Detailed Description

A cardinal B-spline basis function.

A cardinal B-Spline of order m or degree k = m - 1 is a piecewise continuous polynomial of degree k defined over the domain [0, k+1]. Such a function is defined by k different polynomials, each of which has a domain [i, i+1] for an integer i with 0 <= i <=k. For k > 0, the function and k-1 derivatives are continuous.

A CardinalBSpline object of degree k has k Polynomial<double> objects, indexed by an integer 0 <= i <= k, each of which defines the polynomial with a domain [i,i+1].

If object b is a CardinalBSpline of degree k, then:

Operator b[i] returns the Polynomial<double> for domain [i,i+1]
Operator b(x) returns the value of basis function b for real x.

Definition at line 42 of file CardinalBSpline.h.

#include <CardinalBSpline.h>

Public Member Functions
Polynomial< double > const &	operator[] (int i) const
	Get Polynomial<double> object for domain [i,i+1]. More...

double	operator() (double x) const
	Compute the value of the spline basis function. More...

int	degree () const
	Return degree of basis function (i.e., degree of polynomials). More...

Constructor and Destructor
	CardinalBSpline (int degree, bool verbose=false)
	Construct a spline basis of specified degree. More...

	~CardinalBSpline ()
	Destructor. More...

Constructor & Destructor Documentation

Util::CardinalBSpline::CardinalBSpline	(	int	degree,
		bool	verbose = `false`
	)

Construct a spline basis of specified degree.

Parameters

degree	degree of the function (i.e., degree of polynomials)
verbose	if true, write verbose report to std::cout

Definition at line 17 of file CardinalBSpline.cpp.

References Util::DArray< Data >::allocate(), and UTIL_CHECK.

Util::CardinalBSpline::~CardinalBSpline ( )

Destructor.

Definition at line 125 of file CardinalBSpline.cpp.

Member Function Documentation

Polynomial< double > const & Util::CardinalBSpline::operator[] ( int i ) const

inline

Get Polynomial<double> object for domain [i,i+1].

If b is a CardinalBSpline, b[i] returns the Polynomial<double> object (the polynomial with double precision floating point coefficients) associated with the domain [i,i+1].

Parameters

i	integer index in range 0 <= i <= degree.

Returns: polynomial associated with domain [i, i+1]

Definition at line 119 of file CardinalBSpline.h.

double Util::CardinalBSpline::operator() ( double x ) const

inline

Compute the value of the spline basis function.

If b is a CardinalBSpline, b(x) returns the value of the spline function for specified floating point argument x, giving a nonzero value only for 0 < x < degree + 1.

Parameters

x	argument of spline basis function

Definition at line 126 of file CardinalBSpline.h.

References UTIL_ASSERT.

int Util::CardinalBSpline::degree ( ) const

inline

Return degree of basis function (i.e., degree of polynomials).

Definition at line 139 of file CardinalBSpline.h.

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

Detailed Description

Public Member Functions

Constructor & Destructor Documentation

Member Function Documentation