Revision 39b13612ebd645a65eda854771b517371f2f858a authored by ennetws on 13 March 2015, 18:17:18 UTC, committed by ennetws on 13 March 2015, 18:17:18 UTC
1 parent c702819
BSplineData.inl
/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
Redistributions of source code must retain the above copyright notice, this list of
conditions and the following disclaimer. Redistributions in binary form must reproduce
the above copyright notice, this list of conditions and the following disclaimer
in the documentation and/or other materials provided with the distribution.
Neither the name of the Johns Hopkins University nor the names of its contributors
may be used to endorse or promote products derived from this software without specific
prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO THE IMPLIED WARRANTIES
OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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*/
/////////////////
// BSplineData //
/////////////////
// Support[i]:
// Odd: i +/- 0.5 * ( 1 + Degree )
// i - 0.5 * ( 1 + Degree ) < 0
// <=> i < 0.5 * ( 1 + Degree )
// i + 0.5 * ( 1 + Degree ) > 0
// <=> i > - 0.5 * ( 1 + Degree )
// i + 0.5 * ( 1 + Degree ) > r
// <=> i > r - 0.5 * ( 1 + Degree )
// i - 0.5 * ( 1 + Degree ) < r
// <=> i < r + 0.5 * ( 1 + Degree )
// Even: i + 0.5 +/- 0.5 * ( 1 + Degree )
// i - 0.5 * Degree < 0
// <=> i < 0.5 * Degree
// i + 1 + 0.5 * Degree > 0
// <=> i > -1 - 0.5 * Degree
// i + 1 + 0.5 * Degree > r
// <=> i > r - 1 - 0.5 * Degree
// i - 0.5 * Degree < r
// <=> i < r + 0.5 * Degree
template< int Degree > inline bool LeftOverlap( unsigned int depth , int offset )
{
offset <<= 1;
if( Degree & 1 ) return (offset < 1+Degree) && (offset > -1-Degree );
else return (offset < Degree) && (offset > -2-Degree );
}
template< int Degree > inline bool RightOverlap( unsigned int depth , int offset )
{
offset <<= 1;
int r = 1<<(depth+1);
if( Degree & 1 ) return (offset > 2-1-Degree) && (offset < 2+1+Degree );
else return (offset > 2-2-Degree) && (offset < 2+ Degree );
}
template< int Degree > inline int ReflectLeft( unsigned int depth , int offset )
{
if( Degree&1 ) return -offset;
else return -1-offset;
}
template< int Degree > inline int ReflectRight( unsigned int depth , int offset )
{
int r = 1<<(depth+1);
if( Degree&1 ) return r -offset;
else return r-1-offset;
}
template< int Degree , class Real >
BSplineData<Degree,Real>::BSplineData( void )
{
vvDotTable = dvDotTable = ddDotTable = NullPointer< Real >();
valueTables = dValueTables = NullPointer< Real >();
functionCount = sampleCount = 0;
SetBSplineElementIntegrals< Degree , Degree >( _vvIntegrals );
SetBSplineElementIntegrals< Degree , Degree-1 >( _vdIntegrals );
SetBSplineElementIntegrals< Degree-1 , Degree >( _dvIntegrals );
SetBSplineElementIntegrals< Degree-1 , Degree-1 >( _ddIntegrals );
_cc_vv_Integrals = _cc_dv_Integrals = _cc_vd_Integrals = _cc_dd_Integrals = NullPointer< _CCIntegrals >();
_cp_vv_Integrals = _cp_dv_Integrals = _cp_vd_Integrals = _cp_dd_Integrals = NullPointer< _CPIntegrals >();
}
template< int Degree , class Real >
BSplineData< Degree , Real >::~BSplineData(void)
{
if( functionCount )
{
if( vvDotTable ) DeletePointer( vvDotTable );
if( dvDotTable ) DeletePointer( dvDotTable );
if( ddDotTable ) DeletePointer( ddDotTable );
if( valueTables ) DeletePointer( valueTables );
if( dValueTables ) DeletePointer( dValueTables );
}
functionCount = 0;
}
template< int Degree , class Real >
double BSplineData< Degree , Real >::Integrator::dot( int depth , int off1 , int off2 , bool d1 , bool d2 , bool childParent ) const
{
if( depth<0 || depth>=int( iTables.size() ) ) return 0.;
const typename Integrator::IntegralTables& iTable = iTables[depth];
if( childParent )
{
int c = off1&1;
off1 >>= 1 , depth--;
int ii , d = off2-off1 , res = (1<<depth);
if( depth<0 || off1<0 || off2<0 || off1>=res || off2>=res || d<-Degree || d>Degree ) return 0;
if ( off1< Degree ) ii = off1;
else if( off1>=res-Degree ) ii = 2*Degree + off1 - (res-1);
else ii = Degree;
if ( d1 && d2 ) return iTable.dd_cpIntegrals[2*ii+c][d+Degree];
else if( d1 ) return iTable.dv_cpIntegrals[2*ii+c][d+Degree];
else if( d2 ) return iTable.vd_cpIntegrals[2*ii+c][d+Degree];
else return iTable.vv_cpIntegrals[2*ii+c][d+Degree];
}
else
{
int ii , d = off2-off1 , res = (1<<depth);
if( off1<0 || off2<0 || off1>=res || off2>=res || d<-Degree || d>Degree ) return 0;
if ( off1< Degree ) ii = off1;
else if( off1>=res-Degree ) ii = 2*Degree + off1 - (res-1);
else ii = Degree;
if ( d1 && d2 ) return iTable.dd_ccIntegrals[ii][d+Degree];
else if( d1 ) return iTable.dv_ccIntegrals[ii][d+Degree];
else if( d2 ) return iTable.vd_ccIntegrals[ii][d+Degree];
else return iTable.vv_ccIntegrals[ii][d+Degree];
}
}
template< int Degree , class Real >
template< int Radius >
double BSplineData< Degree , Real >::CenterEvaluator< Radius >::value( int depth , int off1 , int off2 , bool d , bool childParent ) const
{
if( depth<0 || depth>=int(vTables.size()) ) return 0.;
if( childParent )
{
int c = off1&1;
off1 >>= 1 , depth--;
const typename CenterEvaluator::ValueTables& vTable = vTables[depth];
int ii , dd = off1-off2 , res = (1<<depth);
if( depth<0 || off1<0 || off2<0 || off1>=res || off2>=res || dd<-Radius || dd>Radius ) return 0;
if ( off2< Degree ) ii = off2;
else if( off2>=res-Degree ) ii = 2*Degree + off2 - (res-1);
else ii = Degree;
if( d ) return vTable.dValues[ii][(dd+Radius)*3+2*c];
else return vTable.vValues[ii][(dd+Radius)*3+2*c];
}
else
{
const typename CenterEvaluator::ValueTables& vTable = vTables[depth];
int ii , dd = off1-off2 , res = (1<<depth);
if( off1<0 || off2<0 || off1>=res || off2>=res || dd<-Radius || dd>Radius ) return 0;
if ( off2< Degree ) ii = off2;
else if( off2>=res-Degree ) ii = 2*Degree + off2 - (res-1);
else ii = Degree;
if( d ) return vTable.dValues[ii][(dd+Radius)*3+1];
else return vTable.vValues[ii][(dd+Radius)*3+1];
}
}
template< int Degree , class Real >
template< int Radius >
double BSplineData< Degree , Real >::CornerEvaluator< Radius >::value( int depth , int off1 , int c1 , int off2 , bool d , bool childParent ) const
{
if( c1<0 || c1>=2 )
{
fprintf( stderr , "[WARNING] Clamping corner to {0,1}\n" );
c1 = std::max< int >( 0 , std::min< int >( c1 , 1 ) );
}
if( depth<0 || depth>=int( vTables.size() ) ) return 0.;
if( childParent )
{
int c = off1&1;
off1 >>= 1 , depth--;
const typename CornerEvaluator::ValueTables& vTable = vTables[depth];
int ii , dd = off1-off2 , res = (1<<depth);
if( depth<0 || off1<0 || off2<0 || off1>=res || off2>=res || dd<-Radius || dd>Radius ) return 0;
if ( off2< Degree ) ii = off2;
else if( off2>=res-Degree ) ii = 2*Degree + off2 - (res-1);
else ii = Degree;
if( d ) return vTable.dValues[ii][(dd+Radius)*2+c+c1];
else return vTable.vValues[ii][(dd+Radius)*2+c+c1];
}
else
{
const typename CornerEvaluator::ValueTables& vTable = vTables[depth];
int ii , dd = off1-off2 , res = (1<<depth);
if( off1<0 || off2<0 || off1>=res || off2>=res || dd<-Radius || dd>Radius ) return 0;
if ( off2< Degree ) ii = off2;
else if( off2>=res-Degree ) ii = 2*Degree + off2 - (res-1);
else ii = Degree;
if( d ) return vTable.dValues[ii][(dd+Radius)*2+2*c1];
else return vTable.vValues[ii][(dd+Radius)*2+2*c1];
}
}
template< int Degree , class Real >
void BSplineData<Degree,Real>::set( int maxDepth , bool useDotRatios , int boundaryType )
{
_useDotRatios = useDotRatios;
_boundaryType = boundaryType;
depth = maxDepth;
// [Warning] This assumes that the functions spacing is dual
functionCount = BinaryNode< double >::CumulativeCenterCount( depth );
sampleCount = BinaryNode< double >::CenterCount( depth ) + BinaryNode< double >::CornerCount( depth );
baseFunctions = NewPointer< PPolynomial< Degree > >( functionCount );
baseBSplines = NewPointer< BSplineComponents >( functionCount );
baseFunction = PPolynomial< Degree >::BSpline();
for( int i=0 ; i<=Degree ; i++ ) baseBSpline[i] = Polynomial< Degree >::BSplineComponent( i ).shift( double(-(Degree+1)/2) + i - 0.5 );
dBaseFunction = baseFunction.derivative();
StartingPolynomial< Degree > sPolys[Degree+4];
for( int i=0 ; i<Degree+3 ; i++ )
{
sPolys[i].start = double(-(Degree+1)/2) + i - 1.5;
sPolys[i].p *= 0;
if( i<=Degree ) sPolys[i].p += baseBSpline[i ].shift( -1 ) * _boundaryType;
if( i>=1 && i<=Degree+1 ) sPolys[i].p += baseBSpline[i-1];
for( int j=0 ; j<i ; j++ ) sPolys[i].p -= sPolys[j].p;
}
leftBaseFunction.set( sPolys , Degree+3 );
for( int i=0 ; i<Degree+3 ; i++ )
{
sPolys[i].start = double(-(Degree+1)/2) + i - 0.5;
sPolys[i].p *= 0;
if( i<=Degree ) sPolys[i].p += baseBSpline[i ];
if( i>=1 && i<=Degree+1 ) sPolys[i].p += baseBSpline[i-1].shift( 1 ) * _boundaryType;
for( int j=0 ; j<i ; j++ ) sPolys[i].p -= sPolys[j].p;
}
rightBaseFunction.set( sPolys , Degree+3 );
for( int i=0 ; i<Degree+4 ; i++ )
{
sPolys[i].start = double(-(Degree+1)/2) + i - 1.5;
sPolys[i].p *= 0;
if( i<=Degree ) sPolys[i].p += baseBSpline[i ].shift( -1 ) * _boundaryType; // The left-shifted B-spline
if( i>=1 && i<=Degree+1 ) sPolys[i].p += baseBSpline[i-1]; // The centered B-Spline
if( i>=2 && i<=Degree+2 ) sPolys[i].p += baseBSpline[i-2].shift( 1 ) * _boundaryType; // The right-shifted B-spline
for( int j=0 ; j<i ; j++ ) sPolys[i].p -= sPolys[j].p;
}
leftRightBaseFunction.set( sPolys , Degree+4 );
dLeftBaseFunction = leftBaseFunction.derivative();
dRightBaseFunction = rightBaseFunction.derivative();
dLeftRightBaseFunction = leftRightBaseFunction.derivative();
leftRightBSpline = leftBSpline = rightBSpline = baseBSpline;
leftBSpline [1] += leftBSpline[2].shift( -1 ) , leftBSpline[0] *= 0;
rightBSpline[1] += rightBSpline[0].shift( 1 ) , rightBSpline[2] *= 0;
leftRightBSpline[1] += leftRightBSpline[2].shift( -1 ) + leftRightBSpline[0].shift( 1 ) , leftRightBSpline[0] *= 0 , leftRightBSpline[2] *= 0 ;
double c , w;
for( size_t i=0 ; i<functionCount ; i++ )
{
BinaryNode< double >::CenterAndWidth( int(i) , c , w );
baseFunctions[i] = baseFunction.scale(w).shift(c);
baseBSplines[i] = baseBSpline.scale(w).shift(c);
if( _boundaryType )
{
int d , off , r;
BinaryNode< double >::DepthAndOffset( int(i) , d , off );
r = 1<<d;
if ( off==0 && off==r-1 ) baseFunctions[i] = leftRightBaseFunction.scale(w).shift(c);
else if( off==0 ) baseFunctions[i] = leftBaseFunction.scale(w).shift(c);
else if( off==r-1 ) baseFunctions[i] = rightBaseFunction.scale(w).shift(c);
if ( off==0 && off==r-1 ) baseBSplines [i] = leftRightBSpline.scale(w).shift(c);
else if( off==0 ) baseBSplines [i] = leftBSpline.scale(w).shift(c);
else if( off==r-1 ) baseBSplines [i] = rightBSpline.scale(w).shift(c);
}
}
}
template< int Degree , class Real >
template< bool D1 , bool D2 >
double BSplineData< Degree , Real >::_dot( int depth1 , int off1 , int depth2 , int off2 , bool inset ) const
{
const int _Degree1 = (D1 ? (Degree-1) : Degree) , _Degree2 = (D2 ? (Degree-1) : Degree);
int sums[ _Degree1+1 ][ _Degree2+1 ];
int depth = std::max< int >( depth1 , depth2 );
BSplineElements< Degree > b1( 1<<depth1 , off1 , _boundaryType , inset ? ( 1<<(depth1-2) ) : 0 ) , b2( 1<<depth2 , off2 , _boundaryType , inset ? ( 1<<(depth2-2) ) : 0 );
BSplineElements< Degree > b;
while( depth1<depth ) b=b1 , b.upSample( b1 ) , depth1++;
while( depth2<depth ) b=b2 , b.upSample( b2 ) , depth2++;
BSplineElements< Degree-1 > db1 , db2;
b1.differentiate( db1 ) , b2.differentiate( db2 );
int start1=-1 , end1=-1 , start2=-1 , end2=-1;
for( int i=0 ; i<int( b1.size() ) ; i++ ) for( int j=0 ; j<=Degree ; j++ )
{
if( b1[i][j] && start1==-1 ) start1 = i;
if( b1[i][j] ) end1 = i+1;
if( b2[i][j] && start2==-1 ) start2 = i;
if( b2[i][j] ) end2 = i+1;
}
if( start1==end1 || start2==end2 || start1>=end2 || start2>=end1 ) return Real(0);
int start = std::max< int >( start1 , start2 ) , end = std::min< int >( end1 , end2 );
memset( sums , 0 , sizeof( sums ) );
for( int i=start ; i<end ; i++ ) for( int j=0 ; j<=_Degree1 ; j++ ) for( int k=0 ; k<=_Degree2 ; k++ ) sums[j][k] += ( D1 ? db1[i][j] : b1[i][j] ) * ( D2 ? db2[i][k] : b2[i][k] );
double _dot = 0;
if ( D1 && D2 ) for( int j=0 ; j<=_Degree1 ; j++ ) for( int k=0 ; k<=_Degree2 ; k++ ) _dot += _ddIntegrals[j][k] * sums[j][k];
else if( D1 ) for( int j=0 ; j<=_Degree1 ; j++ ) for( int k=0 ; k<=_Degree2 ; k++ ) _dot += _dvIntegrals[j][k] * sums[j][k];
else if( D2 ) for( int j=0 ; j<=_Degree1 ; j++ ) for( int k=0 ; k<=_Degree2 ; k++ ) _dot += _vdIntegrals[j][k] * sums[j][k];
else for( int j=0 ; j<=_Degree1 ; j++ ) for( int k=0 ; k<=_Degree2 ; k++ ) _dot += _vvIntegrals[j][k] * sums[j][k];
_dot /= b1.denominator;
_dot /= b2.denominator;
if ( D1 && D2 ) return _dot * (1<<depth);
else if( D1 || D2 ) return _dot;
else return _dot / (1<<depth);
}
template< int Degree , class Real >
double BSplineData< Degree , Real >::value( int depth , int off , double smoothingRadius , double s , bool d , bool inset ) const
{
inset = inset;
PPolynomial< Degree+1 > function;
PPolynomial< Degree > dFunction;
if( off<0 || off>=(1<<depth) ) return 0;
int idx = BinaryNode< Real >::CenterIndex( depth , off );
if( smoothingRadius>0 ) function = baseFunctions[idx].MovingAverage( smoothingRadius );
else function = baseFunctions[idx];
dFunction = function.derivative();
if( d ) return dFunction(s);
else return function(s);
}
template< int Degree , class Real >
void BSplineData< Degree , Real >::setIntegrator( Integrator& integrator , bool inset ) const
{
integrator.iTables.resize( depth+1 );
for( int d=0 ; d<=depth ; d++ ) for( int i=0 ; i<=2*Degree ; i++ ) for( int j=-Degree ; j<=Degree ; j++ )
{
int res = 1<<d , ii = (i<=Degree ? i : i+res-1 - 2*Degree );
integrator.iTables[d].vv_ccIntegrals[i][j+Degree] = _dot< false , false >( d , ii , d , ii+j , inset );
integrator.iTables[d].dv_ccIntegrals[i][j+Degree] = _dot< true , false >( d , ii , d , ii+j , inset );
integrator.iTables[d].vd_ccIntegrals[i][j+Degree] = _dot< false , true >( d , ii , d , ii+j , inset );
integrator.iTables[d].dd_ccIntegrals[i][j+Degree] = _dot< true , true >( d , ii , d , ii+j , inset );
}
for( int d=1 ; d<=depth ; d++ ) for( int i=0 ; i<=2*Degree ; i++ ) for( int j=-Degree ; j<=Degree ; j++ )
{
int res = 1<<d , ii = (i<=Degree ? i : i+(res/2)-1 - 2*Degree );
for( int c=0 ; c<2 ; c++ )
{
integrator.iTables[d].vv_cpIntegrals[2*i+c][j+Degree] = _dot< false , false >( d , 2*ii+c , d-1 , ii+j , inset );
integrator.iTables[d].dv_cpIntegrals[2*i+c][j+Degree] = _dot< true , false >( d , 2*ii+c , d-1 , ii+j , inset );
integrator.iTables[d].vd_cpIntegrals[2*i+c][j+Degree] = _dot< false , true >( d , 2*ii+c , d-1 , ii+j , inset );
integrator.iTables[d].dd_cpIntegrals[2*i+c][j+Degree] = _dot< true , true >( d , 2*ii+c , d-1 , ii+j , inset );
}
}
}
template< int Degree , class Real >
template< int Radius >
void BSplineData< Degree , Real >::setCenterEvaluator( CenterEvaluator< Radius >& evaluator , double smoothingRadius , double dSmoothingRadius , bool inset ) const
{
evaluator.vTables.resize( depth+1 );
for( int d=0 ; d<=depth ; d++ ) for( int i=0 ; i<=2*Degree ; i++ ) for( int j=-Radius ; j<=Radius ; j++ ) for( int k=-1 ; k<=1 ; k++ )
{
int res = 1<<d , ii = (i<=Degree ? i : i+res-1 - 2*Degree );
double s = 0.5+ii+j+0.25*k;
evaluator.vTables[d].vValues[i][(j+Radius)*3+(k+1)] = value( d , ii , smoothingRadius , s/res , false , inset );
evaluator.vTables[d].dValues[i][(j+Radius)*3+(k+1)] = value( d , ii , dSmoothingRadius , s/res , true , inset );
}
}
template< int Degree , class Real >
template< int Radius >
void BSplineData< Degree , Real >::setCornerEvaluator( CornerEvaluator< Radius >& evaluator , double smoothingRadius , double dSmoothingRadius , bool inset ) const
{
evaluator.vTables.resize( depth+1 );
for( int d=0 ; d<=depth ; d++ ) for( int i=0 ; i<=2*Degree ; i++ ) for( int j=-Radius ; j<=Radius ; j++ ) for( int k=0 ; k<=2 ; k++ )
{
int res = 1<<d , ii = (i<=Degree ? i : i+res-1 - 2*Degree );
double s = ii+j+0.5*k;
evaluator.vTables[d].vValues[i][(j+Radius)*2+k] = value( d , ii , smoothingRadius , s/res , false , inset );
evaluator.vTables[d].dValues[i][(j+Radius)*2+k] = value( d , ii , dSmoothingRadius , s/res , true , inset );
}
}
template<int Degree,class Real>
void BSplineData< Degree , Real >::setDotTables( int flags , bool full , bool inset )
{
clearDotTables( flags );
_cc_vv_Integrals = NewPointer< _CCIntegrals >( depth+1 );
_cc_dv_Integrals = NewPointer< _CCIntegrals >( depth+1 );
_cc_vd_Integrals = NewPointer< _CCIntegrals >( depth+1 );
_cc_dd_Integrals = NewPointer< _CCIntegrals >( depth+1 );
_cp_vv_Integrals = NewPointer< _CPIntegrals >( depth+1 );
_cp_dv_Integrals = NewPointer< _CPIntegrals >( depth+1 );
_cp_vd_Integrals = NewPointer< _CPIntegrals >( depth+1 );
_cp_dd_Integrals = NewPointer< _CPIntegrals >( depth+1 );
for( int d=0 ; d<=depth ; d++ ) for( int i=0 ; i<=2*Degree ; i++ ) for( int j=-Degree ; j<=Degree ; j++ )
{
int res = 1<<d , ii = (i<=Degree ? i : i+res-1 - 2*Degree );
_cc_vv_Integrals[d].integrals[i][j+Degree] = _dot< false , false >( d , ii , d , ii+j , inset );
_cc_dv_Integrals[d].integrals[i][j+Degree] = _dot< true , false >( d , ii , d , ii+j , inset );
_cc_vd_Integrals[d].integrals[i][j+Degree] = _dot< false , true >( d , ii , d , ii+j , inset );
_cc_dd_Integrals[d].integrals[i][j+Degree] = _dot< true , true >( d , ii , d , ii+j , inset );
}
for( int d=1 ; d<=depth ; d++ ) for( int i=0 ; i<=2*Degree ; i++ ) for( int j=-Degree ; j<=Degree ; j++ )
{
int res = 1<<d , ii = (i<=Degree ? i : i+(res/2)-1 - 2*Degree );
for( int c=0 ; c<2 ; c++ )
{
_cp_vv_Integrals[d].integrals[2*i+c][j+Degree] = _dot< false , false >( d , 2*ii+c , d-1 , ii+j , inset );
_cp_dv_Integrals[d].integrals[2*i+c][j+Degree] = _dot< true , false >( d , 2*ii+c , d-1 , ii+j , inset );
_cp_vd_Integrals[d].integrals[2*i+c][j+Degree] = _dot< false , true >( d , 2*ii+c , d-1 , ii+j , inset );
_cp_dd_Integrals[d].integrals[2*i+c][j+Degree] = _dot< true , true >( d , 2*ii+c , d-1 , ii+j , inset );
}
}
if( full )
{
size_t size = ( functionCount*functionCount + functionCount )>>1;
size_t fullSize = functionCount*functionCount;
if( flags & VV_DOT_FLAG )
{
vvDotTable = NewPointer< Real >( size );
memset( vvDotTable , 0 , sizeof(Real)*size );
}
if( flags & DV_DOT_FLAG )
{
dvDotTable = NewPointer< Real >( fullSize );
memset( dvDotTable , 0 , sizeof(Real)*fullSize );
}
if( flags & DD_DOT_FLAG )
{
ddDotTable = NewPointer< Real >( size );
memset( ddDotTable , 0 , sizeof(Real)*size );
}
double vvIntegrals[Degree+1][Degree+1];
double vdIntegrals[Degree+1][Degree ];
double dvIntegrals[Degree ][Degree+1];
double ddIntegrals[Degree ][Degree ];
int vvSums[Degree+1][Degree+1];
int vdSums[Degree+1][Degree ];
int dvSums[Degree ][Degree+1];
int ddSums[Degree ][Degree ];
SetBSplineElementIntegrals< Degree , Degree >( vvIntegrals );
SetBSplineElementIntegrals< Degree , Degree-1 >( vdIntegrals );
SetBSplineElementIntegrals< Degree-1 , Degree >( dvIntegrals );
SetBSplineElementIntegrals< Degree-1 , Degree-1 >( ddIntegrals );
for( int d1=0 ; d1<=depth ; d1++ )
for( int off1=0 ; off1<(1<<d1) ; off1++ )
{
int ii = BinaryNode< Real >::CenterIndex( d1 , off1 );
BSplineElements< Degree > b1( 1<<d1 , off1 , _boundaryType , inset ? ( 1<<(d1-2) ) : 0 );
BSplineElements< Degree-1 > db1;
b1.differentiate( db1 );
int start1 , end1;
start1 = -1 , end1 = -1;
for( int i=0 ; i<int(b1.size()) ; i++ ) for( int j=0 ; j<=Degree ; j++ )
{
if( b1[i][j] && start1==-1 ) start1 = i;
if( b1[i][j] ) end1 = i+1;
}
if( start1==end1 ) continue;
for( int d2=d1 ; d2<=depth ; d2++ )
{
for( int off2=0 ; off2<(1<<d2) ; off2++ )
{
int start2 = off2-Degree;
int end2 = off2+Degree+1;
if( start2>=end1 || start1>=end2 ) continue;
start2 = std::max< int >( start1 , start2 );
end2 = std::min< int >( end1 , end2 );
if( d1==d2 && off2<off1 ) continue;
int jj = BinaryNode< Real >::CenterIndex( d2 , off2 );
BSplineElements< Degree > b2( 1<<d2 , off2 , _boundaryType , inset ? ( 1<<(d2-2) ) : 0 );
BSplineElements< Degree-1 > db2;
b2.differentiate( db2 );
size_t idx = SymmetricIndex( ii , jj );
size_t idx1 = Index( ii , jj ) , idx2 = Index( jj , ii );
memset( vvSums , 0 , sizeof( int ) * ( Degree+1 ) * ( Degree+1 ) );
memset( vdSums , 0 , sizeof( int ) * ( Degree+1 ) * ( Degree ) );
memset( dvSums , 0 , sizeof( int ) * ( Degree ) * ( Degree+1 ) );
memset( ddSums , 0 , sizeof( int ) * ( Degree ) * ( Degree ) );
for( int i=start2 ; i<end2 ; i++ )
{
for( int j=0 ; j<=Degree ; j++ ) for( int k=0 ; k<=Degree ; k++ ) vvSums[j][k] += b1[i][j] * b2[i][k];
for( int j=0 ; j<=Degree ; j++ ) for( int k=0 ; k< Degree ; k++ ) vdSums[j][k] += b1[i][j] * db2[i][k];
for( int j=0 ; j< Degree ; j++ ) for( int k=0 ; k<=Degree ; k++ ) dvSums[j][k] += db1[i][j] * b2[i][k];
for( int j=0 ; j< Degree ; j++ ) for( int k=0 ; k< Degree ; k++ ) ddSums[j][k] += db1[i][j] * db2[i][k];
}
double vvDot = 0 , dvDot = 0 , vdDot = 0 , ddDot = 0;
for( int j=0 ; j<=Degree ; j++ ) for( int k=0 ; k<=Degree ; k++ ) vvDot += vvIntegrals[j][k] * vvSums[j][k];
for( int j=0 ; j<=Degree ; j++ ) for( int k=0 ; k< Degree ; k++ ) vdDot += vdIntegrals[j][k] * vdSums[j][k];
for( int j=0 ; j< Degree ; j++ ) for( int k=0 ; k<=Degree ; k++ ) dvDot += dvIntegrals[j][k] * dvSums[j][k];
for( int j=0 ; j< Degree ; j++ ) for( int k=0 ; k< Degree ; k++ ) ddDot += ddIntegrals[j][k] * ddSums[j][k];
vvDot /= (1<<d2);
ddDot *= (1<<d2);
vvDot /= ( b1.denominator * b2.denominator );
dvDot /= ( b1.denominator * b2.denominator );
vdDot /= ( b1.denominator * b2.denominator );
ddDot /= ( b1.denominator * b2.denominator );
if( fabs(vvDot)<1e-15 ) continue;
if( flags & VV_DOT_FLAG ) vvDotTable [idx] = Real( vvDot );
if( _useDotRatios )
{
if( flags & DV_DOT_FLAG ) dvDotTable[idx1] = Real( dvDot / vvDot );
if( flags & DV_DOT_FLAG ) dvDotTable[idx2] = Real( vdDot / vvDot );
if( flags & DD_DOT_FLAG ) ddDotTable[idx ] = Real( ddDot / vvDot );
}
else
{
if( flags & DV_DOT_FLAG ) dvDotTable[idx1] = Real( dvDot );
if( flags & DV_DOT_FLAG ) dvDotTable[idx2] = Real( dvDot );
if( flags & DD_DOT_FLAG ) ddDotTable[idx ] = Real( ddDot );
}
}
BSplineElements< Degree > b;
b = b1;
b.upSample( b1 );
b1.differentiate( db1 );
start1 = -1;
for( int i=0 ; i<int(b1.size()) ; i++ ) for( int j=0 ; j<=Degree ; j++ )
{
if( b1[i][j] && start1==-1 ) start1 = i;
if( b1[i][j] ) end1 = i+1;
}
}
}
}
}
template<int Degree,class Real>
void BSplineData<Degree,Real>::clearDotTables( int flags )
{
if( (flags & VV_DOT_FLAG) && vvDotTable ) DeletePointer( vvDotTable );
if( (flags & DV_DOT_FLAG) && dvDotTable ) DeletePointer( dvDotTable );
if( (flags & DD_DOT_FLAG) && ddDotTable ) DeletePointer( ddDotTable );
if( _cc_vv_Integrals ) DeletePointer( _cc_vv_Integrals );
if( _cc_vd_Integrals ) DeletePointer( _cc_vd_Integrals );
if( _cc_dv_Integrals ) DeletePointer( _cc_dv_Integrals );
if( _cc_dd_Integrals ) DeletePointer( _cc_dd_Integrals );
if( _cp_vv_Integrals ) DeletePointer( _cp_vv_Integrals );
if( _cp_vd_Integrals ) DeletePointer( _cp_vd_Integrals );
if( _cp_dv_Integrals ) DeletePointer( _cp_dv_Integrals );
if( _cp_dd_Integrals ) DeletePointer( _cp_dd_Integrals );
}
template< int Degree , class Real >
void BSplineData< Degree , Real >::setSampleSpan( int idx , int& start , int& end , double smooth ) const
{
int d , off , res;
BinaryNode< double >::DepthAndOffset( idx , d , off );
res = 1<<d;
double _start = ( off + 0.5 - 0.5*(Degree+1) ) / res - smooth;
double _end = ( off + 0.5 + 0.5*(Degree+1) ) / res + smooth;
// (start)/(sampleCount-1) >_start && (start-1)/(sampleCount-1)<=_start
// => start > _start * (sampleCount-1 ) && start <= _start*(sampleCount-1) + 1
// => _start * (sampleCount-1) + 1 >= start > _start * (sampleCount-1)
start = int( floor( _start * (sampleCount-1) + 1 ) );
if( start<0 ) start = 0;
// (end)/(sampleCount-1)<_end && (end+1)/(sampleCount-1)>=_end
// => end < _end * (sampleCount-1 ) && end >= _end*(sampleCount-1) - 1
// => _end * (sampleCount-1) > end >= _end * (sampleCount-1) - 1
end = int( ceil( _end * (sampleCount-1) - 1 ) );
if( end>=int(sampleCount) ) end = int(sampleCount)-1;
}
template<int Degree,class Real>
void BSplineData<Degree,Real>::setValueTables( int flags , double smooth )
{
clearValueTables();
if( flags & VALUE_FLAG ) valueTables = NewPointer< Real >( functionCount*sampleCount );
if( flags & D_VALUE_FLAG ) dValueTables = NewPointer< Real >( functionCount*sampleCount );
PPolynomial<Degree+1> function;
PPolynomial<Degree> dFunction;
for( size_t i=0 ; i<functionCount ; i++ )
{
if(smooth>0)
{
function = baseFunctions[i].MovingAverage(smooth);
dFunction = baseFunctions[i].derivative().MovingAverage(smooth);
}
else
{
function = baseFunctions[i];
dFunction = baseFunctions[i].derivative();
}
for( size_t j=0 ; j<sampleCount ; j++ )
{
double x=double(j)/(sampleCount-1);
if( flags & VALUE_FLAG ) valueTables[j*functionCount+i] = Real( function(x) );
if( flags & D_VALUE_FLAG ) dValueTables[j*functionCount+i] = Real( dFunction(x) );
}
}
}
template<int Degree,class Real>
void BSplineData<Degree,Real>::setValueTables( int flags , double valueSmooth , double derivativeSmooth )
{
clearValueTables();
if(flags & VALUE_FLAG) valueTables = NewPointer< Real >( functionCount*sampleCount );
if(flags & D_VALUE_FLAG) dValueTables = NewPointer< Real >( functionCount*sampleCount );
PPolynomial<Degree+1> function;
PPolynomial<Degree> dFunction;
for( size_t i=0 ; i<functionCount ; i++ )
{
if( valueSmooth>0 ) function=baseFunctions[i].MovingAverage( valueSmooth );
else function=baseFunctions[i];
if( derivativeSmooth>0 ) dFunction=baseFunctions[i].derivative().MovingAverage( derivativeSmooth );
else dFunction=baseFunctions[i].derivative();
for( size_t j=0 ; j<sampleCount ; j++ )
{
double x=double(j)/(sampleCount-1);
if( flags & VALUE_FLAG ) valueTables[j*functionCount+i] = Real( function(x));
if( flags & D_VALUE_FLAG ) dValueTables[j*functionCount+i] = Real(dFunction(x));
}
}
}
template<int Degree,class Real>
void BSplineData<Degree,Real>::clearValueTables(void){
if( valueTables ) DeletePointer( valueTables );
if( dValueTables ) DeletePointer( dValueTables );
}
template< int Degree , class Real >
inline size_t BSplineData< Degree , Real >::Index( int i1 , int i2 ) const { return size_t(i1)*functionCount + size_t(i2); }
template< int Degree , class Real >
inline size_t BSplineData<Degree,Real>::SymmetricIndex( int i1 , int i2 )
{
size_t _i1 = i1 , _i2 = i2;
if( i1>i2 ) return ((_i1*_i1+i1)>>1)+_i2;
else return ((_i2*_i2+i2)>>1)+_i1;
}
template< int Degree , class Real >
inline int BSplineData< Degree , Real >::SymmetricIndex( int i1 , int i2 , size_t& index )
{
size_t _i1 = i1 , _i2 = i2;
if( i1<i2 )
{
index = ((_i2*_i2+_i2)>>1)+_i1;
return 1;
}
else
{
index = ((_i1*_i1+_i1)>>1)+_i2;
return 0;
}
}
/////////////////////
// BSplineElements //
/////////////////////
template< int Degree >
BSplineElements< Degree >::BSplineElements( int res , int offset , int boundary , int inset )
{
denominator = 1;
resize( res , BSplineElementCoefficients< Degree >() );
for( int i=0 ; i<=Degree ; i++ )
{
int idx = -_off + offset + i;
if( idx>=0 && idx<res ) (*this)[idx][i] = 1;
}
if( boundary!=0 )
{
_addLeft( offset-2*res , boundary ) , _addRight( offset+2*res , boundary );
if( Degree&1 ) _addLeft( offset-res , boundary ) , _addRight( offset+res , boundary );
else _addLeft( -offset-1 , boundary ) , _addRight( -offset-1+2*res , boundary );
}
if( inset ) for( int i=0 ; i<inset && i<res ; i++ ) for( int j=0 ; j<=Degree ; j++ ) (*this)[i][j] = (*this)[res-1-i][j] = 0;
}
template< int Degree >
void BSplineElements< Degree >::_addLeft( int offset , int boundary )
{
int res = int( this->size() );
bool set = false;
for( int i=0 ; i<=Degree ; i++ )
{
int idx = -_off + offset + i;
if( idx>=0 && idx<res ) (*this)[idx][i] += boundary , set = true;
}
if( set ) _addLeft( offset-2*res , boundary );
}
template< int Degree >
void BSplineElements< Degree >::_addRight( int offset , int boundary )
{
int res = int( this->size() );
bool set = false;
for( int i=0 ; i<=Degree ; i++ )
{
int idx = -_off + offset + i;
if( idx>=0 && idx<res ) (*this)[idx][i] += boundary , set = true;
}
if( set ) _addRight( offset+2*res , boundary );
}
template< int Degree >
void BSplineElements< Degree >::upSample( BSplineElements< Degree >& high ) const
{
fprintf( stderr , "[ERROR] B-spline up-sampling not supported for degree %d\n" , Degree );
exit( 0 );
}
template<>
void BSplineElements< 1 >::upSample( BSplineElements< 1 >& high ) const
{
high.resize( size()*2 );
high.assign( high.size() , BSplineElementCoefficients<1>() );
for( int i=0 ; i<int(size()) ; i++ )
{
high[2*i+0][0] += 1 * (*this)[i][0];
high[2*i+0][1] += 0 * (*this)[i][0];
high[2*i+1][0] += 2 * (*this)[i][0];
high[2*i+1][1] += 1 * (*this)[i][0];
high[2*i+0][0] += 1 * (*this)[i][1];
high[2*i+0][1] += 2 * (*this)[i][1];
high[2*i+1][0] += 0 * (*this)[i][1];
high[2*i+1][1] += 1 * (*this)[i][1];
}
high.denominator = denominator * 2;
}
template<>
void BSplineElements< 2 >::upSample( BSplineElements< 2 >& high ) const
{
// /----\
// / \
// / \ = 1 /--\ +3 /--\ +3 /--\ +1 /--\
// / \ / \ / \ / \ / \
// |----------| |----------| |----------| |----------| |----------|
high.resize( size()*2 );
high.assign( high.size() , BSplineElementCoefficients<2>() );
for( int i=0 ; i<int(size()) ; i++ )
{
high[2*i+0][0] += 1 * (*this)[i][0];
high[2*i+0][1] += 0 * (*this)[i][0];
high[2*i+0][2] += 0 * (*this)[i][0];
high[2*i+1][0] += 3 * (*this)[i][0];
high[2*i+1][1] += 1 * (*this)[i][0];
high[2*i+1][2] += 0 * (*this)[i][0];
high[2*i+0][0] += 3 * (*this)[i][1];
high[2*i+0][1] += 3 * (*this)[i][1];
high[2*i+0][2] += 1 * (*this)[i][1];
high[2*i+1][0] += 1 * (*this)[i][1];
high[2*i+1][1] += 3 * (*this)[i][1];
high[2*i+1][2] += 3 * (*this)[i][1];
high[2*i+0][0] += 0 * (*this)[i][2];
high[2*i+0][1] += 1 * (*this)[i][2];
high[2*i+0][2] += 3 * (*this)[i][2];
high[2*i+1][0] += 0 * (*this)[i][2];
high[2*i+1][1] += 0 * (*this)[i][2];
high[2*i+1][2] += 1 * (*this)[i][2];
}
high.denominator = denominator * 4;
}
template< int Degree >
void BSplineElements< Degree >::differentiate( BSplineElements< Degree-1 >& d ) const
{
d.resize( this->size() );
d.assign( d.size() , BSplineElementCoefficients< Degree-1 >() );
for( int i=0 ; i<int(this->size()) ; i++ ) for( int j=0 ; j<=Degree ; j++ )
{
if( j-1>=0 ) d[i][j-1] -= (*this)[i][j];
if( j<Degree ) d[i][j ] += (*this)[i][j];
}
d.denominator = denominator;
}
// If we were really good, we would implement this integral table to store
// rational values to improve precision...
template< int Degree1 , int Degree2 >
void SetBSplineElementIntegrals( double integrals[Degree1+1][Degree2+1] )
{
for( int i=0 ; i<=Degree1 ; i++ )
{
Polynomial< Degree1 > p1 = Polynomial< Degree1 >::BSplineComponent( i );
for( int j=0 ; j<=Degree2 ; j++ )
{
Polynomial< Degree2 > p2 = Polynomial< Degree2 >::BSplineComponent( j );
integrals[i][j] = ( p1 * p2 ).integral( 0 , 1 );
}
}
}
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