B-Spline Module


Classes
class	imaging::Bspline< DATA_t >
	Class template for B-Splines of arbitrary data type. More...
class	imaging::PeriodicBspline< DATA_t >
	Class template for periodic B-Splines of arbitrary data type. More...
class	imaging::imaging::xml_handler< PeriodicBspline< DATA_t > >
class	imaging::imaging::xml_handler< Bspline< DATA_t > >
Functions
GraphicsInterface &	imaging::operator<< (GraphicsInterface &out, const Bspline< ublas::fixed_vector< float_t, 2 > > &curve)
GraphicsInterface &	imaging::operator<< (GraphicsInterface &out, const PeriodicBspline< ublas::fixed_vector< float_t, 2 > > &curve)
void	imaging::basis_spline (size_t i, Bspline< float_t > &spline)
void	imaging::basis_spline (size_t i, PeriodicBspline< float_t > &spline)
void	imaging::interpolation_matrix (const Bspline< float_t > &spline, const ublas::vector< float_t > &values, ublas::compressed_matrix< float_t > &matrix)
void	imaging::interpolation_matrix (const PeriodicBspline< float_t > &spline, const ublas::vector< float_t > &values, ublas::compressed_matrix< float_t > &matrix)
void	imaging::basis_spline_matrix (const PeriodicBspline< float_t > &spline, const ublas::vector< float_t > &values, ublas::compressed_matrix< float_t > &matrix)
void	imaging::basis_spline_matrix (const Bspline< float_t > &spline, const ublas::vector< float_t > &values, ublas::compressed_matrix< float_t > &matrix)

Detailed Description

The B-spline module includes classes for B-spline and periodic B-spline functions. This includes spline functions and curves of arbitrary dimension. The module provides functions to read/write B-splines from/to XML files and to display planar spline curves. It contains utility functions to solve the spline interpolation problem.

Function Documentation

void imaging::basis_spline	(	size_t	i,
		PeriodicBspline< float_t > &	spline
	)

#include <spline/utilities.hpp>

Sets the i-th spline coefficient of spline to 1 and all the others to 0.

Referenced by imaging::basis_spline().

void imaging::basis_spline	(	size_t	i,
		Bspline< float_t > &	spline
	)

#include <spline/utilities.hpp>

Sets the i-th spline coefficient of spline to 1 and all the others to 0.

References imaging::basis_spline().

void imaging::basis_spline_matrix	(	const Bspline< float_t > &	spline,
		const ublas::vector< float_t > &	values,
		ublas::compressed_matrix< float_t > &	matrix
	)

#include <spline/utilities.hpp>

Computes the matrix which is the result of the spline interpolation problem. Assume a B-spline function

$s(\tau) = \sum_{i = 0}^n a_i b_i(\tau)$

and consider the interpolation problem

$s(\tau_k) = y_k\,,\quad 0 \leq k \leq N\,.$

Then the least squares solution of this problem is defined by the system of linear equations

$\sum_{i=0}^n a_i \underbrace{\sum_{k=0}^N b_i(\tau_k)b_j(\tau_k)}_{A_{ij}} = \sum_{j=0}^N \underbrace{b_j(\tau_k)}_{B_{jk}} y_k\,,\quad 0 \leq j \leq n\,.$

If $s$ is given by spline and $(\tau_k)_{0\leq k \leq N}$ by values, then this function writes $B$ to matrix.

void imaging::basis_spline_matrix	(	const PeriodicBspline< float_t > &	spline,
		const ublas::vector< float_t > &	values,
		ublas::compressed_matrix< float_t > &	matrix
	)

#include <spline/utilities.hpp>

Computes the matrix which is the result of the spline interpolation problem. Assume a B-spline function

$s(\tau) = \sum_{i = 0}^n a_i b_i(\tau)$

and consider the interpolation problem

$s(\tau_k) = y_k\,,\quad 0 \leq k \leq N\,.$

Then the least squares solution of this problem is defined by the system of linear equations

$\sum_{i=0}^n a_i \underbrace{\sum_{k=0}^N b_i(\tau_k)b_j(\tau_k)}_{A_{ij}} = \sum_{j=0}^N \underbrace{b_j(\tau_k)}_{B_{jk}} y_k\,,\quad 0 \leq j \leq n\,.$

If $s$ is given by spline and $(\tau_k)_{0\leq k \leq N}$ by values, then this function writes $B$ to matrix.

void imaging::interpolation_matrix	(	const PeriodicBspline< float_t > &	spline,
		const ublas::vector< float_t > &	values,
		ublas::compressed_matrix< float_t > &	matrix
	)

#include <spline/utilities.hpp>

Computes the matrix which is the result of the spline interpolation problem. Assume a B-spline function

$s(\tau) = \sum_{i = 0}^n a_i b_i(\tau)$

and consider the interpolation problem

$s(\tau_k) = y_k\,,\quad 0 \leq k \leq N\,.$

Then the least squares solution of this problem is defined by the system of linear equations

$\sum_{i=0}^n a_i \underbrace{\sum_{k=0}^N b_i(\tau_k)b_j(\tau_k)}_{A_{ij}} = \sum_{j=0}^N \underbrace{b_j(\tau_k)}_{B_{jk}} y_k\,,\quad 0 \leq j \leq n\,.$

If $s$ is given by spline and $(\tau_k)_{0\leq k \leq N}$ by values, then this function writes $A$ to matrix.

Referenced by imaging::interpolation_matrix().

void imaging::interpolation_matrix	(	const Bspline< float_t > &	spline,
		const ublas::vector< float_t > &	values,
		ublas::compressed_matrix< float_t > &	matrix
	)

#include <spline/utilities.hpp>

Computes the matrix which is the result of the spline interpolation problem. Assume a B-spline function

$s(\tau) = \sum_{i = 0}^n a_i b_i(\tau)$

and consider the interpolation problem

$s(\tau_k) = y_k\,,\quad 0 \leq k \leq N\,.$

Then the least squares solution of this problem is defined by the system of linear equations

$\sum_{i=0}^n a_i \underbrace{\sum_{k=0}^N b_i(\tau_k)b_j(\tau_k)}_{A_{ij}} = \sum_{j=0}^N \underbrace{b_j(\tau_k)}_{B_{jk}} y_k\,,\quad 0 \leq j \leq n\,.$

If $s$ is given by spline and $(\tau_k)_{0\leq k \leq N}$ by values, then this function writes $A$ to matrix.

References imaging::interpolation_matrix().

GraphicsInterface & imaging::operator<<	(	GraphicsInterface &	out,
		const PeriodicBspline< ublas::fixed_vector< float_t, 2 > > &	curve
	)

#include <spline/gio.hpp>

Draws the 2-dimensional B-Spline curve curve in the graphics output.

GraphicsInterface & imaging::operator<<	(	GraphicsInterface &	out,
		const Bspline< ublas::fixed_vector< float_t, 2 > > &	curve
	)

#include <spline/gio.hpp>

Draws the 2-dimensional B-Spline curve curve in the graphics output.

B-Spline Module

Classes

Functions

Detailed Description

Function Documentation