 e3 = NegativeMultiplySubtract( b, betax_sum, e2 );
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Vec4 e4 = MultiplyAdd( two, e3, e1 );
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// apply the metric to the error term
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Vec4 e5 = e4*m_metric;
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Vec4 error = e5.SplatX() + e5.SplatY() + e5.SplatZ();
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// keep the solution if it wins
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if( CompareAnyLessThan( error, besterror ) )
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{
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beststart = a;
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bestend = b;
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besterror = error;
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besti = i;
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bestj = j;
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bestk = k;
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bestiteration = iterationIndex;
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}
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// advance
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if( k == count )
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break;
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part2 += m_points_weights[k];
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++k;
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}
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// advance
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if( j == count )
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break;
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part1 += m_points_weights[j];
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++j;
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}
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// advance
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part0 += m_points_weights[i];
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}
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// stop if we didn't improve in this iteration
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if( bestiteration != iterationIndex )
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break;
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// advance if possible
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++iterationIndex;
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if( iterationIndex == m_iterationCount )
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break;
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// stop if a new iteration is an ordering that has already been tried
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Vec3 axis = ( bestend - beststart ).GetVec3();
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if( !ConstructOrdering( axis, iterationIndex ) )
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break;
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}
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// save the block if necessary
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if( CompareAnyLessThan( besterror, m_besterror ) )
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{
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// remap the indices
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u8 const* order = ( u8* )m_order + 16*bestiteration;
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u8 unordered[16];
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for( int m = 0; m < besti; ++m )
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unordered[order[m]] = 0;
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for( int m = besti; m < bestj; ++m )
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unordered[order[m]] = 2;
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for( int m = bestj; m < bestk; ++m )
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unordered[order[m]] = 3;
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for( int m = bestk; m < count; ++m )
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unordered[order[m]] = 1;
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m_colours->RemapIndices( unordered, bestindices );
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// save the block
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WriteColourBlock4( beststart.GetVec3(), bestend.GetVec3(), bestindices, block );
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// save the error
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m_besterror = besterror;
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}
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}
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} // namespace squish
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