#include <vpNurbs.h>

Inheritance diagram for vpNurbs:

Public Member Functions
	vpNurbs ()
	vpNurbs (const vpNurbs &nurbs)
void	get_weights (std::list< double > &list) const
void	set_weights (const std::list< double > &list)
vpImagePoint	computeCurvePoint (double u)
vpImagePoint *	computeCurveDersPoint (double u, unsigned int der)
void	curveKnotIns (double u, unsigned int s=0, unsigned int r=1)
void	refineKnotVectCurve (double *x, unsigned int r)
unsigned int	removeCurveKnot (double l_u, unsigned int l_r, unsigned int l_num, double l_TOL)
void	globalCurveInterp (vpList< vpMeSite > &l_crossingPoints)
void	globalCurveInterp (const std::list< vpImagePoint > &l_crossingPoints)
void	globalCurveInterp (const std::list< vpMeSite > &l_crossingPoints)
void	globalCurveInterp ()
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)
unsigned int	get_p () const
void	get_controlPoints (std::list< vpImagePoint > &list) const
void	get_knots (std::list< double > &list) const
void	get_crossingPoints (std::list< vpImagePoint > &list) const
void	set_p (unsigned int degree)
void	set_controlPoints (const std::list< vpImagePoint > &list)
void	set_knots (const std::list< double > &list)
void	set_crossingPoints (const std::list< vpImagePoint > &list)
unsigned int	findSpan (double u) const
vpBasisFunction *	computeBasisFuns (double u) const
vpBasisFunction **	computeDersBasisFuns (double u, unsigned int der) const
vpImagePoint	computeCurvePoint (double u) const
vpImagePoint *	computeCurveDers (double u, unsigned int der) const

Static Public Member Functions
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)
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)
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)
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)
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)
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)
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)
static unsigned int	findSpan (double l_u, unsigned int l_p, const std::vector< double > &l_knots)
static vpBasisFunction *	computeBasisFuns (double l_u, unsigned int l_i, unsigned int l_p, const std::vector< double > &l_knots)
static vpBasisFunction **	computeDersBasisFuns (double l_u, unsigned int l_i, unsigned int l_p, unsigned int l_der, const std::vector< double > &l_knots)
static vpImagePoint	computeCurvePoint (double l_u, unsigned int l_i, unsigned int l_p, const std::vector< double > &l_knots, const std::vector< vpImagePoint > &l_controlPoints)
static vpImagePoint *	computeCurveDers (double l_u, unsigned int l_i, unsigned int l_p, unsigned int l_der, const std::vector< double > &l_knots, const std::vector< vpImagePoint > &l_controlPoints)

Public Attributes
	: std::vector<vpImagePoint> controlPoints
std::vector< double >	knots
unsigned int	p
std::vector< vpImagePoint >	crossingPoints

Protected Member Functions
vpMatrix	computeCurveDers (double u, unsigned int der)

Static Protected Member Functions
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)

Protected Attributes
std::vector< double >	weights

Detailed Description

Class that provides tools to compute and manipulate a Non Uniform Rational B-Spline curve.

The different parameters are :

The knot vector $U = {u_0, ... , u_m}$ where the knots are real number such as $u_i < u_{i+1} i = 0, ...,m$ . To define a curve, the knot vector is such as : $U = {a , ... , a, u_{p+1} , ... , u_{m-p-1} , b , ... , b}$ where and are real numbers and p is the degree of the B-Spline basis functions.
The B-Spline basis functions $N_{i,p}$ defined as :
$\‍[ N_{i,0}(u) = \left\{\begin{array}{cc} 1 & \mbox{if } u_i \leq u_{i+1} \\ 0 & else \end{array}\right.\‍]$

$\‍[ N_{i,p}(u) = \frac{u-u_i}{u_{i+p}-u_i}N_{i,p-1}(u)+\frac{u_{i+p+1}-u}{u_{i+p+1}-u_{i+1}}N_{i+1,p-1}(u)\‍]$

where and p is the degree of the B-Spline basis functions.

The control points ${P_i}$ which are defined by the coordinates of a point in an image.
The weight ${w_i}$ associated to each control points. The weights value is upper than 0.

It is possible to compute the coordinates of a point corresponding to the knots ( $u \in [u_0,u_m]$ ) thanks to the formula :

$\‍[ C(u) = \frac{\sum_{i=0}^n (N_{i,p}(u)w_iP_i)}{\sum_{i=0}^n (N_{i,p}(u)w_i)}\‍]$

You can find much more information about the B-Splines and the implementation of all the methods in the Nurbs Book.

Examples: testNurbs.cpp.

Definition at line 92 of file vpNurbs.h.

Constructor & Destructor Documentation

◆ vpNurbs() [1/2]

vpNurbs::vpNurbs ( )

Basic constructor.

The degree of the NURBS basis functions is set to 3 to compute cubic NURBS.

Definition at line 52 of file vpNurbs.cpp.

References vpBSpline::p, and weights.

Referenced by vpNurbs().

◆ vpNurbs() [2/2]

vpNurbs::vpNurbs ( const vpNurbs & nurbs )

Copy constructor.

Definition at line 54 of file vpNurbs.cpp.

References vpBSpline::vpBSpline(), vpNurbs(), and weights.

Member Function Documentation

◆ computeBasisFuns() [1/2]

vpBasisFunction * vpBSpline::computeBasisFuns	(	double	l_u,
		unsigned int	l_i,
		unsigned int	l_p,
		const std::vector< double > &	l_knots )

staticinherited

Compute the nonvanishing basis functions at which is in the th knot interval. All the basis functions are stored in an array such as :

N = $N_{l_i,0}(l_u)$ , $N_{l_i-1,1}(l_u)$ , $N_{l_i,1}(l_u)$ , ... , $N_{l_i-k,k}(l_u)$ , ..., $N_{l_i,k}(l_u)$ , ... , $N_{l_i-p,p}(l_u)$ , ... , $N_{l_i,p}(l_u)$

Parameters

l_u	: A real number which is between the extremities of the knot vector.
l_i	: The number of the knot interval in which lies.
l_p	: Degree of the B-Spline basis functions.
l_knots	: The knot vector.

Returns: An array containing the nonvanishing basis functions at . The size of the array is .

Examples: BSpline.cpp, and testNurbs.cpp.

Definition at line 124 of file vpBSpline.cpp.

Referenced by computeBasisFuns(), computeCurvePoint(), computeCurvePoint(), vpNurbs::computeCurvePoint(), vpNurbs::computeCurvePoint(), vpNurbs::globalCurveApprox(), and vpNurbs::globalCurveInterp().

◆ computeBasisFuns() [2/2]

vpBasisFunction * vpBSpline::computeBasisFuns ( double u ) const

inherited

Compute the nonvanishing basis functions at . All the basis functions are stored in an array such as :

N = $N_{i,0}(u)$ , $N_{i-1,1}(u)$ , $N_{i,1}(u)$ , ... , $N_{i-k,k}(u)$ , ..., $N_{i,k}(u)$ , ... , $N_{i-p,p}(u)$ , ... , $N_{i,p}(u)$

where i the number of the knot interval in which lies.

Parameters

u	: A real number which is between the extremities of the knot vector

Returns: An array containing the nonvanishing basis functions at . The size of the array is .

Definition at line 175 of file vpBSpline.cpp.

References computeBasisFuns(), findSpan(), knots, and p.

◆ computeCurveDers() [1/4]

vpImagePoint * vpBSpline::computeCurveDers	(	double	l_u,
		unsigned int	l_i,
		unsigned int	l_p,
		unsigned int	l_der,
		const std::vector< double > &	l_knots,
		const std::vector< vpImagePoint > &	l_controlPoints )

staticinherited

Compute the kth derivatives of for $k = 0, ... , l_{der}$ .

The formula used is the following :

$\‍[ C^{(k)}(u) = \sum_{i=0}^n (N_{i,p}^{(k)}(u)P_i) \‍]$

where is the knot interval number in which lies and is the degree of the B-Spline basis function.

Parameters

l_u	: A real number which is between the extremities of the knot vector.
l_i	: The number of the knot interval in which lies
l_p	: Degree of the B-Spline basis functions.
l_der	: The last derivative to be computed.
l_knots	: The knot vector.
l_controlPoints	: The list of control points.

Returns: An array of size l_der+1 containing the coordinates $C^{(k)}(u)$ for . The kth derivative is in the kth cell of the array.

Definition at line 428 of file vpBSpline.cpp.

References computeDersBasisFuns(), vpImagePoint::set_i(), vpImagePoint::set_ij(), vpImagePoint::set_j(), and vpTRACE.

◆ computeCurveDers() [2/4]

vpImagePoint * vpBSpline::computeCurveDers	(	double	u,
		unsigned int	der ) const

inherited

Compute the kth derivatives of for .

The formula used is the following :

$\‍[ C^{(k)}(u) = \sum_{i=0}^n (N_{i,p}^{(k)}(u)P_i) \‍]$

where is the knot interval number in which lies and is the degree of the B-Spline basis function.

Parameters

u	: A real number which is between the extremities of the knot vector
der	: The last derivative to be computed.

Returns: An array of size der+1 containing the coordinates $C^{(k)}(u)$ for . The kth derivative is in the kth cell of the array.

Definition at line 474 of file vpBSpline.cpp.

References computeDersBasisFuns(), p, vpImagePoint::set_i(), vpImagePoint::set_ij(), vpImagePoint::set_j(), and vpTRACE.

◆ computeCurveDers() [3/4]

vpMatrix vpNurbs::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 )

staticprotected

This function is used in the computeCurveDersPoint method.

Compute the kth derivatives of for $k = 0, ... , l_{der}$ .

The formula used is the following :

$\‍[ C^{(k)}(u) = \sum_{i=0}^n (N_{i,p}^{(k)}(u)Pw_i) \‍]$

where is the knot interval number in which lies, is the degree of the NURBS basis function and contains the control points and the associated weights.

Parameters

l_u	: A real number which is between the extremities of the knot vector.
l_i	: the number of the knot interval in which lies.
l_p	: Degree of the NURBS basis functions.
l_der	: The last derivative to be computed.
l_knots	: The knot vector.
l_controlPoints	: the list of control points.
l_weights	: the list of weights.

Returns: a matrix of size (l_der+1)x3 containing the coordinates $C^{(k)}(u)$ for $k = 0, ... , l_{der}$ . The kth derivative is in the kth line of the matrix. For each lines the first and the second column corresponds to the coordinates (i,j) of the point and the third column corresponds to the associated weight.

Definition at line 105 of file vpNurbs.cpp.

References vpBSpline::computeDersBasisFuns().

Referenced by computeCurveDersPoint().

◆ computeCurveDers() [4/4]

vpMatrix vpNurbs::computeCurveDers	(	double	u,
		unsigned int	der )

protected

This function is used in the computeCurveDersPoint method.

Compute the kth derivatives of for .

The formula used is the following :

$\‍[ C^{(k)}(u) = \sum_{i=0}^n (N_{i,p}^{(k)}(u)Pw_i) \‍]$

where is the knot interval number in which lies, is the degree of the NURBS basis function and contains the control points and the associated weights.

Parameters

u	: A real number which is between the extremities of the knot vector
der	: The last derivative to be computed.

Returns: a matrix of size (l_der+1)x3 containing the coordinates $C^{(k)}(u)$ for . The kth derivative is in the kth line of the matrix. For each lines the first and the second column corresponds to the coordinates (i,j) of the point and the third column corresponds to the associated weight.

Definition at line 133 of file vpNurbs.cpp.

References vpBSpline::computeDersBasisFuns(), vpBSpline::p, and weights.

◆ computeCurveDersPoint() [1/2]

vpImagePoint * vpNurbs::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 )

static

Compute the kth derivatives of for $k = 0, ... , l_{der}$ .

To see how the derivatives are computed refers to the Nurbs book.

Parameters

l_u	: A real number which is between the extremities of the knot vector.
l_i	: the number of the knot interval in which lies.
l_p	: Degree of the NURBS basis functions.
l_der	: The last derivative to be computed.
l_knots	: The knot vector.
l_controlPoints	: the list of control points.
l_weights	: the list of weights.

Returns: an array of size l_der+1 containing the coordinates $C^{(k)}(u)$ for $k = 0, ... , l_{der}$ . The kth derivative is in the kth cell of the array.

Definition at line 156 of file vpNurbs.cpp.

References vpMath::comb(), computeCurveDers(), vpImagePoint::get_i(), vpImagePoint::get_j(), vpImagePoint::set_i(), vpImagePoint::set_ij(), and vpImagePoint::set_j().

Referenced by computeCurveDersPoint().

◆ computeCurveDersPoint() [2/2]

vpImagePoint * vpNurbs::computeCurveDersPoint	(	double	u,
		unsigned int	der )

Compute the kth derivatives of for $k = 0, ... , l_{der}$ .

To see how the derivatives are computed refers to the Nurbs book.

Parameters

u	: A real number which is between the extremities of the knot vector
der	: The last derivative to be computed.

Returns: an array of size l_der+1 containing the coordinates $C^{(k)}(u)$ for . The kth derivative is in the kth cell of the array.

Definition at line 187 of file vpNurbs.cpp.

References computeCurveDersPoint(), vpBSpline::findSpan(), vpBSpline::knots, vpBSpline::p, and weights.

◆ computeCurvePoint() [1/4]

vpImagePoint vpBSpline::computeCurvePoint	(	double	l_u,
		unsigned int	l_i,
		unsigned int	l_p,
		const std::vector< double > &	l_knots,
		const std::vector< vpImagePoint > &	l_controlPoints )

staticinherited

Compute the coordinates of a point $C(u) = \sum_{i=0}^n (N_{i,p}(u)P_i)$ corresponding to the knot .

Parameters

l_u	: A real number which is between the extremities of the knot vector.
l_i	: The number of the knot interval in which lies.
l_p	: Degree of the B-Spline basis functions.
l_knots	: The knot vector.
l_controlPoints	: the list of control points.

Returns: The coordinates of a point corresponding to the knot .

Examples: BSpline.cpp.

Definition at line 359 of file vpBSpline.cpp.

References computeBasisFuns(), vpImagePoint::set_i(), and vpImagePoint::set_j().

◆ computeCurvePoint() [2/4]

vpImagePoint vpBSpline::computeCurvePoint ( double u ) const

inherited

Compute the coordinates of a point $C(u) = \sum_{i=0}^n (N_{i,p}(u)P_i)$ corresponding to the knot .

Parameters

u	: A real number which is between the extremities of the knot vector.

Returns: The coordinates of a point corresponding to the knot .

Definition at line 388 of file vpBSpline.cpp.

References computeBasisFuns(), p, vpImagePoint::set_i(), and vpImagePoint::set_j().

◆ computeCurvePoint() [3/4]

vpImagePoint vpNurbs::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 )

static

Compute the coordinates of a point $C(u) = \frac{\sum_{i=0}^n (N_{i,p}(u)w_iP_i)}{\sum_{i=0}^n (N_{i,p}(u)w_i)}$ corresponding to the knot .

Parameters

l_u	: A real number which is between the extremities of the knot vector.
l_i	: the number of the knot interval in which lies.
l_p	: Degree of the NURBS basis functions.
l_knots	: The knot vector.
l_controlPoints	: the list of control points.
l_weights	: the list of weights.

Returns: The coordinates of a point corresponding to the knot .

Examples: testNurbs.cpp.

Definition at line 56 of file vpNurbs.cpp.

References vpBSpline::computeBasisFuns(), vpImagePoint::set_i(), and vpImagePoint::set_j().

Referenced by vpMeNurbs::display(), and vpMeNurbs::display().

◆ computeCurvePoint() [4/4]

vpImagePoint vpNurbs::computeCurvePoint ( double u )

Compute the coordinates of a point $C(u) = \frac{\sum_{i=0}^n (N_{i,p}(u)w_iP_i)}{\sum_{i=0}^n (N_{i,p}(u)w_i)}$ corresponding to the knot .

Parameters

u	: A real number which is between the extremities of the knot vector

return the coordinates of a point corresponding to the knot .

Definition at line 81 of file vpNurbs.cpp.

References vpBSpline::computeBasisFuns(), vpBSpline::p, vpImagePoint::set_i(), vpImagePoint::set_j(), and weights.

◆ computeDersBasisFuns() [1/2]

vpBasisFunction ** vpBSpline::computeDersBasisFuns	(	double	l_u,
		unsigned int	l_i,
		unsigned int	l_p,
		unsigned int	l_der,
		const std::vector< double > &	l_knots )

staticinherited

Compute the nonzero basis functions and their derivatives until the th derivative. All the functions are computed at l_u.

Warning: The value of must be under or equal .

The result is given as an array of size l_der+1 x l_p+1. The kth line corresponds to the kth basis functions derivatives.

The formula to compute the kth derivative at is :

$\‍[ N_{i,p}^{(k)}(u) =p \left( \frac{N_{i,p-1}^{(k-1)}}{u_{i+p}-u_i} - \frac{N_{i+1,p-1}^{(k-1)}}{u_{i+p+1}-u_{i+1}} \right) \‍]$

where is the knot interval number in which lies and is the degree of the B-Spline basis function.

Parameters

l_u	: A real number which is between the extremities of the knot vector.
l_i	: The number of the knot interval in which lies.
l_p	: Degree of the B-Spline basis functions.
l_der	: The last derivative to be computed.
l_knots	: The knot vector.

Returns: the basis functions and their derivatives as an array of size l_der+1 x l_p+1. The kth line corresponds to the kth basis functions derivatives.

Example : return[0] is the list of the 0th derivatives ie the basis functions. return[k] is the list of the kth derivatives.

Examples: BSpline.cpp, and testNurbs.cpp.

Definition at line 211 of file vpBSpline.cpp.

References vpTRACE.

Referenced by computeCurveDers(), computeCurveDers(), vpNurbs::computeCurveDers(), vpNurbs::computeCurveDers(), and computeDersBasisFuns().

◆ computeDersBasisFuns() [2/2]

vpBasisFunction ** vpBSpline::computeDersBasisFuns	(	double	u,
		unsigned int	der ) const

inherited

Compute the nonzero basis functions and their derivatives until the th derivative. All the functions are computed at u.

Warning: The value of must be under or equal .

The result is given as an array of size der+1 x p+1. The kth line corresponds to the kth basis functions derivatives.

The formula to compute the kth derivative at is :

$\‍[ N_{i,p}^{(k)}(u) =p \left( \frac{N_{i,p-1}^{(k-1)}}{u_{i+p}-u_i} - \frac{N_{i+1,p-1}^{(k-1)}}{u_{i+p+1}-u_{i+1}} \right) \‍]$

where is the knot interval number in which lies and is the degree of the B-Spline basis function.

Parameters

u	: A real number which is between the extremities of the knot vector
der	: The last derivative to be computed.

Returns: The basis functions and their derivatives as an array of size der+1 x p+1. The kth line corresponds to the kth basis functions derivatives.

Example : return[0] is the list of the 0th derivatives ie the basis functions. return[k] is the list of the kth derivatives.

Definition at line 341 of file vpBSpline.cpp.

References computeDersBasisFuns(), findSpan(), knots, and p.

◆ curveKnotIns() [1/2]

void vpNurbs::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 )

static

Insert times a knot in the th interval of the knot vector. The inserted knot has multiplicity .

Of course the knot vector changes. But The list of control points and the list of the associated weights change too.

Parameters

l_u	: A real number which is between the extremities of the knot vector and which has to be inserted.
l_k	: The number of the knot interval in which lies.
l_s	: Multiplicity of
l_r	: Number of times has to be inserted.
l_p	: Degree of the NURBS basis functions.
l_knots	: The knot vector
l_controlPoints	: the list of control points.
l_weights	: the list of weights.

Definition at line 194 of file vpNurbs.cpp.

References vpImagePoint::set_ij().

Referenced by curveKnotIns().

◆ curveKnotIns() [2/2]

void vpNurbs::curveKnotIns	(	double	u,
		unsigned int	s = 0,
		unsigned int	r = 1 )

Insert times a knot in the th interval of the knot vector. The inserted knot has multiplicity .

Of course the knot vector changes. But The list of control points and the list of the associated weights change too.

Parameters

u	: A real number which is between the extremities of the knot vector and which has to be inserted.
s	: Multiplicity of .
r	: Number of times has to be inserted.

Definition at line 246 of file vpNurbs.cpp.

References curveKnotIns(), vpBSpline::findSpan(), vpBSpline::knots, vpBSpline::p, and weights.

◆ findSpan() [1/2]

unsigned int vpBSpline::findSpan	(	double	l_u,
		unsigned int	l_p,
		const std::vector< double > &	l_knots )

staticinherited

Find the knot interval in which the parameter lies. Indeed $l_u \in [u_i, u_{i+1}[$ .

Example : The knot vector is the following $U = \{0, 0 , 1 , 2 ,3 , 3\}$ with is equal to 1.

For equal to 0.5 the method will return 1.
For equal to 2.5 the method will return 3.
For equal to 3 the method will return 3.

Parameters

l_u	: The knot whose knot interval is seeked.
l_p	: Degree of the B-Spline basis functions.
l_knots	: The knot vector.

Returns: the number of the knot interval in which lies.

Examples: BSpline.cpp, and testNurbs.cpp.

Definition at line 63 of file vpBSpline.cpp.

References vpMath::maximum(), and vpMath::round().

Referenced by computeBasisFuns(), vpNurbs::computeCurveDersPoint(), computeDersBasisFuns(), vpNurbs::curveKnotIns(), findSpan(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), and vpNurbs::refineKnotVectCurve().

◆ findSpan() [2/2]

unsigned int vpBSpline::findSpan ( double u ) const

inherited

Find the knot interval in which the parameter lies. Indeed $u \in [u_i, u_{i+1}[$ .

Example : The knot vector is the following $U = \{0, 0 , 1 , 2 ,3 , 3\}$ with is equal to 1.

For equal to 0.5 the method will return 1.
For equal to 2.5 the method will return 3.
For equal to 3 the method will return 3.

Parameters

u	: The knot whose knot interval is seeked.

Returns: the number of the knot interval in which lies.

Definition at line 106 of file vpBSpline.cpp.

References findSpan(), knots, and p.

◆ get_controlPoints()

void vpBSpline::get_controlPoints ( std::list< vpImagePoint > & list ) const

inlineinherited

Gets all the control points.

Parameters

list	: A std::list containing the coordinates of the control points.

Examples: BSpline.cpp, and testNurbs.cpp.

Definition at line 135 of file vpBSpline.h.

◆ get_crossingPoints()

void vpBSpline::get_crossingPoints ( std::list< vpImagePoint > & list ) const

inlineinherited

Gets all the crossing points (used in the interpolation method)

Parameters

list	: A std::list containing the coordinates of the crossing points.

Definition at line 162 of file vpBSpline.h.

References crossingPoints.

◆ get_knots()

void vpBSpline::get_knots ( std::list< double > & list ) const

inlineinherited

Gets all the knots.

Parameters

list	: A std::list containing the value of the knots.

Examples: BSpline.cpp, and testNurbs.cpp.

Definition at line 148 of file vpBSpline.h.

References knots.

◆ get_p()

unsigned int vpBSpline::get_p ( ) const

inlineinherited

Gets the degree of the B-Spline.

Returns: the degree of the B-Spline.

Examples: BSpline.cpp, and testNurbs.cpp.

Definition at line 127 of file vpBSpline.h.

References p.

◆ get_weights()

void vpNurbs::get_weights ( std::list< double > & list ) const

inline

Gets all the weights relative to the control points.

Parameters

list	[out] : A std::list containing weights relative to the control points.

Examples: testNurbs.cpp.

Definition at line 178 of file vpNurbs.h.

References weights.

◆ globalCurveApprox() [1/5]

void vpNurbs::globalCurveApprox	(	const std::list< vpImagePoint > &	l_crossingPoints,
		unsigned int	n )

Method which enables to compute a NURBS curve approximating a set of data points.

The data points are approximated thanks to a least square method.

The result of the method is composed by a knot vector, a set of control points and a set of associated weights.

Parameters

l_crossingPoints	: The list of data points which have to be interpolated.
n	: The desired number of control points. The parameter n must be under or equal to the number of data points.

Definition at line 728 of file vpNurbs.cpp.

References globalCurveApprox(), vpBSpline::knots, vpBSpline::p, and weights.

◆ globalCurveApprox() [2/5]

void vpNurbs::globalCurveApprox	(	const std::list< vpMeSite > &	l_crossingPoints,
		unsigned int	n )

Method which enables to compute a NURBS curve approximating a set of data points.

The data points are approximated thanks to a least square method.

The result of the method is composed by a knot vector, a set of control points and a set of associated weights.

Parameters

l_crossingPoints	: The list of data points which have to be interpolated.
n	: The desired number of control points. This parameter n must be under or equal to the number of data points.

Definition at line 737 of file vpNurbs.cpp.

References globalCurveApprox(), vpBSpline::knots, vpBSpline::p, and weights.

◆ globalCurveApprox() [3/5]

void vpNurbs::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 )

static

Method which enables to compute a NURBS curve approximating a set of data points.

The data points are approximated thanks to a least square method.

The result of the method is composed by a knot vector, a set of control points and a set of associated weights.

Parameters

l_crossingPoints	: The list of data points which have to be interpolated.
l_p	: Degree of the NURBS basis functions.
l_n	: The desired number of control points. l_n must be under or equal to the number of data points.
l_knots	: The knot vector.
l_controlPoints	: the list of control points.
l_weights	: the list of weights.

Examples: testNurbs.cpp.

Definition at line 595 of file vpNurbs.cpp.

References vpMatrix::AtA(), vpBSpline::computeBasisFuns(), vpBSpline::findSpan(), vpMatrix::pseudoInverse(), and vpImagePoint::set_ij().

Referenced by globalCurveApprox(), globalCurveApprox(), globalCurveApprox(), and globalCurveApprox().

◆ globalCurveApprox() [4/5]

void vpNurbs::globalCurveApprox ( unsigned int n )

Method which enables to compute a NURBS curve approximating a set of data points.

The data points are approximated thanks to a least square method.

The result of the method is composed by a knot vector, a set of control points and a set of associated weights.

Definition at line 747 of file vpNurbs.cpp.

References vpBSpline::crossingPoints, globalCurveApprox(), vpBSpline::knots, vpBSpline::p, and weights.

◆ globalCurveApprox() [5/5]

void vpNurbs::globalCurveApprox	(	vpList< vpMeSite > &	l_crossingPoints,
		unsigned int	n )

Method which enables to compute a NURBS curve approximating a set of data points.

The data points are approximated thanks to a least square method.

The result of the method is composed by a knot vector, a set of control points and a set of associated weights.

Parameters

l_crossingPoints	: The list of data points which have to be interpolated.
n	: The desired number of control points. This parameter n must be under or equal to the number of data points.

Definition at line 714 of file vpNurbs.cpp.

References vpList< type >::front(), globalCurveApprox(), vpBSpline::knots, vpList< type >::next(), vpList< type >::outside(), vpBSpline::p, vpList< type >::value(), and weights.

◆ globalCurveInterp() [1/5]

void vpNurbs::globalCurveInterp ( )

Method which enables to compute a NURBS curve passing through a set of data points.

The result of the method is composed by a knot vector, a set of control points and a set of associated weights.

Definition at line 593 of file vpNurbs.cpp.

References vpBSpline::crossingPoints, globalCurveInterp(), vpBSpline::knots, vpBSpline::p, and weights.

Referenced by globalCurveInterp(), globalCurveInterp(), globalCurveInterp(), and globalCurveInterp().

◆ globalCurveInterp() [2/5]

void vpNurbs::globalCurveInterp ( const std::list< vpImagePoint > & l_crossingPoints )

Method which enables to compute a NURBS curve passing through a set of data points.

The result of the method is composed by a knot vector, a set of control points and a set of associated weights.

Parameters

l_crossingPoints : The list of data points which have to be interpolated.

Definition at line 564 of file vpNurbs.cpp.

References globalCurveInterp(), vpBSpline::knots, vpBSpline::p, and weights.

◆ globalCurveInterp() [3/5]

void vpNurbs::globalCurveInterp ( const std::list< vpMeSite > & l_crossingPoints )

Method which enables to compute a NURBS curve passing through a set of data points.

The result of the method is composed by a knot vector, a set of control points and a set of associated weights.

Parameters

l_crossingPoints : The list of data points which have to be interpolated.

Definition at line 574 of file vpNurbs.cpp.

References vpImagePoint::distance(), globalCurveInterp(), vpBSpline::knots, vpBSpline::p, and weights.

◆ globalCurveInterp() [4/5]

void vpNurbs::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 )

static

Method which enables to compute a NURBS curve passing through a set of data points.

The result of the method is composed by a knot vector, a set of control points and a set of associated weights.

Parameters

l_crossingPoints	: The list of data points which have to be interpolated.
l_p	: Degree of the NURBS basis functions. This value need to be > 0.
l_knots	: The knot vector.
l_controlPoints	: The list of control points.
l_weights	: the list of weights.

Examples: testNurbs.cpp.

Definition at line 466 of file vpNurbs.cpp.

References vpException::badValue, vpBSpline::computeBasisFuns(), vpBSpline::findSpan(), vpMatrix::pseudoInverse(), and vpImagePoint::set_ij().

◆ globalCurveInterp() [5/5]

void vpNurbs::globalCurveInterp ( vpList< vpMeSite > & l_crossingPoints )

Method which enables to compute a NURBS curve passing through a set of data points.

The result of the method is composed by a knot vector, a set of control points and a set of associated weights.

Parameters

l_crossingPoints : The list of data points which have to be interpolated.

Definition at line 543 of file vpNurbs.cpp.

References vpImagePoint::distance(), vpList< type >::front(), globalCurveInterp(), vpBSpline::knots, vpList< type >::next(), vpList< type >::outside(), vpBSpline::p, vpImagePoint::set_ij(), vpList< type >::value(), and weights.

◆ refineKnotVectCurve() [1/2]

void vpNurbs::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 )

static

Insert knots in the knot vector.

Of course the knot vector changes. But The list of control points and the list of the associated weights change too.

Parameters

l_x	: Several real numbers which are between the extremities of the knot vector and which have to be inserted.
l_r	: Number of knot in the array .
l_p	: Degree of the NURBS basis functions.
l_knots	: The knot vector
l_controlPoints	: the list of control points.
l_weights	: the list of weights.

Definition at line 253 of file vpNurbs.cpp.

References vpBSpline::findSpan().

Referenced by refineKnotVectCurve().

◆ refineKnotVectCurve() [2/2]

void vpNurbs::refineKnotVectCurve	(	double *	x,
		unsigned int	r )

Insert knots in the knot vector.

Of course the knot vector changes. But The list of control points and the list of the associated weights change too.

Parameters

x	: Several real numbers which are between the extremities of the knot vector and which have to be inserted.
r	: Number of knot in the array .

Definition at line 333 of file vpNurbs.cpp.

References vpBSpline::knots, vpBSpline::p, refineKnotVectCurve(), and weights.

◆ removeCurveKnot() [1/2]

unsigned int vpNurbs::removeCurveKnot	(	double	l_u,
		unsigned int	l_r,
		unsigned int	l_num,
		double	l_TOL )

Remove times the knot from the knot vector. The removed knot is the th vector in the knot vector.

Of course the knot vector changes. But The list of control points and the list of the associated weights change too.

Parameters

l_u	: A real number which is between the extremities of the knot vector and which has to be removed.
l_r	: Index of in the knot vector.
l_num	: Number of times has to be removed.
l_TOL	: A parameter which has to be computed.

Returns: The number of time that l_u was removed.

$TOL = \frac{dw_{min}}{1+|P|_{max}}$

where $w_{min}$ is the minimal weight on the original curve, $|P|_{max}$ is the maximum distance of any point on the original curve from the origin and is the desired bound on deviation.

Definition at line 461 of file vpNurbs.cpp.

References vpBSpline::knots, vpBSpline::p, removeCurveKnot(), and weights.

◆ removeCurveKnot() [2/2]

unsigned int vpNurbs::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 )

static

Remove times the knot from the knot vector. The removed knot is the th vector in the knot vector.

Of course the knot vector changes. But The list of control points and the list of the associated weights change too.

Parameters

l_u	: A real number which is between the extremities of the knot vector and which has to be removed.
l_r	: Index of in the knot vector.
l_num	: Number of times has to be removed.
l_TOL	: A parameter which has to be computed.
l_s	: Multiplicity of .
l_p	: Degree of the NURBS basis functions.
l_knots	: The knot vector
l_controlPoints	: the list of control points.
l_weights	: the list of weights.

Returns: The number of time that l_u was removed.

$l_{TOL} = \frac{dw_{min}}{1+|P|_{max}}$

where $w_{min}$ is the minimal weight on the original curve, $|P|_{max}$ is the maximum distance of any point on the original curve from the origin and is the desired bound on deviation.

Definition at line 338 of file vpNurbs.cpp.

References vpImagePoint::get_i(), vpImagePoint::get_j(), vpImagePoint::set_i(), vpImagePoint::set_j(), and vpMath::sqr().

Referenced by removeCurveKnot().

◆ set_controlPoints()

void vpBSpline::set_controlPoints ( const std::list< vpImagePoint > & list )

inlineinherited

Sets all the control points.

Parameters

list	: A std::list containing the coordinates of the control points

Examples: BSpline.cpp, and testNurbs.cpp.

Definition at line 182 of file vpBSpline.h.

◆ set_crossingPoints()

void vpBSpline::set_crossingPoints ( const std::list< vpImagePoint > & list )

inlineinherited

Sets all the crossing points (used in the interpolation method)

Parameters

list	: A std::list containing the coordinates of the crossing points

Definition at line 209 of file vpBSpline.h.

References crossingPoints.

◆ set_knots()

void vpBSpline::set_knots ( const std::list< double > & list )

inlineinherited

Sets all the knots.

Parameters

list	: A std::list containing the value of the knots.

Examples: BSpline.cpp, and testNurbs.cpp.

Definition at line 195 of file vpBSpline.h.

References knots.

◆ set_p()

void vpBSpline::set_p ( unsigned int degree )

inlineinherited

Sets the degree of the B-Spline.

Parameters

degree : the degree of the B-Spline.

Examples: BSpline.cpp, and testNurbs.cpp.

Definition at line 175 of file vpBSpline.h.

◆ set_weights()

void vpNurbs::set_weights ( const std::list< double > & list )

inline

Sets all the knots.

Parameters

list	: A std::list containing the value of the knots.

Examples: testNurbs.cpp.

Definition at line 190 of file vpNurbs.h.

References weights.

Member Data Documentation

◆ pad0

vpBSpline::__pad0__

inherited

Definition at line 236 of file vpBSpline.h.

◆ crossingPoints

std::vector<vpImagePoint> vpBSpline::crossingPoints

inherited

Vector which contains the points used during the interpolation method.

Definition at line 117 of file vpBSpline.h.

Referenced by get_crossingPoints(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), set_crossingPoints(), and vpBSpline().

◆ knots

std::vector<double> vpBSpline::knots

inherited

Vector which contain the knots .

Definition at line 113 of file vpBSpline.h.

Referenced by computeBasisFuns(), vpNurbs::computeCurveDersPoint(), computeDersBasisFuns(), vpNurbs::curveKnotIns(), findSpan(), get_knots(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), vpNurbs::globalCurveInterp(), vpNurbs::globalCurveInterp(), vpNurbs::globalCurveInterp(), vpNurbs::refineKnotVectCurve(), vpNurbs::removeCurveKnot(), set_knots(), and vpBSpline().

◆ p

unsigned int vpBSpline::p

inherited

Degree of the B-Spline basis functions.

Definition at line 115 of file vpBSpline.h.

◆ weights

std::vector<double> vpNurbs::weights

protected

Vector which contains the weights associated to each control Points.

Definition at line 96 of file vpNurbs.h.

Referenced by computeCurveDers(), computeCurveDersPoint(), computeCurvePoint(), curveKnotIns(), visp.python.rbt.xfeat.RBXFeatFeatureTracker.RBXFeatFeatureTracker::display(), get_weights(), globalCurveApprox(), globalCurveApprox(), globalCurveApprox(), globalCurveApprox(), globalCurveInterp(), globalCurveInterp(), globalCurveInterp(), globalCurveInterp(), visp.python.rbt.xfeat.RBXFeatFeatureTracker.RBXFeatFeatureTracker::initVVS(), refineKnotVectCurve(), removeCurveKnot(), set_weights(), vpNurbs(), and vpNurbs().

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ vpNurbs() [1/2]

◆ vpNurbs() [2/2]

Member Function Documentation

◆ computeBasisFuns() [1/2]

◆ computeBasisFuns() [2/2]

◆ computeCurveDers() [1/4]

◆ computeCurveDers() [2/4]

◆ computeCurveDers() [3/4]

◆ computeCurveDers() [4/4]

◆ computeCurveDersPoint() [1/2]

◆ computeCurveDersPoint() [2/2]

◆ computeCurvePoint() [1/4]

◆ computeCurvePoint() [2/4]

◆ computeCurvePoint() [3/4]

◆ computeCurvePoint() [4/4]

◆ computeDersBasisFuns() [1/2]

◆ computeDersBasisFuns() [2/2]

◆ curveKnotIns() [1/2]

◆ curveKnotIns() [2/2]

◆ findSpan() [1/2]

◆ findSpan() [2/2]

◆ get_controlPoints()

◆ get_crossingPoints()

◆ get_knots()

◆ get_p()

◆ get_weights()

◆ globalCurveApprox() [1/5]

◆ globalCurveApprox() [2/5]

◆ globalCurveApprox() [3/5]

◆ globalCurveApprox() [4/5]

◆ globalCurveApprox() [5/5]

◆ globalCurveInterp() [1/5]

◆ globalCurveInterp() [2/5]

◆ globalCurveInterp() [3/5]

◆ globalCurveInterp() [4/5]

◆ globalCurveInterp() [5/5]

◆ refineKnotVectCurve() [1/2]

◆ refineKnotVectCurve() [2/2]

◆ removeCurveKnot() [1/2]

◆ removeCurveKnot() [2/2]

◆ set_controlPoints()

◆ set_crossingPoints()

◆ set_knots()

◆ set_p()

◆ set_weights()

Member Data Documentation

◆ __pad0__

◆ crossingPoints

◆ knots

◆ p

◆ weights

◆ pad0