/usr/include/x86_64-linux-gnu/visp3/me/vpNurbs.h is in libvisp-me-dev 3.0.0-4.
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*
* This file is part of the ViSP software.
* Copyright (C) 2005 - 2015 by Inria. All rights reserved.
*
* This software is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License
* ("GPL") version 2 as published by the Free Software Foundation.
* See the file LICENSE.txt at the root directory of this source
* distribution for additional information about the GNU GPL.
*
* For using ViSP with software that can not be combined with the GNU
* GPL, please contact Inria about acquiring a ViSP Professional
* Edition License.
*
* See http://visp.inria.fr for more information.
*
* This software was developed at:
* Inria Rennes - Bretagne Atlantique
* Campus Universitaire de Beaulieu
* 35042 Rennes Cedex
* France
*
* If you have questions regarding the use of this file, please contact
* Inria at visp@inria.fr
*
* This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
* WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*
* Description:
* This class implements the Non Uniform Rational B-Spline (NURBS)
*
* Authors:
* Nicolas Melchior
*
*****************************************************************************/
#ifndef vpNurbs_H
#define vpNurbs_H
/*!
\file vpNurbs.h
\brief Class that provides tools to compute and manipulate a Non Uniform Rational B-Spline curve.
*/
#include <visp3/core/vpImagePoint.h>
#include <visp3/core/vpMatrix.h>
#include <visp3/core/vpMath.h>
#include <visp3/me/vpMeSite.h>
#include <visp3/core/vpBSpline.h>
#include <visp3/core/vpList.h>
#include <list>
/*!
\class vpNurbs
\ingroup module_me
\brief Class that provides tools to compute and manipulate a Non Uniform Rational B-Spline curve.
The different parameters are :
- The knot vector \f$ U = {u_0, ... , u_m} \f$ where the knots \f$ u_i, i = 0, ...,m \f$ are real number such as \f$ u_i < u_{i+1} i = 0, ...,m \f$.
To define a curve, the knot vector is such as : \f$ U = {a , ... , a, u_{p+1} , ... , u_{m-p-1} , b , ... , b} \f$ where \f$ a \f$ and \f$ b \f$ are real numbers and p is the degree of the B-Spline basis functions.
- The B-Spline basis functions \f$ N_{i,p} \f$ defined as :
\f[ N_{i,0}(u) = \left\{\begin{array}{cc}
1 & \mbox{if } u_i \leq u_{i+1} \\ 0 & else
\end{array}\right.\f]
\f[ N_{i,p}(u) = \frac{u-u_i}{u_{i+p}-u_i}N_{i,p-1}(u)+\frac{u_{i+p+1}-u}{u_{i+p+1}-u_{i+1}}N_{i+1,p-1}(u)\f]
where \f$ i = 0 , ... , m-1 \f$ and p is the degree of the B-Spline basis functions.
- The control points \f$ {P_i} \f$ which are defined by the coordinates \f$ (i,j) \f$ of a point in an image.
- The weight \f$ {w_i} \f$ associated to each control points.The wheights value is upper than 0.
It is possible to compute the coordinates of a point corresponding to the knots \f$ u \f$ (\f$ u \in [u_0,u_m]\f$) thanks to the formula :
\f[ C(u) = \frac{\sum_{i=0}^n (N_{i,p}(u)w_iP_i)}{\sum_{i=0}^n (N_{i,p}(u)w_i)}\f]
You can find much more information about the B-Splines and the implementation of all the methods in the Nurbs Book.
*/
class VISP_EXPORT vpNurbs : public vpBSpline
{
protected:
std::vector<double> weights; //Vector which contains the weights associated to each control Points
protected:
static vpMatrix computeCurveDers(double l_u, unsigned int l_i, unsigned int l_p, unsigned int l_der, std::vector<double> &l_knots, std::vector<vpImagePoint> &l_controlPoints, std::vector<double> &l_weights);
vpMatrix computeCurveDers(double u, unsigned int der);
public:
vpNurbs();
vpNurbs(const vpNurbs &nurbs);
virtual ~vpNurbs();
/*!
Gets all the weights relative to the control points.
\return list : A std::list containing weights relative to the control points.
*/
inline void get_weights(std::list<double>& list) const {
list.clear();
for (unsigned int i = 0; i < weights.size(); i++)
list.push_back(*(&(weights[0])+i));
}
/*!
Sets all the knots.
\param list : A std::list containing the value of the knots.
*/
inline void set_weights(const std::list<double> &list) {
weights.clear();
for(std::list<double>::const_iterator it=list.begin(); it!=list.end(); ++it){
weights.push_back(*it);
}
}
static vpImagePoint computeCurvePoint(double l_u, unsigned int l_i, unsigned int l_p, std::vector<double> &l_knots, std::vector<vpImagePoint> &l_controlPoints, std::vector<double> &l_weights);
vpImagePoint computeCurvePoint(double u);
static vpImagePoint* computeCurveDersPoint(double l_u, unsigned int l_i, unsigned int l_p, unsigned int l_der, std::vector<double> &l_knots, std::vector<vpImagePoint> &l_controlPoints, std::vector<double> &l_weights);
vpImagePoint* computeCurveDersPoint(double u, unsigned int der);
static void curveKnotIns(double l_u, unsigned int l_k, unsigned int l_s, unsigned int l_r, unsigned int l_p, std::vector<double> &l_knots, std::vector<vpImagePoint> &l_controlPoints, std::vector<double> &l_weights);
void curveKnotIns(double u, unsigned int s = 0, unsigned int r = 1);
static void refineKnotVectCurve(double* l_x, unsigned int l_r, unsigned int l_p, std::vector<double> &l_knots, std::vector<vpImagePoint> &l_controlPoints, std::vector<double> &l_weights);
void refineKnotVectCurve(double* x, unsigned int r);
static unsigned int removeCurveKnot(double l_u, unsigned int l_r, unsigned int l_num, double l_TOL, unsigned int l_s, unsigned int l_p, std::vector<double> &l_knots, std::vector<vpImagePoint> &l_controlPoints, std::vector<double> &l_weights);
unsigned int removeCurveKnot(double l_u, unsigned int l_r, unsigned int l_num, double l_TOL);
static void globalCurveInterp(std::vector<vpImagePoint> &l_crossingPoints, unsigned int l_p, std::vector<double> &l_knots, std::vector<vpImagePoint> &l_controlPoints, std::vector<double> &l_weights);
void globalCurveInterp(vpList<vpMeSite>& l_crossingPoints);
void globalCurveInterp(const std::list<vpImagePoint>& l_crossingPoints);
void globalCurveInterp(const std::list<vpMeSite>& l_crossingPoints);
void globalCurveInterp();
static void globalCurveApprox(std::vector<vpImagePoint> &l_crossingPoints, unsigned int l_p, unsigned int l_n, std::vector<double> &l_knots, std::vector<vpImagePoint> &l_controlPoints, std::vector<double> &l_weights);
void globalCurveApprox(vpList<vpMeSite>& l_crossingPoints, unsigned int n);
void globalCurveApprox(const std::list<vpImagePoint>& l_crossingPoints, unsigned int n);
void globalCurveApprox(const std::list<vpMeSite>& l_crossingPoints, unsigned int n);
void globalCurveApprox(unsigned int n);
};
#endif
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