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Public Member Functions | Static Public Member Functions | Protected Member Functions | Static Protected Member Functions | Protected Attributes | List of all members
vpNurbs Class Reference
ViSP capabilities » Mathematics » Other tools

#include <vpNurbs.h>

+ Inheritance diagram for vpNurbs:

Public Member Functions

 vpNurbs ()
 
 vpNurbs (const vpNurbs &nurbs)
 
virtual ~vpNurbs ()
 
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)
 
vpBasisFunction * computeBasisFuns (double u)
 
vpBasisFunction ** computeDersBasisFuns (double u, unsigned int der)
 
Deprecated functions
vp_deprecated vpList< double > get_weights () const
 
vp_deprecated void set_weights (vpList< double > &list)
 
vp_deprecated void globalCurveApprox (vpList< vpImagePoint > &l_crossingPoints, unsigned int n)
 
vp_deprecated void globalCurveInterp (vpList< vpImagePoint > &l_crossingPoints)
 
Deprecated functions
vp_deprecated vpList< vpImagePoint > get_controlPoints () const
 
vp_deprecated vpList< double > get_knots () const
 
vp_deprecated vpList< vpImagePoint > get_crossingPoints () const
 
vp_deprecated void set_controlPoints (vpList< vpImagePoint > &list)
 
vp_deprecated void set_knots (vpList< double > &list)
 
vp_deprecated void set_crossingPoints (vpList< vpImagePoint > &list)
 

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, std::vector< double > &l_knots)
 
static vpBasisFunction * computeBasisFuns (double l_u, unsigned int l_i, unsigned int l_p, std::vector< double > &l_knots)
 
static vpBasisFunction ** computeDersBasisFuns (double l_u, unsigned int l_i, unsigned int l_p, unsigned int l_der, std::vector< double > &l_knots)
 
static vpImagePoint computeCurvePoint (double l_u, unsigned int l_i, unsigned int l_p, std::vector< double > &l_knots, std::vector< vpImagePoint > &l_controlPoints)
 
static vpImagePoint * 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)
 

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 $ u_i, i = 0, ...,m $ 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 $ a $ and $ b $ 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 $ i = 0 , ... , m-1 $ and p is the degree of the B-Spline basis functions.

  • The control points $ {P_i} $ which are defined by the coordinates $ (i,j) $ of a point in an image.
  • The weight $ {w_i} $ 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 $ u $ ( $ 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:
Nurbs.cpp.

Definition at line 89 of file vpNurbs.h.

Constructor & Destructor Documentation

vpNurbs::vpNurbs ( )

Basic constructor.

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

Definition at line 66 of file vpNurbs.cpp.

vpNurbs::vpNurbs ( const vpNurbs &  nurbs)

Copy constructor.

Definition at line 75 of file vpNurbs.cpp.

References weights.

vpNurbs::~vpNurbs ( )
virtual

Basic destructor

Definition at line 83 of file vpNurbs.cpp.

Member Function Documentation

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

Compute the nonvanishing basis functions at $ l_u $ which is in the $ l_i $ 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 extrimities of the knot vector
l_i: the number of the knot interval in which $ l_u $ lies
l_p: Degree of the B-Spline basis functions.
l_knots: The knot vector
Returns
An array containing the nonvanishing basis functions at $ l_u $. The size of the array is $ l_p +1 $.
Examples:
BSpline.cpp, and Nurbs.cpp.

Definition at line 152 of file vpBSpline.cpp.

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

vpBasisFunction * vpBSpline::computeBasisFuns ( double  u)
inherited

Compute the nonvanishing basis functions at $ u $. 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 $ u $ lies.

Parameters
u: A real number which is between the extrimities of the knot vector
Returns
An array containing the nonvanishing basis functions at $ u $. The size of the array is $ p +1 $.

Definition at line 203 of file vpBSpline.cpp.

References vpBSpline::computeBasisFuns(), and vpBSpline::findSpan().

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 $ C(u) $ 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 $ i $ is the knot interval number in which $ u $ lies, $ p $ is the degree of the NURBS basis function and $ Pw_i = (P_i w_i) $ contains the control points and the associatede weights.

Parameters
l_u: A real number which is between the extrimities of the knot vector
l_i: the number of the knot interval in which $ l_u $ 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 coresponds to the coordinates (i,j) of the point and the third column corresponds to the associated weight.

Definition at line 181 of file vpNurbs.cpp.

References vpBSpline::computeDersBasisFuns().

Referenced by computeCurveDersPoint().

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

This function is used in the computeCurveDersPoint method.

Compute the kth derivatives of $ C(u) $ for $ k = 0, ... , der $.

The formula used is the following :

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

where $ i $ is the knot interval number in which $ u $ lies, $ p $ is the degree of the NURBS basis function and $ Pw_i = (P_i w_i) $ contains the control points and the associatede weights.

Parameters
u: A real number which is between the extrimities 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 $ k = 0, ... , der $. The kth derivative is in the kth line of the matrix. For each lines the first and the second column coresponds to the coordinates (i,j) of the point and the third column corresponds to the associated weight.

Definition at line 229 of file vpNurbs.cpp.

References vpBSpline::computeDersBasisFuns(), and weights.

vpImagePoint * vpBSpline::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 
)
staticinherited

Compute the kth derivatives of $ C(u) $ 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 $ i $ is the knot interval number in which $ u $ lies and $ p $ is the degree of the B-Spline basis function.

Parameters
l_u: A real number which is between the extrimities of the knot vector
l_i: the number of the knot interval in which $ l_u $ 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 $ k = 0, ... , l_der $. The kth derivative is in the kth cell of the array.

Definition at line 456 of file vpBSpline.cpp.

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

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 $ C(u) $ 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 extrimities of the knot vector
l_i: the number of the knot interval in which $ l_u $ 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 270 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(), vpMeNurbs::localReSample(), vpMeNurbs::sample(), vpMeNurbs::seekExtremities(), and vpMeNurbs::updateDelta().

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

Compute the kth derivatives of $ C(u) $ 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 extrimities 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 $ k = 0, ... , der $. The kth derivative is in the kth cell of the array.

Definition at line 317 of file vpNurbs.cpp.

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

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 $ u $.

Parameters
l_u: A real number which is between the extrimities of the knot vector
l_i: the number of the knot interval in which $ l_u $ 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.

return the coordinates of a point corresponding to the knot $ u $.

Examples:
Nurbs.cpp.

Definition at line 100 of file vpNurbs.cpp.

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

Referenced by vpMeNurbs::display(), vpMeNurbs::localReSample(), vpMeNurbs::track(), and vpMeNurbs::updateDelta().

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 $ u $.

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

return the coordinates of a point corresponding to the knot $ u $.

Definition at line 134 of file vpNurbs.cpp.

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

vpImagePoint vpBSpline::computeCurvePoint ( double  l_u,
unsigned int  l_i,
unsigned int  l_p,
std::vector< double > &  l_knots,
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 $ u $.

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

return the coordinates of a point corresponding to the knot $ u $.

Examples:
BSpline.cpp.

Definition at line 387 of file vpBSpline.cpp.

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

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

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

Warning
$ l_der $ must be under or equal $ l_p $.

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 $ u $ 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 $ i $ is the knot interval number in which $ u $ lies and $ p $ is the degree of the B-Spline basis function.

Parameters
l_u: A real number which is between the extrimities of the knot vector
l_i: the number of the knot interval in which $ l_u $ 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 Nurbs.cpp.

Definition at line 233 of file vpBSpline.cpp.

References vpTRACE.

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

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

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

Warning
$ der $ must be under or equal $ p $.

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 $ u $ 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 $ i $ is the knot interval number in which $ u $ lies and $ p $ is the degree of the B-Spline basis function.

Parameters
u: A real number which is between the extrimities 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 369 of file vpBSpline.cpp.

References vpBSpline::computeDersBasisFuns(), and vpBSpline::findSpan().

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 $ l_r $ times a knot in the $ l_k $ th interval of the knot vector. The inserted knot $ l_u $ has multiplicity $ l_s $.

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 extrimities of the knot vector and which has to be inserted.
l_k: The number of the knot interval in which $ l_u $ lies.
l_s: Multiplicity of $ l_u $
l_r: Number of times $ l_u $ 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 338 of file vpNurbs.cpp.

References vpMatrix::insert(), and vpImagePoint::set_ij().

Referenced by curveKnotIns().

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

Insert $ r $ times a knot in the $ k $ th interval of the knot vector. The inserted knot $ u $ has multiplicity $ s $.

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 extrimities of the knot vector and which has to be inserted.
s: Multiplicity of $ l_u $
r: Number of times $ l_u $ has to be inserted.

Definition at line 402 of file vpNurbs.cpp.

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

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

Find the knot interval in which the parameter $ l_u $ 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 $ p $ is equal to 1.

  • For $ l_u $ equal to 0.5 the method will retun 1.
  • For $ l_u $ equal to 2.5 the method will retun 3.
  • For $ l_u $ equal to 3 the method will retun 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 $ l_u $ lies.
Examples:
BSpline.cpp, and Nurbs.cpp.

Definition at line 92 of file vpBSpline.cpp.

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

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

unsigned int vpBSpline::findSpan ( double  u)
inherited

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

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

  • For $ u $ equal to 0.5 the method will retun 1.
  • For $ u $ equal to 2.5 the method will retun 3.
  • For $ u $ equal to 3 the method will retun 3.
Parameters
u: The knot whose knot interval is seeked.
Returns
the number of the knot interval in which $ u $ lies.

Definition at line 134 of file vpBSpline.cpp.

References vpBSpline::findSpan().

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 Nurbs.cpp.

Definition at line 139 of file vpBSpline.h.

vp_deprecated vpList<vpImagePoint> vpBSpline::get_controlPoints ( ) const
inlineinherited
Deprecated:
This method is deprecated. You should use get_controlPoints(std::list<vpImagePoint> &) const instead.

Gets all the control points.
Returns
list : A vpList containing the coordinates of the control points

Definition at line 237 of file vpBSpline.h.

References vpList< type >::addRight().

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 161 of file vpBSpline.h.

vp_deprecated vpList<vpImagePoint> vpBSpline::get_crossingPoints ( ) const
inlineinherited
Deprecated:
This method is deprecated. You should use get_crossingPoints(std::list<vpImagePoint> &) const instead.

Gets all the crossing points (used in the interpolation method)
Returns
list : A vpList containing the coordinates of the crossing points

Definition at line 259 of file vpBSpline.h.

References vpList< type >::addRight().

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 Nurbs.cpp.

Definition at line 150 of file vpBSpline.h.

vp_deprecated vpList<double> vpBSpline::get_knots ( ) const
inlineinherited
Deprecated:
This method is deprecated. You should use get_knots(std::list<double> &) const instead.

Gets all the knots.
Returns
list : A vpList containing the value of the knots.

Definition at line 248 of file vpBSpline.h.

References vpList< type >::addRight().

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 Nurbs.cpp.

Definition at line 132 of file vpBSpline.h.

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

Gets all the weights relative to the control points.

Returns
list : A std::list containing weights relative to the control points.
Examples:
Nurbs.cpp.

Definition at line 110 of file vpNurbs.h.

vp_deprecated vpList<double> vpNurbs::get_weights ( ) const
inline
Deprecated:
This method is deprecated. You should use get_weights(std::list<double> &) const instead.

Gets all the weights relative to the control points.
Returns
list : A list containing weights relative to the control points.

Definition at line 165 of file vpNurbs.h.

References vpList< type >::addRight().

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:
Nurbs.cpp.

Definition at line 876 of file vpNurbs.cpp.

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

Referenced by globalCurveApprox(), and vpMeNurbs::track().

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 1015 of file vpNurbs.cpp.

References vpList< type >::front(), globalCurveApprox(), vpMeSite::ifloat, vpMeSite::jfloat, vpList< type >::next(), vpList< type >::outside(), vpList< type >::value(), and weights.

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 1039 of file vpNurbs.cpp.

References globalCurveApprox(), and weights.

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 1064 of file vpNurbs.cpp.

References globalCurveApprox(), and weights.

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 1082 of file vpNurbs.cpp.

References globalCurveApprox(), and weights.

void vpNurbs::globalCurveApprox ( vpList< vpImagePoint > &  l_crossingPoints,
unsigned int  n 
)
Deprecated:
This method is deprecated. You should use globalCurveApprox(const std::list<vpImagePoint> &, unsigned int) instead.

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 1121 of file vpNurbs.cpp.

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

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:
Nurbs.cpp.

Definition at line 700 of file vpNurbs.cpp.

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

Referenced by vpMeNurbs::initTracking().

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 785 of file vpNurbs.cpp.

References vpImagePoint::distance(), vpList< type >::front(), globalCurveInterp(), vpMeSite::ifloat, vpMeSite::jfloat, vpList< type >::next(), vpList< type >::outside(), vpImagePoint::set_ij(), vpList< type >::value(), and weights.

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 815 of file vpNurbs.cpp.

References globalCurveInterp(), and weights.

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 832 of file vpNurbs.cpp.

References vpImagePoint::distance(), globalCurveInterp(), vpMeSite::ifloat, vpMeSite::jfloat, and weights.

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 856 of file vpNurbs.cpp.

References weights.

Referenced by globalCurveInterp().

void vpNurbs::globalCurveInterp ( vpList< vpImagePoint > &  l_crossingPoints)
Deprecated:
This method is deprecated. You should use globalCurveInterp(const std::list<vpImagePoint> &) instead.

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 1097 of file vpNurbs.cpp.

References vpList< type >::front(), globalCurveInterp(), vpList< type >::next(), vpList< type >::outside(), vpList< type >::value(), and weights.

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 $ l_r $ 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 extrimities of the knot vector and which have to be inserted.
l_r: Number of knot in the array $ l_x $.
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 421 of file vpNurbs.cpp.

References vpBSpline::findSpan(), and vpImagePoint::set_i().

Referenced by refineKnotVectCurve().

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

Insert $ r $ 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 extrimities of the knot vector and which have to be inserted.
r: Number of knot in the array $ l_x $.

Definition at line 514 of file vpNurbs.cpp.

References refineKnotVectCurve(), and weights.

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 $ l_num $ times the knot $ l_u $ from the knot vector. The removed knot $ l_u $ is the $ l_r $ 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 extrimities of the knot vector and which has to be removed.
l_r: Index of $ l_u $ in the knot vector.
l_num: Number of times $ l_u $ has to be removed.
l_TOL: A parameter which has to be computed.
l_s: Multiplicity of $ l_u $.
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 $ d $ is the desired bound on deviation.

Definition at line 542 of file vpNurbs.cpp.

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

Referenced by removeCurveKnot().

unsigned int vpNurbs::removeCurveKnot ( double  u,
unsigned int  r,
unsigned int  num,
double  TOL 
)

Remove $ num $ times the knot $ u $ from the knot vector. The removed knot $ u $ is the $ r $ 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
u: A real number which is between the extrimities of the knot vector and which has to be removed.
r: Index of $ l_u $ in the knot vector.
num: Number of times $ l_u $ has to be removed.
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 $ d $ is the desired bound on deviation.

Definition at line 683 of file vpNurbs.cpp.

References removeCurveKnot(), and weights.

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 Nurbs.cpp.

Definition at line 181 of file vpBSpline.h.

vp_deprecated void vpBSpline::set_controlPoints ( vpList< vpImagePoint > &  list)
inlineinherited
Deprecated:
This method is deprecated. You should use set_controlPoints(const std::list<vpImagePoint> &) instead.

Sets all the control points.
Parameters
list: A vpList containing the coordinates of the control points

Definition at line 270 of file vpBSpline.h.

References vpList< type >::front(), vpList< type >::nbElements(), vpList< type >::next(), and vpList< type >::value().

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 205 of file vpBSpline.h.

vp_deprecated void vpBSpline::set_crossingPoints ( vpList< vpImagePoint > &  list)
inlineinherited
Deprecated:
This method is deprecated. You should use set_crossingPoints(const std::list<vpImagePoint> &) instead.

Sets all the crossing points (used in the interpolation method)
Parameters
list: A vpList containing the coordinates of the crossing points

Definition at line 302 of file vpBSpline.h.

References vpList< type >::front(), vpList< type >::nbElements(), vpList< type >::next(), and vpList< type >::value().

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 Nurbs.cpp.

Definition at line 193 of file vpBSpline.h.

vp_deprecated void vpBSpline::set_knots ( vpList< double > &  list)
inlineinherited
Deprecated:
This method is deprecated. You should use set_knots(const std::list<double> &) instead.

Sets all the knots.
Parameters
list: A vpList containing the value of the knots.

Definition at line 286 of file vpBSpline.h.

References vpList< type >::front(), vpList< type >::nbElements(), vpList< type >::next(), and vpList< type >::value().

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 Nurbs.cpp.

Definition at line 173 of file vpBSpline.h.

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:
Nurbs.cpp.

Definition at line 121 of file vpNurbs.h.

vp_deprecated void vpNurbs::set_weights ( vpList< double > &  list)
inline
Deprecated:
This method is deprecated. You should use set_weights(const std::list<double>&) instead.

Sets all the knots.
Parameters
list: A list containing the value of the knots.

Definition at line 176 of file vpNurbs.h.

References vpList< type >::front(), vpList< type >::nbElements(), vpList< type >::next(), and vpList< type >::value().

Member Data Documentation

std::vector<double> vpNurbs::weights
protected

Definition at line 92 of file vpNurbs.h.

Referenced by computeCurveDers(), computeCurveDersPoint(), computeCurvePoint(), curveKnotIns(), globalCurveApprox(), globalCurveInterp(), refineKnotVectCurve(), removeCurveKnot(), and vpNurbs().