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Visual Servoing Platform
version 3.3.0
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#include <vpNurbs.h>
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) |
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 |
Class that provides tools to compute and manipulate a Non Uniform Rational B-Spline curve.
The different parameters are :
The B-Spline basis functions defined as :
where and p is the degree of the B-Spline basis functions.
It is possible to compute the coordinates of a point corresponding to the knots (
) thanks to the formula :
You can find much more information about the B-Splines and the implementation of all the methods in the Nurbs Book.
vpNurbs::vpNurbs | ( | ) |
Basic constructor.
The degree of the NURBS basis functions is set to 3 to compute cubic NURBS.
Definition at line 59 of file vpNurbs.cpp.
vpNurbs::vpNurbs | ( | const vpNurbs & | nurbs | ) |
Copy constructor.
Definition at line 64 of file vpNurbs.cpp.
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virtual |
Basic destructor
Definition at line 69 of file vpNurbs.cpp.
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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 = ,
,
, ... ,
, ...,
, ... ,
, ... ,
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_p | : Degree of the B-Spline basis functions. |
l_knots | : The knot vector |
Definition at line 147 of file vpBSpline.cpp.
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inherited |
Compute the nonvanishing basis functions at . All the basis functions are stored in an array such as :
N = ,
,
, ... ,
, ...,
, ... ,
, ... ,
where i the number of the knot interval in which lies.
u | : A real number which is between the extrimities of the knot vector |
Definition at line 198 of file vpBSpline.cpp.
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staticinherited |
Compute the kth derivatives of for
.
The formula used is the following :
where is the knot interval number in which
lies and
is the degree of the B-Spline basis function.
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_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. |
Definition at line 450 of file vpBSpline.cpp.
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staticprotected |
This function is used in the computeCurveDersPoint method.
Compute the kth derivatives of for
.
The formula used is the following :
where is the knot interval number in which
lies,
is the degree of the NURBS basis function and
contains the control points and the associatede weights.
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_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. |
Definition at line 169 of file vpNurbs.cpp.
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protected |
This function is used in the computeCurveDersPoint method.
Compute the kth derivatives of for
.
The formula used is the following :
where is the knot interval number in which
lies,
is the degree of the NURBS basis function and
contains the control points and the associatede weights.
u | : A real number which is between the extrimities of the knot vector |
der | : The last derivative to be computed. |
Definition at line 219 of file vpNurbs.cpp.
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static |
Compute the kth derivatives of for
.
To see how the derivatives are computed refers to the Nurbs book.
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_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. |
Definition at line 259 of file vpNurbs.cpp.
vpImagePoint * vpNurbs::computeCurveDersPoint | ( | double | u, |
unsigned int | der | ||
) |
Compute the kth derivatives of for
.
To see how the derivatives are computed refers to the Nurbs book.
u | : A real number which is between the extrimities of the knot vector |
der | : The last derivative to be computed. |
Definition at line 302 of file vpNurbs.cpp.
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staticinherited |
Compute the coordinates of a point corresponding to the knot
.
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_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 .
Definition at line 380 of file vpBSpline.cpp.
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static |
Compute the coordinates of a point corresponding to the knot
.
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_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 .
Definition at line 84 of file vpNurbs.cpp.
vpImagePoint vpNurbs::computeCurvePoint | ( | double | u | ) |
Compute the coordinates of a point corresponding to the knot
.
u | : A real number which is between the extrimities of the knot vector |
return the coordinates of a point corresponding to the knot .
Definition at line 118 of file vpNurbs.cpp.
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staticinherited |
Compute the nonzero basis functions and their derivatives until the th derivative. All the functions are computed at l_u.
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 :
where is the knot interval number in which
lies and
is the degree of the B-Spline basis function.
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_p | : Degree of the B-Spline basis functions. |
l_der | : The last derivative to be computed. |
l_knots | : The knot vector |
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 233 of file vpBSpline.cpp.
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inherited |
Compute the nonzero basis functions and their derivatives until the th derivative. All the functions are computed at u.
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 :
where is the knot interval number in which
lies and
is the degree of the B-Spline basis function.
u | : A real number which is between the extrimities of the knot vector |
der | : The last derivative to be computed. |
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 363 of file vpBSpline.cpp.
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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.
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_s | : Multiplicity of ![]() |
l_r | : Number of times ![]() |
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 324 of file vpNurbs.cpp.
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.
u | : A real number which is between the extrimities of the knot vector and which has to be inserted. |
s | : Multiplicity of ![]() |
r | : Number of times ![]() |
Definition at line 387 of file vpNurbs.cpp.
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staticinherited |
Find the knot interval in which the parameter lies. Indeed
Example : The knot vector is the following with
is equal to 1.
l_u | : The knot whose knot interval is seeked. |
l_p | : Degree of the B-Spline basis functions. |
l_knots | : The knot vector |
Definition at line 83 of file vpBSpline.cpp.
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inherited |
Find the knot interval in which the parameter lies. Indeed
Example : The knot vector is the following with
is equal to 1.
u | : The knot whose knot interval is seeked. |
Definition at line 128 of file vpBSpline.cpp.
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inlineinherited |
Gets all the control points.
list | : A std::list containing the coordinates of the control points. |
Definition at line 139 of file vpBSpline.h.
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inlineinherited |
Gets all the crossing points (used in the interpolation method)
list | : A std::list containing the coordinates of the crossing points. |
Definition at line 166 of file vpBSpline.h.
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inlineinherited |
Gets all the knots.
list | : A std::list containing the value of the knots. |
Definition at line 152 of file vpBSpline.h.
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inlineinherited |
Gets the degree of the B-Spline.
Definition at line 131 of file vpBSpline.h.
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inline |
Gets all the weights relative to the control points.
list | [out] : A std::list containing weights relative to the control points. |
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.
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 1022 of file vpNurbs.cpp.
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.
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 1047 of file vpNurbs.cpp.
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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.
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. |
Definition at line 865 of file vpNurbs.cpp.
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 1066 of file vpNurbs.cpp.
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.
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 996 of file vpNurbs.cpp.
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 847 of file vpNurbs.cpp.
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.
l_crossingPoints | : The list of data points which have to be interpolated. |
Definition at line 802 of file vpNurbs.cpp.
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.
l_crossingPoints | : The list of data points which have to be interpolated. |
Definition at line 821 of file vpNurbs.cpp.
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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.
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. |
Definition at line 684 of file vpNurbs.cpp.
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.
l_crossingPoints | : The list of data points which have to be interpolated. |
Definition at line 771 of file vpNurbs.cpp.
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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.
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_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 406 of file vpNurbs.cpp.
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.
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 ![]() |
Definition at line 495 of file vpNurbs.cpp.
unsigned int vpNurbs::removeCurveKnot | ( | double | u, |
unsigned int | r, | ||
unsigned int | num, | ||
double | 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.
u | : A real number which is between the extrimities of the knot vector and which has to be removed. |
r | : Index of ![]() |
num | : Number of times ![]() |
TOL | : A parameter which has to be computed. |
where is the minimal weight on the original curve,
is the maximum distance of any point on the original curve from the origin and
is the desired bound on deviation.
Definition at line 667 of file vpNurbs.cpp.
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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.
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_num | : Number of times ![]() |
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. |
where is the minimal weight on the original curve,
is the maximum distance of any point on the original curve from the origin and
is the desired bound on deviation.
Definition at line 525 of file vpNurbs.cpp.
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inlineinherited |
Sets all the control points.
list | : A std::list containing the coordinates of the control points |
Definition at line 186 of file vpBSpline.h.
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inlineinherited |
Sets all the crossing points (used in the interpolation method)
list | : A std::list containing the coordinates of the crossing points |
Definition at line 213 of file vpBSpline.h.
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inlineinherited |
Sets all the knots.
list | : A std::list containing the value of the knots. |
Definition at line 199 of file vpBSpline.h.
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inlineinherited |
Sets the degree of the B-Spline.
degree | : the degree of the B-Spline. |
Definition at line 179 of file vpBSpline.h.
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inline |
Sets all the knots.
list | : A std::list containing the value of the knots. |