polynomial.h

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/*
Copyright (c) 2019, Michael Kazhdan
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#ifndef POLYNOMIAL_INCLUDED
#define POLYNOMIAL_INCLUDED
#include <iostream>
#include <Util/geometry.h>
#include <Util/algebra.h>
 
namespace Util
{
    template< unsigned int D1 , unsigned int D2 > struct Min{ static const unsigned int Value = D1<D2 ? D1 : D2; };
    template< unsigned int D1 , unsigned int D2 > struct Max{ static const unsigned int Value = D1>D2 ? D1 : D2; };

    template< unsigned int Dim , unsigned int Degree >
    class Polynomial : public VectorSpace< Polynomial< Dim , Degree > >
    {
        template< unsigned int _Dim , unsigned int _Degree > friend class Polynomial;
        template< unsigned int _Dim , unsigned int Degree1 , unsigned int Degree2 > friend Polynomial< _Dim , Degree1 + Degree2 > operator * ( const Polynomial< _Dim , Degree1 > & , const Polynomial< _Dim , Degree2 > & );
        template< unsigned int _Dim , unsigned int Degree1 , unsigned int Degree2 > friend Polynomial< _Dim , Max< Degree1 , Degree2 >::Value > operator + ( const Polynomial< _Dim , Degree1 > & , const Polynomial< _Dim , Degree2 > & );
        template< unsigned int _Dim , unsigned int Degree1 , unsigned int Degree2 > friend Polynomial< _Dim , Max< Degree1 , Degree2 >::Value > operator - ( const Polynomial< _Dim , Degree1 > & , const Polynomial< _Dim , Degree2 > & );
        template< unsigned int _Dim , unsigned int _Degree > friend std::ostream &operator << ( std::ostream & , const Polynomial< _Dim , _Degree > & );

        Polynomial< Dim-1 , Degree > _polynomials[Degree+1];

        const double &_coefficient( const unsigned int indices[] , unsigned int maxDegree ) const;

        double &_coefficient( const unsigned int indices[] , unsigned int maxDegree );

        double _evaluate( const double coordinates[] , unsigned int maxDegree ) const;

        Polynomial< 1, Degree > _evaluate( const Ray< Dim > &ray , unsigned int maxDegree ) const;

        bool _isZero( unsigned int maxDegree ) const;

        bool _isConstant( unsigned int maxDegree ) const;
 
    public:
        Polynomial( void );

        Polynomial( double c );

        template< unsigned int _Degree >
        Polynomial( const Polynomial< Dim , _Degree > &p );

        template< unsigned int _Degree >
        Polynomial &operator= ( const Polynomial< Dim , _Degree > &p );

        template< typename ... UnsignedInts >
        const double &coefficient( UnsignedInts ... indices ) const;

        template< typename ... UnsignedInts >
        double &coefficient( UnsignedInts ... indices );

        template< typename ... Doubles >
        double operator()( Doubles ... coordinates ) const;

        double operator()( Point< Dim > p ) const;

        Polynomial< Dim , Degree-1 > d( int dim ) const;

        Polynomial< 1 , Degree > operator()( const Ray< Dim > &ray ) const;

        // VectorSpace methods //

        Polynomial operator * ( double s ) const;

        Polynomial operator + ( const Polynomial & p ) const;
    };

    template< unsigned int Dim , unsigned int Degree1 , unsigned int Degree2 >
    Polynomial< Dim , Degree1 + Degree2 > operator * ( const Polynomial< Dim , Degree1 > &p1 , const Polynomial< Dim , Degree2 > &p2 );

    template< unsigned int Dim , unsigned int Degree1 , unsigned int Degree2 >
    Polynomial< Dim , Max< Degree1 , Degree2 >::Value > operator + ( const Polynomial< Dim , Degree1 > &p1 , const Polynomial< Dim , Degree2 > &p2 );

    template< unsigned int Dim , unsigned int Degree1 , unsigned int Degree2 >
    Polynomial< Dim , Max< Degree1 , Degree2 >::Value > operator - ( const Polynomial< Dim , Degree1 > &p1 , const Polynomial< Dim , Degree2 > &p2 );

    template< unsigned int Dim , unsigned int Degree >
    std::ostream &operator << ( std::ostream &stream , const Polynomial< Dim , Degree > &poly );

    template< unsigned int Degree >
    class Polynomial< 1 , Degree > : public VectorSpace< Polynomial< 1 , Degree > >
    {
        template< unsigned int _Dim , unsigned int _Degree > friend class Polynomial;
        template< unsigned int Degree1 , unsigned int Degree2 > friend Polynomial< 1 , Degree1 + Degree2 > operator * ( const Polynomial< 1 , Degree1 > & , const Polynomial< 1 , Degree2 > & );
        template< unsigned int Degree1 , unsigned int Degree2 > friend Polynomial< 1 , Max< Degree1 , Degree2 >::Value > operator + ( const Polynomial< 1 , Degree1 > & , const Polynomial< 1 , Degree2 > & );
        template< unsigned int Degree1 , unsigned int Degree2 > friend Polynomial< 1 , Max< Degree1 , Degree2 >::Value > operator - ( const Polynomial< 1 , Degree1 > & , const Polynomial< 1 , Degree2 > & );
        template< unsigned int _Degree > friend std::ostream &operator << ( std::ostream & , const Polynomial< 1 , _Degree > & );
        template< unsigned int Dim , unsigned int Degree1 , unsigned int Degree2 > friend Polynomial< Dim , Degree1 + Degree2 > operator * ( const Polynomial< Dim , Degree1 > & , const Polynomial< Dim , Degree2 > & );
        template< unsigned int Dim , unsigned int Degree1 , unsigned int Degree2 > friend Polynomial< Dim , Max< Degree1 , Degree2 >::Value > operator + ( const Polynomial< Dim , Degree1 > & , const Polynomial< Dim , Degree2 > & );
        template< unsigned int Dim , unsigned int Degree1 , unsigned int Degree2 > friend Polynomial< Dim , Max< Degree1 , Degree2 >::Value > operator - ( const Polynomial< Dim , Degree1 > & , const Polynomial< Dim , Degree2 > & );
        template< unsigned int Dim , unsigned int _Degree > friend std::ostream &operator << ( std::ostream & , const Polynomial< Dim , _Degree > & );

        double _coefficients[Degree+1];

        const double &_coefficient( const unsigned int indices[] , unsigned int maxDegree ) const;

        double &_coefficient( const unsigned int indices[] , unsigned int maxDegree );

        double _evaluate( const double coordinates[] , unsigned int maxDegree ) const;

        Polynomial _evaluate( const Ray< 1 > &ray , unsigned int maxDegree ) const;

        bool _isZero( unsigned int maxDegree ) const;

        bool _isConstant( unsigned int maxDegree ) const;
    public:
        Polynomial( void );

        Polynomial( double c );

        template< typename ... Doubles >
        Polynomial( Doubles ... coefficients );

        template< unsigned int _Degree >
        Polynomial( const Polynomial< 1 , _Degree > &p );

        template< unsigned int _Degree >
        Polynomial &operator= ( const Polynomial< 1 , _Degree > &p );

        const double &coefficient( unsigned int d ) const;

        double &coefficient( unsigned int d );

        double operator()( double x ) const;

        Polynomial< 1 , Degree-1 > d( unsigned int d=0 ) const;

        Polynomial operator()( const Ray< 1 > &ray ) const;

        unsigned int roots( double *r ) const;

        // VectorSpace methods //

        Polynomial operator * ( double s ) const;

        Polynomial operator + ( const Polynomial & p ) const;
 
    };

    template< unsigned int Degree1 , unsigned int Degree2 >
    Polynomial< 1 , Degree1 + Degree2 > operator * ( const Polynomial< 1 , Degree1 > &p1 , const Polynomial< 1 , Degree2 > &p2 );

    template< unsigned int Degree1 , unsigned int Degree2 >
    Polynomial< 1 , Max< Degree1 , Degree2 >::Value > operator + ( const Polynomial< 1 , Degree1 > &p1 , const Polynomial< 1 , Degree2 > &p2 );

    template< unsigned int Degree1 , unsigned int Degree2 >
    Polynomial< 1 , Max< Degree1 , Degree2 >::Value > operator - ( const Polynomial< 1 , Degree1 > &p1 , const Polynomial< 1 , Degree2 > &p2 );

    template< unsigned int Degree >
    std::ostream &operator << ( std::ostream &stream , const Polynomial< 1 , Degree > &poly );

    // Classes specialized for 1D, 2D, 3D, and 4D //

    template< unsigned int Degree >
    using Polynomial1D = Polynomial< 1 , Degree >;

    template< unsigned int Degree >
    using Polynomial2D = Polynomial< 2 , Degree >;

    template< unsigned int Degree >
    using Polynomial3D = Polynomial< 3 , Degree >;

    template< unsigned int Degree >
    using Polynomial4D = Polynomial< 4 , Degree >;
}
#include "polynomial.inl"
#endif // POLYNOMIAL_INCLUDED