saberbud/PoissonRecon
1
0
Fork 0
mirror of https://github.com/CloudCompare/PoissonRecon.git synced 2026-08-29 16:40:28 +08:00
Code Issues Packages Projects Releases Wiki Activity
Files
2e9c3fc6faa611780eeaf29fc80252bf80b54a65
PoissonRecon/Src/BSplineData.inl
T
mkazhdan d59a521763 Version 7.0 
Added support for color extrapolation from the input.
Bug fix with SAMPLE_SCALE use.
2015-07-20 17:39:00 -04:00

734 lines
30 KiB
C++
Raw Blame History

/*
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,
INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
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
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
DAMAGE.
*/
/////////////////
// 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 >
BSplineData< Degree >::BSplineData( void )
{
functionCount = sampleCount = 0;
SetBSplineElementIntegrals< Degree , Degree >( _vvIntegrals );
SetBSplineElementIntegrals< Degree , Degree-1 >( _vdIntegrals );
SetBSplineElementIntegrals< Degree-1 , Degree >( _dvIntegrals );
SetBSplineElementIntegrals< Degree-1 , Degree-1 >( _ddIntegrals );
}
template< int Degree >
double BSplineData< Degree >::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 >
template< int Radius >
double BSplineData< Degree >::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 >
template< int Radius >
double BSplineData< Degree >::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 >
void BSplineData< Degree >::set( int maxDepth , int boundaryType )
{
_boundaryType = boundaryType>0 ? 1 : ( boundaryType<0 ? -1 : 0 );
depth = maxDepth;
// [Warning] This assumes that the functions spacing is dual
functionCount = BinaryNode::CumulativeCenterCount( depth );
sampleCount = BinaryNode::CenterCount( depth ) + BinaryNode::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::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::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 >
double BSplineData< Degree >::dot( int depth1 , int off1 , int depth2 , int off2 , bool d1 , bool d2 , bool inset ) const
{
const int _Degree1 = (d1 ? (Degree-1) : Degree) , _Degree2 = (d2 ? (Degree-1) : Degree);
int sums[ Degree+1 ][ Degree+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 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 >
double BSplineData< Degree >::value( int depth , int off , double smoothingRadius , double s , bool d , bool inset ) const
{
PPolynomial< Degree+1 > function;
PPolynomial< Degree > dFunction;
if( off<0 || off>=(1<<depth) ) return 0;
int idx = BinaryNode::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 >
void BSplineData< Degree >::setIntegrator( Integrator& integrator , bool inset , bool useDotRatios ) 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( d , ii , d , ii+j , false , false , inset );
integrator.iTables[d].dv_ccIntegrals[i][j+Degree] = dot( d , ii , d , ii+j , true , false , inset );
integrator.iTables[d].vd_ccIntegrals[i][j+Degree] = dot( d , ii , d , ii+j , false , true , inset );
integrator.iTables[d].dd_ccIntegrals[i][j+Degree] = dot( d , ii , d , ii+j , true , true , inset );
if( useDotRatios )
{
integrator.iTables[d].dv_ccIntegrals[i][j+Degree] /= integrator.iTables[d].vv_ccIntegrals[i][j+Degree];
integrator.iTables[d].vd_ccIntegrals[i][j+Degree] /= integrator.iTables[d].vv_ccIntegrals[i][j+Degree];
integrator.iTables[d].dd_ccIntegrals[i][j+Degree] /= integrator.iTables[d].vv_ccIntegrals[i][j+Degree];
}
}
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( d , 2*ii+c , d-1 , ii+j , false , false , inset );
integrator.iTables[d].dv_cpIntegrals[2*i+c][j+Degree] = dot( d , 2*ii+c , d-1 , ii+j , true , false , inset );
integrator.iTables[d].vd_cpIntegrals[2*i+c][j+Degree] = dot( d , 2*ii+c , d-1 , ii+j , false , true , inset );
integrator.iTables[d].dd_cpIntegrals[2*i+c][j+Degree] = dot( d , 2*ii+c , d-1 , ii+j , true , true , inset );
if( useDotRatios )
{
integrator.iTables[d].dv_cpIntegrals[2*i+c][j+Degree] /= integrator.iTables[d].vv_cpIntegrals[2*i+c][j+Degree];
integrator.iTables[d].vd_cpIntegrals[2*i+c][j+Degree] /= integrator.iTables[d].vv_cpIntegrals[2*i+c][j+Degree];
integrator.iTables[d].dd_cpIntegrals[2*i+c][j+Degree] /= integrator.iTables[d].vv_cpIntegrals[2*i+c][j+Degree];
}
}
}
}
template< int Degree >
template< int Radius >
void BSplineData< Degree >::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 >
template< int Radius >
void BSplineData< Degree >::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 >
template< class Real >
BSplineData< Degree >::DotTables< Real >::DotTables( void )
{
vvDotTable = NullPointer( Real );
dvDotTable = NullPointer( Real );
ddDotTable = NullPointer( Real );
}
template< int Degree >
template< class Real >
BSplineData< Degree >::DotTables< Real >::~DotTables( void )
{
DeletePointer( vvDotTable );
DeletePointer( dvDotTable );
DeletePointer( ddDotTable );
}
template< int Degree >
template< class Real >
inline size_t BSplineData< Degree >::DotTables< Real >::Index( int i1 , int i2 ) const { return size_t(i1)*functionCount + size_t(i2); }
template< int Degree >
template< class Real >
inline size_t BSplineData< Degree >::DotTables< 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 >
template< class Real >
inline int BSplineData< Degree >::DotTables< 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;
}
}
template< int Degree >
template< class Real >
typename BSplineData< Degree >::template DotTables< Real > BSplineData< Degree >::getDotTables( int flags , bool useDotRatios , bool inset ) const
{
typename BSplineData< Degree >::template DotTables< Real > dTables;
dTables.functionCount = functionCount;
size_t size = ( functionCount*functionCount + functionCount )>>1;
size_t fullSize = functionCount*functionCount;
if( flags & VV_DOT_FLAG )
{
dTables.vvDotTable = NewPointer< Real >( size );
memset( dTables.vvDotTable , 0 , sizeof(Real)*size );
}
if( flags & DV_DOT_FLAG )
{
dTables.dvDotTable = NewPointer< Real >( fullSize );
memset( dTables.dvDotTable , 0 , sizeof(Real)*fullSize );
}
if( flags & DD_DOT_FLAG )
{
dTables.ddDotTable = NewPointer< Real >( size );
memset( dTables.ddDotTable , 0 , sizeof(Real)*size );
}
int vvSums[Degree+1][Degree+1];
int vdSums[Degree+1][Degree ];
int dvSums[Degree ][Degree+1];
int ddSums[Degree ][Degree ];
double vvIntegrals[Degree+1][Degree+1];
double vdIntegrals[Degree+1][Degree ];
double dvIntegrals[Degree ][Degree+1];
double ddIntegrals[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::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::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 = DotTables< Real >::SymmetricIndex( ii , jj );
size_t idx1 = DotTables< Real >::Index( ii , jj ) , idx2 = DotTables< Real >::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 ) dTables.vvDotTable[idx] = Real( vvDot );
if( flags & DV_DOT_FLAG ) dTables.dvDotTable[idx1] = Real( dvDot );
if( flags & DV_DOT_FLAG ) dTables.dvDotTable[idx2] = Real( dvDot );
if( flags & DD_DOT_FLAG ) dTables.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;
}
}
}
return dTables;
}
template< int Degree >
template< class Real >
BSplineData< Degree >::ValueTables< Real >::ValueTables( void )
{
valueTable = NullPointer( Real );
dValueTable = NullPointer( Real );
}
template< int Degree >
template< class Real >
BSplineData< Degree >::ValueTables< Real >::~ValueTables( void )
{
DeletePointer( valueTable );
DeletePointer( dValueTable );
}
template< int Degree >
template< class Real >
inline size_t BSplineData< Degree >::ValueTables< Real >::Index( int i1 , int i2 ) const { return size_t(i1)*functionCount + size_t(i2); }
template< int Degree >
template< class Real >
typename BSplineData< Degree >::template ValueTables< Real > BSplineData< Degree >::getValueTables( int flags , double valueSmooth , double derivativeSmooth ) const
{
typename BSplineData< Degree >::template ValueTables< Real > vTables;
vTables.functionCount = functionCount;
vTables.sampleCount = sampleCount;
if( flags & VALUE_FLAG ) vTables.valueTable = NewPointer< Real >( functionCount*sampleCount );
if( flags & D_VALUE_FLAG ) vTables.dValueTable = 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 ) vTables.valueTable[j*functionCount+i] = Real( function(x));
if( flags & D_VALUE_FLAG ) vTables.dValueTable[j*functionCount+i] = Real(dFunction(x));
}
}
return vTables;
}
template< int Degree >
template< class Real >
void BSplineData< Degree >::ValueTables< Real >::setSampleSpan( int idx , int& start , int& end , double smooth ) const
{
int d , off , res;
BinaryNode::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;
}
/////////////////////
// BSplineElements //
/////////////////////
template< int Degree >
BSplineElements< Degree >::BSplineElements( int res , int offset , int boundary , int inset )
{
denominator = 1;
std::vector< BSplineElementCoefficients< Degree > >::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( std::vector< BSplineElementCoefficients< Degree > >::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( std::vector< BSplineElementCoefficients< Degree > >::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( std::vector< BSplineElementCoefficients< Degree > >::size() );
d.assign( d.size() , BSplineElementCoefficients< Degree-1 >() );
for( int i=0 ; i<int(std::vector< BSplineElementCoefficients< Degree > >::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 );
}
}
}
Reference in New Issue View Git Blame Copy Permalink