Util::CardinalBSpline Class Reference

A cardinal B-spline basis function. More...

#include <CardinalBSpline.h>

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

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.

Constructor & Destructor Documentation

CardinalBSpline()

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(), degree(), and UTIL_CHECK.

~CardinalBSpline()

Util::CardinalBSpline::~CardinalBSpline

(

)

Destructor.

Definition at line 125 of file CardinalBSpline.cpp.

Member Function Documentation

operator[]()

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.

operator()()

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.

degree()

int Util::CardinalBSpline::degree ( ) const

inline

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

Definition at line 139 of file CardinalBSpline.h.

Referenced by CardinalBSpline().

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

• CardinalBSpline.h
• CardinalBSpline.cpp