BSplineData.h

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/*
Copyright (c) 2006, Michael Kazhdan and Matthew Bolitho
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#ifndef BSPLINE_DATA_INCLUDED
#define BSPLINE_DATA_INCLUDED
 
#define NEW_BSPLINE_CODE 1
 
#include "BinaryNode.h"
#include "PPolynomial.h"
#include "Array.h"
 
// This class represents a function that is a linear combination of B-spline elements,
// with the coeff member indicating how much of each element is present.
// [WARNING] The ordering of B-spline elements is in the opposite order from that returned by Polynomial::BSplineComponent
template< int Degree >
struct BSplineElementCoefficients
{
    int coeffs[Degree+1];
    BSplineElementCoefficients( void ){ memset( coeffs , 0 , sizeof( int ) * ( Degree+1 ) ); }
    int& operator[]( int idx ){ return coeffs[idx]; }
    const int& operator[]( int idx ) const { return coeffs[idx]; }
};
 
// This class represents a function on the the interval, partitioned into "res" blocks.
// On each block, the function is a degree-Degree polynomial, represented by the coefficients
// in the associated BSplineElementCoefficients.
// [NOTE] This representation of a function is agnostic to the type of boundary conditions (though the constructor is not).
template< int Degree >
struct BSplineElements : public std::vector< BSplineElementCoefficients< Degree > >
{
    static const bool _Primal = (Degree&1)==1;
    static const int _Off = (Degree+1)/2;
    static int _ReflectLeft ( int offset , int res );
    static int _ReflectRight( int offset , int res );
    static int _RotateLeft  ( int offset , int res );
    static int _RotateRight ( int offset , int res );
    template< bool Left > void _addPeriodic( int offset , bool negate );
public:
    // Coefficients are ordered as "/" "-" "\"
    // [WARNING] This is the opposite of the order in Polynomial::BSplineComponent
    int denominator;
 
    BSplineElements( void ) { denominator = 1; }
    BSplineElements( int res , int offset , bool dirichlet );
 
    void upSample( BSplineElements& high ) const;
    void differentiate( BSplineElements< Degree-1 >& d ) const;
 
    void print( FILE* fp=stdout ) const
    {
        for( int i=0 ; i<std::vector< BSplineElementCoefficients< Degree > >::size() ; i++ )
        {
            printf( "%d]" , i );
            for( int j=0 ; j<=Degree ; j++ ) printf( " %d" , (*this)[i][j] );
            printf( " (%d)\n" , denominator );
        }
    }
};
#define BSPLINE_SET_BOUNDS( name , s , e ) \
    static const int name ## Start = (s); \
    static const int name ## End   = (e); \
    static const int name ## Size  = (e)-(s)+1
 
// Assumes that x is non-negative
#define _FLOOR_OF_HALF( x ) (   (x)    >>1 )
#define  _CEIL_OF_HALF( x ) ( ( (x)+1 )>>1 )
// Done with the assumption
#define FLOOR_OF_HALF( x ) ( (x)<0 ? -  _CEIL_OF_HALF( -(x) ) : _FLOOR_OF_HALF( x ) )
#define  CEIL_OF_HALF( x ) ( (x)<0 ? - _FLOOR_OF_HALF( -(x) ) :  _CEIL_OF_HALF( x ) )
#define SMALLEST_INTEGER_LARGER_THAN_HALF( x ) (  CEIL_OF_HALF( (x)+1 ) )
#define LARGEST_INTEGER_SMALLER_THAN_HALF( x ) ( FLOOR_OF_HALF( (x)-1 ) )
#define SMALLEST_INTEGER_LARGER_THAN_OR_EQUAL_TO_HALF( x ) (  CEIL_OF_HALF( x ) )
#define LARGEST_INTEGER_SMALLER_THAN_OR_EQUAL_TO_HALF( x ) ( FLOOR_OF_HALF( x ) )
 
template< int Degree >
class BSplineEvaluationData
{
public:
    BSplineEvaluationData( void );
    static double Value( int depth , int off , double s , bool dirichlet , bool derivative );
 
    static int Dimension( int depth ){ return ( 1<<depth ) + ( Degree&1 ); }
    // An index is interiorly supported if its support is in the range [0,1<<depth)
    inline static void InteriorSupportedSpan( int depth , int& begin , int& end ){ begin = -SupportStart , end = (1<<depth)-SupportEnd; }
 
    // If the degree is even, we use a dual basis and functions are centered at the center of the interval
    // It the degree is odd, we use a primal basis and functions are centered at the left end of the interval
    // The function at index I is supported in:
    //  Support( I ) = [ I - (Degree+1-Inset)/2 , I + (Degree+1+Inset)/2 ]
    // [NOTE] The value of ( Degree + 1 +/- Inset ) is always even
    static const int Inset = (Degree&1) ? 0 : 1;
    BSPLINE_SET_BOUNDS(      Support , -( (Degree+1)/2 ) , Degree/2           );
    BSPLINE_SET_BOUNDS( ChildSupport ,    2*SupportStart , 2*(SupportEnd+1)-1 );
    BSPLINE_SET_BOUNDS(       Corner ,    SupportStart+1 , SupportEnd         );
    BSPLINE_SET_BOUNDS(  ChildCorner ,  2*SupportStart+1 , 2*SupportEnd + 1   );
 
    // Setting I=0, we are looking for the smallest/largest integers J such that:
    //      Support( 0 ) CONTAINS Support( J )
    // <=>  [-(Degree+1-Inset) , (Degree+1+Inset) ] CONTAINS [ J-(Degree+1-Inset)/2 , J+(Degree+1+Inset)/2 ]
    // Which is the same as the smallest/largest integers J such that:
    //      J - (Degree+1-Inset)/2 >= -(Degree+1-Inset) | J + (Degree+1+Inset)/2 <= (Degree+1+Inset)
    // <=>  J >= -(Degree+1-Inset)/2                    | J <= (Degree+1+Inset)/2
    BSPLINE_SET_BOUNDS( UpSample , - ( Degree + 1 - Inset ) / 2 , ( Degree + 1 + Inset ) /2 );
 
    // Setting I=0/1, we are looking for the smallest/largest integers J such that:
    //      Support( J ) CONTAINS Support( 0/1 )
    // <=>  [ 2*J - (Degree+1-Inset) , 2*J + (Degree+1+Inset) ] CONTAINS [ 0/1 - (Degree+1-Inset)/2 , 0/1 + (Degree+1+Inset)/2 ]
    // Which is the same as the smallest/largest integers J such that:
    //      2*J + (Degree+1+Inset) >= 0/1 + (Degree+1+Inset)/2  | 2*J - (Degree+1-Inset) <= 0/1 - (Degree+1-Inset)/2
    // <=>  2*J >= 0/1 - (Degree+1+Inset)/2                     | 2*J <= 0/1 + (Degree+1-Inset)/2
    BSPLINE_SET_BOUNDS( DownSample0 , SMALLEST_INTEGER_LARGER_THAN_OR_EQUAL_TO_HALF( 0 - ( Degree + 1 + Inset ) / 2 ) , LARGEST_INTEGER_SMALLER_THAN_OR_EQUAL_TO_HALF( 0 + ( Degree + 1 - Inset ) / 2 ) );
    BSPLINE_SET_BOUNDS( DownSample1 , SMALLEST_INTEGER_LARGER_THAN_OR_EQUAL_TO_HALF( 1 - ( Degree + 1 + Inset ) / 2 ) , LARGEST_INTEGER_SMALLER_THAN_OR_EQUAL_TO_HALF( 1 + ( Degree + 1 - Inset ) / 2 ) );
    static const int DownSampleStart[] , DownSampleEnd[] , DownSampleSize[];
 
    // Note that this struct stores the components in left-to-right order
    struct BSplineComponents
    {
    protected:
        Polynomial< Degree > _polys[Degree+1];
    public:
        BSplineComponents( void ){ ; }
        BSplineComponents( int depth , int offset , bool dirichlet );
        const Polynomial< Degree >& operator[] ( int idx ) const { return _polys[idx]; }
        void printnl( void ) const { for( int d=0 ; d<=Degree ; d++ ) printf( "[%d] " , d ) , _polys[d].printnl(); }
    };
    struct BSplineUpSamplingCoefficients
    {
    protected:
        int _coefficients[ UpSampleSize ];
    public:
        BSplineUpSamplingCoefficients( void ){ ; }
        BSplineUpSamplingCoefficients( int depth , int offset , bool dirichlet );
        double operator[] ( int idx ){ return (double)_coefficients[idx] / (1<<Degree); }
    };
 
    struct CenterEvaluator
    {
        static const int Start = -SupportStart , Stop = SupportEnd , Size = Start + Stop + 1;
 
        static const int Index( int depth , int offset  )
        {
            int dim = BSplineEvaluationData< Degree >::Dimension( depth );
            if     ( offset<Start )     return offset;
            else if( offset>=dim-Stop ) return Start + 1 + offset - ( dim-Stop );
            else                        return Start;
        }
        struct Evaluator
        {
        protected:
            friend BSplineEvaluationData;
            int _depth;
            double _ccValues[2][Size][SupportSize];
        public:
            double value( int fIdx , int cIdx , bool d ) const;
            int depth( void ) const { return _depth; }
        };
        struct ChildEvaluator
        {
        protected:
            friend BSplineEvaluationData;
            int _parentDepth;
            double _pcValues[2][Size][ChildSupportSize];
        public:
            double value( int fIdx , int cIdx , bool d ) const;
            int parentDepth( void ) const { return _parentDepth; }
            int childDepth( void ) const { return _parentDepth+1; }
        };
    };
    static void SetCenterEvaluator( typename CenterEvaluator::Evaluator& evaluator , int depth , bool dirichlet );
    static void SetChildCenterEvaluator( typename CenterEvaluator::ChildEvaluator& evaluator , int parentDepth , bool dirichlet );
 
    struct CornerEvaluator
    {
        static const int Start = -SupportStart , Stop = SupportEnd , Size = Start + Stop + 1;
 
        static const int Index( int depth , int offset  )
        {
            int dim = BSplineEvaluationData< Degree >::Dimension( depth );
            if     ( offset<Start )     return offset;
            else if( offset>=dim-Stop ) return Start + 1 + offset - ( dim-Stop );
            else                        return Start;
        }
        struct Evaluator
        {
        protected:
            friend BSplineEvaluationData;
            int _depth;
            double _ccValues[2][Size][CornerSize];
        public:
            double value( int fIdx , int cIdx , bool d ) const;
            int depth( void ) const { return _depth; }
        };
        struct ChildEvaluator
        {
        protected:
            friend BSplineEvaluationData;
            int _parentDepth;
            double _pcValues[2][Size][ChildCornerSize];
        public:
            double value( int fIdx , int cIdx , bool d ) const;
            int parentDepth( void ) const { return _parentDepth; }
            int childDepth( void ) const { return _parentDepth+1; }
        };
    };
    static void SetCornerEvaluator( typename CornerEvaluator::Evaluator& evaluator , int depth , bool dirichlet );
    static void SetChildCornerEvaluator( typename CornerEvaluator::ChildEvaluator& evaluator , int parentDepth , bool dirichlet );
 
    struct Evaluator
    {
        typename CenterEvaluator::Evaluator centerEvaluator;
        typename CornerEvaluator::Evaluator cornerEvaluator;
        double centerValue( int fIdx , int cIdx , bool d ) const { return centerEvaluator.value( fIdx , cIdx , d ); }
        double cornerValue( int fIdx , int cIdx , bool d ) const { return cornerEvaluator.value( fIdx , cIdx , d ); }
    };
    static void SetEvaluator( Evaluator& evaluator , int depth , bool dirichlet ){ SetCenterEvaluator( evaluator.centerEvaluator , depth , dirichlet ) , SetCornerEvaluator( evaluator.cornerEvaluator , depth , dirichlet ); }
    struct ChildEvaluator
    {
        typename CenterEvaluator::ChildEvaluator centerEvaluator;
        typename CornerEvaluator::ChildEvaluator cornerEvaluator;
        double centerValue( int fIdx , int cIdx , bool d ) const { return centerEvaluator.value( fIdx , cIdx , d ); }
        double cornerValue( int fIdx , int cIdx , bool d ) const { return cornerEvaluator.value( fIdx , cIdx , d ); }
    };
    static void SetChildEvaluator( ChildEvaluator& evaluator , int depth , bool dirichlet ){ SetChildCenterEvaluator( evaluator.centerEvaluator , depth , dirichlet ) , SetChildCornerEvaluator( evaluator.cornerEvaluator , depth , dirichlet ); }
 
    struct UpSampleEvaluator
    {
        static const int Start = - SupportStart , Stop = SupportEnd , Size = Start + Stop + 1;
        static const int Index( int depth , int offset  )
        {
            int dim = BSplineEvaluationData< Degree >::Dimension( depth );
            if     ( offset<Start )     return offset;
            else if( offset>=dim-Stop ) return Start + 1 + offset - ( dim-Stop );
            else                        return Start;
        }
    protected:
        friend BSplineEvaluationData;
        int _lowDepth;
        double _pcValues[Size][UpSampleSize];
    public:
        double value( int pIdx , int cIdx ) const;
        int lowDepth( void ) const { return _lowDepth; }
    };
    static void SetUpSampleEvaluator( UpSampleEvaluator& evaluator , int lowDepth , bool dirichlet );
};
template< int Degree > const int BSplineEvaluationData< Degree >::DownSampleStart[] = { DownSample0Start , DownSample1Start };
template< int Degree > const int BSplineEvaluationData< Degree >::DownSampleEnd  [] = { DownSample0End   , DownSample1End   };
template< int Degree > const int BSplineEvaluationData< Degree >::DownSampleSize [] = { DownSample0Size  , DownSample1Size  };
 
template< int Degree1 , int Degree2 >
class BSplineIntegrationData
{
public:
    static double Dot( int depth1 , int off1 , bool dirichlet1 , bool d1 , int depth2 , int off2 , bool dirichlet2 , bool d2 );
    // An index is interiorly overlapped if the support of its overlapping neighbors is in the range [0,1<<depth)
    inline static void InteriorOverlappedSpan( int depth , int& begin , int& end ){ begin = -OverlapStart-BSplineEvaluationData< Degree2 >::SupportStart , end = (1<<depth)-OverlapEnd-BSplineEvaluationData< Degree2 >::SupportEnd; }
 
    typedef BSplineEvaluationData< Degree1 > EData1;
    typedef BSplineEvaluationData< Degree2 > EData2;
    BSPLINE_SET_BOUNDS(             Overlap , EData1::     SupportStart - EData2::SupportEnd , EData1::     SupportEnd - EData2::SupportStart );
    BSPLINE_SET_BOUNDS(        ChildOverlap , EData1::ChildSupportStart - EData2::SupportEnd , EData1::ChildSupportEnd - EData2::SupportStart );
    BSPLINE_SET_BOUNDS(      OverlapSupport ,      OverlapStart + EData2::SupportStart ,      OverlapEnd + EData2::SupportEnd );
    BSPLINE_SET_BOUNDS( ChildOverlapSupport , ChildOverlapStart + EData2::SupportStart , ChildOverlapEnd + EData2::SupportEnd );
 
    // Setting I=0/1, we are looking for the smallest/largest integers J such that:
    //      Support( 2*J ) * 2 INTERSECTION Support( 0/1 ) NON-EMPTY
    // <=>  [ 2*J - (Degree2+1-Inset2) , 2*J + (Degree2+1+Inset2) ] INTERSECTION [ 0/1 - (Degree1+1-Inset1)/2 , 0/1 + (Degree1+1+Inset1)/2 ] NON-EMPTY
    // Which is the same as the smallest/largest integers J such that:
    //      0/1 - (Degree1+1-Inset1)/2 < 2*J + (Degree2+1+Inset2)           | 0/1 + (Degree1+1+Inset1)/2 > 2*J - (Degree2+1-Inset2) 
    // <=>  2*J > 0/1 - ( 2*Degree2 + Degree1 + 3 + 2*Inset2 - Inset1 ) / 2 | 2*J < 0/1 + ( 2*Degree2 + Degree1 + 3 - 2*Inset2 + Inset1 ) / 2
    BSPLINE_SET_BOUNDS( ParentOverlap0 , SMALLEST_INTEGER_LARGER_THAN_HALF( 0 - ( 2*Degree2 + Degree1 + 3 + 2*EData2::Inset - EData1::Inset ) / 2 ) , LARGEST_INTEGER_SMALLER_THAN_HALF( 0 + ( 2*Degree2 + Degree1 + 3 - 2*EData2::Inset + EData1::Inset ) / 2 ) );
    BSPLINE_SET_BOUNDS( ParentOverlap1 , SMALLEST_INTEGER_LARGER_THAN_HALF( 1 - ( 2*Degree2 + Degree1 + 3 + 2*EData2::Inset - EData1::Inset ) / 2 ) , LARGEST_INTEGER_SMALLER_THAN_HALF( 1 + ( 2*Degree2 + Degree1 + 3 - 2*EData2::Inset + EData1::Inset ) / 2 ) );
    static const int ParentOverlapStart[] , ParentOverlapEnd[] , ParentOverlapSize[];
 
    struct FunctionIntegrator
    {
        static const int Start = - OverlapSupportStart , Stop = OverlapSupportEnd , Size = Start + Stop + 1;
        static const int Index( int depth , int offset  )
        {
            int dim = BSplineEvaluationData< Degree2 >::Dimension( depth );
            if     ( offset<Start )     return offset;
            else if( offset>=dim-Stop ) return Start + 1 + offset - ( dim-Stop );
            else                        return Start;
        }
        struct Integrator
        {
        protected:
            friend BSplineIntegrationData;
            int _depth;
            double _ccIntegrals[2][2][Size][OverlapSize];
        public:
            double dot( int fIdx1 , int fidx2 , bool d1 , bool d2 ) const;
            int depth( void ) const { return _depth; }
        };
        struct ChildIntegrator
        {
        protected:
            friend BSplineIntegrationData;
            int _parentDepth;
            double _pcIntegrals[2][2][Size][ChildOverlapSize];
        public:
            double dot( int fIdx1 , int fidx2 , bool d1 , bool d2 ) const;
            int parentDepth( void ) const { return _parentDepth; }
            int childDepth( void ) const { return _parentDepth+1; }
        };
    };
    static void SetIntegrator( typename FunctionIntegrator::Integrator& integrator , int depth , bool dirichlet1 , bool dirichlet2 );
    static void SetChildIntegrator( typename FunctionIntegrator::ChildIntegrator& integrator , int parentDepth , bool dirichlet1 , bool dirichlet2 );
};
template< int Degree1 , int Degree2 > const int BSplineIntegrationData< Degree1 , Degree2 >::ParentOverlapStart[] = { ParentOverlap0Start , ParentOverlap1Start };
template< int Degree1 , int Degree2 > const int BSplineIntegrationData< Degree1 , Degree2 >::ParentOverlapEnd  [] = { ParentOverlap0End   , ParentOverlap1End   };
template< int Degree1 , int Degree2 > const int BSplineIntegrationData< Degree1 , Degree2 >::ParentOverlapSize [] = { ParentOverlap0Size  , ParentOverlap1Size  };
#undef BSPLINE_SET_BOUNDS
#undef _FLOOR_OF_HALF
#undef  _CEIL_OF_HALF
#undef FLOOR_OF_HALF
#undef  CEIL_OF_HALF
#undef SMALLEST_INTEGER_LARGER_THAN_HALF
#undef LARGEST_INTEGER_SMALLER_THAN_HALF
#undef SMALLEST_INTEGER_LARGER_THAN_OR_EQUAL_TO_HALF
#undef LARGEST_INTEGER_SMALLER_THAN_OR_EQUAL_TO_HALF
 
template< int Degree >
class BSplineData
{
    bool _dirichlet;
public:
 
    inline static int Centers  ( int depth ){ return (1<<depth); }
    inline static int Corners  ( int depth ){ return (1<<depth) + 1; }
    inline static int Dimension( int depth ){ return (1<<depth) + (Degree&1); }
    inline static int FunctionIndex( int depth , int offset ){ return (Degree&1) ? BinaryNode::CornerIndex( depth , offset ) : BinaryNode::CenterIndex( depth , offset ); }
    inline static void FactorFunctionIndex( int idx , int& depth , int& offset ){ return (Degree&1) ? BinaryNode::CornerDepthAndOffset( idx , depth , offset ) : BinaryNode::CenterDepthAndOffset( idx , depth , offset ); }
    inline static int TotalFunctionCount( int depth ){ return (Degree&1) ? BinaryNode::CumulativeCornerCount( depth ) : BinaryNode::CumulativeCenterCount( depth ); }
    inline static int TotalSampleCount( int depth ){ return BinaryNode::CenterCount( depth ) + BinaryNode::CornerCount( depth ); }
    inline static void FunctionSpan( int depth , int& fStart , int& fEnd ){ fStart = (depth>0) ? TotalFunctionCount(depth-1) : 0 , fEnd = TotalFunctionCount(depth); }
    inline static void SampleSpan( int depth , int& sStart , int& sEnd ){ sStart = (depth>0) ? TotalSampleCount(depth-1) : 0 , sEnd = TotalSampleCount(depth); }
 
    inline static int RemapOffset( int depth , int idx , bool& reflect );
 
    int depth;
    size_t functionCount , sampleCount;
    Pointer( typename BSplineEvaluationData< Degree >::BSplineComponents ) baseBSplines;
 
    BSplineData( void );
 
    void set( int maxDepth , bool dirichlet=false );
};
 
template< int Degree1 , int Degree2 > void SetBSplineElementIntegrals( double integrals[Degree1+1][Degree2+1] );
 
 
#include "BSplineData.inl"
#endif // BSPLINE_DATA_INCLUDED