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Visual Servoing Platform version 3.6.0
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#include <vpBSpline.h>
Public Member Functions | |
vpBSpline () | |
vpBSpline (const vpBSpline &bspline) | |
virtual | ~vpBSpline () |
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) |
vpImagePoint | computeCurvePoint (double u) |
vpImagePoint * | computeCurveDers (double u, unsigned int der) |
Static Public Member Functions | |
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) |
Public Attributes | |
: std::vector<vpImagePoint> controlPoints | |
std::vector< double > | knots |
unsigned int | p |
std::vector< vpImagePoint > | crossingPoints |
Class that provides tools to compute and manipulate a B-Spline curve.
The different parameters are :
where
It is possible to compute the coordinates of a point corresponding to the knots
You can find much more information about the B-Splines and the implementation of all the methods in the Nurbs Book.
Definition at line 105 of file vpBSpline.h.
vpBSpline::vpBSpline | ( | ) |
Basic constructor.
The degree
Definition at line 45 of file vpBSpline.cpp.
vpBSpline::vpBSpline | ( | const vpBSpline & | bspline | ) |
Copy constructor.
Definition at line 54 of file vpBSpline.cpp.
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virtual |
Basic destructor.
Definition at line 61 of file vpBSpline.cpp.
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Compute the nonvanishing basis functions at
N =
l_u | : A real number which is between the extremities 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 142 of file vpBSpline.cpp.
Referenced by computeBasisFuns(), computeCurvePoint(), vpNurbs::computeCurvePoint(), computeCurvePoint(), vpNurbs::computeCurvePoint(), vpNurbs::globalCurveApprox(), and vpNurbs::globalCurveInterp().
vpBasisFunction * vpBSpline::computeBasisFuns | ( | double | u | ) |
Compute the nonvanishing basis functions at
N =
where i the number of the knot interval in which
u | : A real number which is between the extremities of the knot vector |
Definition at line 193 of file vpBSpline.cpp.
References computeBasisFuns(), findSpan(), knots, and p.
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Compute the kth derivatives of
The formula used is the following :
where
l_u | : A real number which is between the extremities 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 445 of file vpBSpline.cpp.
References computeDersBasisFuns(), vpImagePoint::set_i(), vpImagePoint::set_ij(), vpImagePoint::set_j(), and vpTRACE.
vpImagePoint * vpBSpline::computeCurveDers | ( | double | u, |
unsigned int | der | ||
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Compute the kth derivatives of
The formula used is the following :
where
u | : A real number which is between the extremities of the knot vector |
der | : The last derivative to be computed. |
Definition at line 492 of file vpBSpline.cpp.
References computeDersBasisFuns(), p, vpImagePoint::set_i(), vpImagePoint::set_ij(), vpImagePoint::set_j(), and vpTRACE.
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Compute the coordinates of a point
l_u | : A real number which is between the extremities 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 375 of file vpBSpline.cpp.
References computeBasisFuns(), vpImagePoint::set_i(), and vpImagePoint::set_j().
vpImagePoint vpBSpline::computeCurvePoint | ( | double | u | ) |
Compute the coordinates of a point
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 404 of file vpBSpline.cpp.
References computeBasisFuns(), p, vpImagePoint::set_i(), and vpImagePoint::set_j().
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Compute the nonzero basis functions and their derivatives until the
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
where
l_u | : A real number which is between the extremities 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 228 of file vpBSpline.cpp.
References vpTRACE.
Referenced by computeCurveDers(), vpNurbs::computeCurveDers(), computeCurveDers(), vpNurbs::computeCurveDers(), and computeDersBasisFuns().
vpBasisFunction ** vpBSpline::computeDersBasisFuns | ( | double | u, |
unsigned int | der | ||
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Compute the nonzero basis functions and their derivatives until the
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
where
u | : A real number which is between the extremities 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 358 of file vpBSpline.cpp.
References computeDersBasisFuns(), findSpan(), knots, and p.
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Find the knot interval in which the parameter
Example : The knot vector is the following
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 79 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().
unsigned int vpBSpline::findSpan | ( | double | u | ) |
Find the knot interval in which the parameter
Example : The knot vector is the following
u | : The knot whose knot interval is seeked. |
Definition at line 123 of file vpBSpline.cpp.
References findSpan(), knots, and p.
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Gets all the control points.
list | : A std::list containing the coordinates of the control points. |
Definition at line 135 of file vpBSpline.h.
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Gets all the crossing points (used in the interpolation method)
list | : A std::list containing the coordinates of the crossing points. |
Definition at line 162 of file vpBSpline.h.
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Gets all the knots.
list | : A std::list containing the value of the knots. |
Definition at line 148 of file vpBSpline.h.
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Gets the degree of the B-Spline.
Definition at line 127 of file vpBSpline.h.
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Sets all the control points.
list | : A std::list containing the coordinates of the control points |
Definition at line 182 of file vpBSpline.h.
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Sets all the crossing points (used in the interpolation method)
list | : A std::list containing the coordinates of the crossing points |
Definition at line 209 of file vpBSpline.h.
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Sets all the knots.
list | : A std::list containing the value of the knots. |
Definition at line 195 of file vpBSpline.h.
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Sets the degree of the B-Spline.
degree | : the degree of the B-Spline. |
Definition at line 175 of file vpBSpline.h.
vpBSpline::__pad0__ |
Definition at line 105 of file vpBSpline.h.
std::vector<vpImagePoint> vpBSpline::crossingPoints |
Vector wich contains the points used during the interpolation method.
Definition at line 115 of file vpBSpline.h.
Referenced by vpNurbs::globalCurveApprox(), and vpNurbs::globalCurveInterp().
std::vector<double> vpBSpline::knots |
Vector which contain the knots
Definition at line 111 of file vpBSpline.h.
Referenced by computeBasisFuns(), vpNurbs::computeCurveDersPoint(), computeDersBasisFuns(), vpNurbs::curveKnotIns(), findSpan(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), vpNurbs::globalCurveInterp(), vpNurbs::globalCurveInterp(), vpNurbs::globalCurveInterp(), vpNurbs::refineKnotVectCurve(), and vpNurbs::removeCurveKnot().
unsigned int vpBSpline::p |
Degree of the B-Spline basis functions.
Definition at line 113 of file vpBSpline.h.
Referenced by computeBasisFuns(), computeCurveDers(), vpNurbs::computeCurveDers(), vpNurbs::computeCurveDersPoint(), computeCurvePoint(), vpNurbs::computeCurvePoint(), computeDersBasisFuns(), vpNurbs::curveKnotIns(), findSpan(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveApprox(), vpNurbs::globalCurveInterp(), vpNurbs::globalCurveInterp(), vpNurbs::globalCurveInterp(), vpNurbs::globalCurveInterp(), vpNurbs::refineKnotVectCurve(), vpNurbs::removeCurveKnot(), and vpNurbs::vpNurbs().