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Util::Polynomial< Dim, Degree > Class Template Reference

#include <polynomial.h>

Inheritance diagram for Util::Polynomial< Dim, Degree >:
Util::VectorSpace< Polynomial< Dim, Degree > >

Public Member Functions

 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
 
Polynomial operator* (double s) const
 
Polynomial operator+ (const Polynomial &p) const
 
template<typename ... Doubles>
 Polynomial (Doubles ... coefficients)
 
template<unsigned int _Degree>
 Polynomial (const Polynomial< 1, _Degree > &p)
 
template<unsigned int _Degree>
Polynomial< 1, Degree > & operator= (const Polynomial< 1, _Degree > &p)
 
template<unsigned int Degree>
const double & coefficient (unsigned int d) const
 
template<unsigned int Degree>
double & coefficient (unsigned int d)
 
template<unsigned int Degree>
double operator() (double x) const
 
template<unsigned int Degree>
Polynomial< 1, Degree > operator() (const Ray< 1 > &ray) const
 
template<unsigned int Degree>
Polynomial< 1, Degree > operator+ (const Polynomial< 1, Degree > &p) const
 
unsigned int roots (double *r) const
 
unsigned int roots (double *r) const
 
unsigned int roots (double *r) const
 
unsigned int roots (double *r) const
 
unsigned int roots (double *r) const
 
template<unsigned int _Degree>
Polynomial< Dim, Degree > & operator= (const Polynomial< Dim, _Degree > &p)
 

Private Member Functions

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
 

Private Attributes

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

Detailed Description

template<unsigned int Dim, unsigned int Degree>
class Util::Polynomial< Dim, Degree >

The generic, recursively defined, Polynomial class of total degree Degree.

Constructor & Destructor Documentation

◆ Polynomial() [1/5]

template<unsigned int Dim, unsigned int Degree>
Util::Polynomial< Dim, Degree >::Polynomial ( void )

The default constructor initializes the coefficients to zero.

◆ Polynomial() [2/5]

template<unsigned int Dim, unsigned int Degree>
Util::Polynomial< Dim, Degree >::Polynomial ( double c)

This constructor creates a constant polynomial

◆ Polynomial() [3/5]

template<unsigned int Dim, unsigned int Degree>
template<unsigned int _Degree>
Util::Polynomial< Dim, Degree >::Polynomial ( const Polynomial< Dim, _Degree > & p)

The constructor copies over as much of the polynomial as will fit.

◆ Polynomial() [4/5]

template<unsigned int Dim, unsigned int Degree>
template<typename ... Doubles>
Util::Polynomial< Dim, Degree >::Polynomial ( Doubles ... coefficients)

◆ Polynomial() [5/5]

template<unsigned int Dim, unsigned int Degree>
template<unsigned int _Degree>
Util::Polynomial< Dim, Degree >::Polynomial ( const Polynomial< 1, _Degree > & p)

Member Function Documentation

◆ _coefficient() [1/2]

template<unsigned int Dim, unsigned int Degree>
double & Util::Polynomial< Dim, Degree >::_coefficient ( const unsigned int indices[],
unsigned int maxDegree )
private

This method returns the specified coefficient of the polynomial.

◆ _coefficient() [2/2]

template<unsigned int Dim, unsigned int Degree>
const double & Util::Polynomial< Dim, Degree >::_coefficient ( const unsigned int indices[],
unsigned int maxDegree ) const
private

This method returns the specified coefficient of the polynomial.

◆ _evaluate() [1/2]

template<unsigned int Dim, unsigned int Degree>
double Util::Polynomial< Dim, Degree >::_evaluate ( const double coordinates[],
unsigned int maxDegree ) const
private

This method evaluates the polynomial at the specified set of coordinates.

◆ _evaluate() [2/2]

template<unsigned int Dim, unsigned int Degree>
Polynomial< 1, Degree > Util::Polynomial< Dim, Degree >::_evaluate ( const Ray< Dim > & ray,
unsigned int maxDegree ) const
private

This method evaluates a Dim-dimensional polynomial along a Dim-dimensional Ray, and returns the associated 1-dimensional polynomial.

◆ _isConstant()

template<unsigned int Dim, unsigned int Degree>
bool Util::Polynomial< Dim, Degree >::_isConstant ( unsigned int maxDegree) const
private

This method returns true if the polynomial is a constant.

◆ _isZero()

template<unsigned int Dim, unsigned int Degree>
bool Util::Polynomial< Dim, Degree >::_isZero ( unsigned int maxDegree) const
private

This method returns true if the polynomial is zero.

◆ coefficient() [1/4]

template<unsigned int Dim, unsigned int Degree>
template<unsigned int Degree>
double & Util::Polynomial< Dim, Degree >::coefficient ( unsigned int d)

◆ coefficient() [2/4]

template<unsigned int Dim, unsigned int Degree>
template<unsigned int Degree>
const double & Util::Polynomial< Dim, Degree >::coefficient ( unsigned int d) const

◆ coefficient() [3/4]

template<unsigned int Dim, unsigned int Degree>
template<typename ... UnsignedInts>
double & Util::Polynomial< Dim, Degree >::coefficient ( UnsignedInts ... indices)

This method returns the associated coefficient of the polynomial

◆ coefficient() [4/4]

template<unsigned int Dim, unsigned int Degree>
template<typename ... UnsignedInts>
const double & Util::Polynomial< Dim, Degree >::coefficient ( UnsignedInts ... indices) const

This method returns the associated coefficient of the polynomial

◆ d()

template<unsigned int Dim, unsigned int Degree>
Polynomial< Dim, Degree-1 > Util::Polynomial< Dim, Degree >::d ( int dim) const

This method returns the partial derivative with respect to the prescribed dimension.

◆ operator()() [1/5]

template<unsigned int Dim, unsigned int Degree>
template<unsigned int Degree>
Polynomial< 1, Degree > Util::Polynomial< Dim, Degree >::operator() ( const Ray< 1 > & ray) const

◆ operator()() [2/5]

template<unsigned int Dim, unsigned int Degree>
Polynomial< 1, Degree > Util::Polynomial< Dim, Degree >::operator() ( const Ray< Dim > & ray) const

This method returns the 1D polynomial obtained by evaluating the polynomial along the ray.

◆ operator()() [3/5]

template<unsigned int Dim, unsigned int Degree>
template<unsigned int Degree>
double Util::Polynomial< Dim, Degree >::operator() ( double x) const

◆ operator()() [4/5]

template<unsigned int Dim, unsigned int Degree>
template<typename ... Doubles>
double Util::Polynomial< Dim, Degree >::operator() ( Doubles ... coordinates) const

This method evaluates the polynomial at the prescribed point.

◆ operator()() [5/5]

template<unsigned int Dim, unsigned int Degree>
double Util::Polynomial< Dim, Degree >::operator() ( Point< Dim > p) const

This method evaluates the polynomial at the prescribed point.

◆ operator*()

template<unsigned int Dim, unsigned int Degree>
Polynomial< Dim, Degree > Util::Polynomial< Dim, Degree >::operator* ( double s) const

This method returns the scalar multiple of the polynomial

◆ operator+() [1/2]

template<unsigned int Dim, unsigned int Degree>
Polynomial< Dim, Degree > Util::Polynomial< Dim, Degree >::operator+ ( const Polynomial< Dim, Degree > & p) const

This method returns the sum of two polynomials

◆ operator+() [2/2]

template<unsigned int Dim, unsigned int Degree>
template<unsigned int Degree>
Polynomial< 1, Degree > Util::Polynomial< Dim, Degree >::operator+ ( const Polynomial< 1, Degree > & p) const

◆ operator=() [1/3]

template<unsigned int Dim, unsigned int Degree>
template<unsigned int _Degree>
Polynomial< 1, Degree > & Util::Polynomial< Dim, Degree >::operator= ( const Polynomial< 1, _Degree > & p)

◆ operator=() [2/3]

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

The equality operator copies over as much of the polynomial as will fit.

◆ operator=() [3/3]

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

◆ roots() [1/5]

unsigned int Util::Polynomial< 1, 1 >::roots ( double * r) const
inline

◆ roots() [2/5]

unsigned int Util::Polynomial< 1, 2 >::roots ( double * r) const
inline

◆ roots() [3/5]

unsigned int Util::Polynomial< 1, 3 >::roots ( double * r) const
inline

◆ roots() [4/5]

unsigned int Util::Polynomial< 1, 4 >::roots ( double * r) const
inline

◆ roots() [5/5]

unsigned int Util::Polynomial< 1, 5 >::roots ( double * r) const
inline

Member Data Documentation

◆ _polynomials

template<unsigned int Dim, unsigned int Degree>
Polynomial< Dim-1 , Degree > Util::Polynomial< Dim, Degree >::_polynomials[Degree+1]
private

The polynomials in Dim-1 dimensions. The total polynomial is assumed to be _polynomials[0] + _polynomials[1] * (x_Dim) + _polynomials[2] * (x_Dim)^2 + ...

The documentation for this class was generated from the following files: