Open CASCADE Technology 6.6.0
|
Describes a rational or non-rational Bezier curve
More...
#include <Geom_BezierCurve.hxx>
Public Member Functions | |
Geom_BezierCurve (const TColgp_Array1OfPnt &CurvePoles) | |
Creates a non rational Bezier curve with a set of poles CurvePoles. The weights are defaulted to all being 1. Raises ConstructionError if the number of poles is greater than MaxDegree + 1 or lower than 2. | |
Geom_BezierCurve (const TColgp_Array1OfPnt &CurvePoles, const TColStd_Array1OfReal &PoleWeights) | |
Creates a rational Bezier curve with the set of poles CurvePoles and the set of weights PoleWeights . If all the weights are identical the curve is considered as non rational. Raises ConstructionError if the number of poles is greater than MaxDegree + 1 or lower than 2 or CurvePoles and CurveWeights have not the same length or one weight value is lower or equal to Resolution from package gp. | |
void | Increase (const Standard_Integer Degree) |
Increases the degree of a bezier curve. Degree is the new degree of <me>. Raises ConstructionError if Degree is greater than MaxDegree or lower than 2 or lower than the initial degree of <me>. | |
void | InsertPoleAfter (const Standard_Integer Index, const gp_Pnt &P) |
Inserts a pole P after the pole of range Index. If the curve <me> is rational the weight value for the new pole of range Index is 1.0. //! raised if Index is not in the range [1, NbPoles] raised if the resulting number of poles is greater than MaxDegree + 1. | |
void | InsertPoleAfter (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight) |
Inserts a pole with its weight in the set of poles after the pole of range Index. If the curve was non rational it can become rational if all the weights are not identical. //! Raised if Index is not in the range [1, NbPoles] Raised if the resulting number of poles is greater than MaxDegree + 1. Raised if Weight is lower or equal to Resolution from package gp. | |
void | InsertPoleBefore (const Standard_Integer Index, const gp_Pnt &P) |
Inserts a pole P before the pole of range Index. If the curve <me> is rational the weight value for the new pole of range Index is 1.0. //! Raised if Index is not in the range [1, NbPoles] Raised if the resulting number of poles is greater than MaxDegree + 1. | |
void | InsertPoleBefore (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight) |
Inserts a pole with its weight in the set of poles after the pole of range Index. If the curve was non rational it can become rational if all the weights are not identical. //! Raised if Index is not in the range [1, NbPoles] Raised if the resulting number of poles is greater than MaxDegree + 1. Raised if Weight is lower or equal to Resolution from package gp. | |
void | RemovePole (const Standard_Integer Index) |
Removes the pole of range Index. If the curve was rational it can become non rational. //! Raised if Index is not in the range [1, NbPoles] //! Raised if Degree is lower than 2. | |
void | Reverse () |
Reverses the direction of parametrization of <me> Value (NewU) = Value (1 - OldU) | |
Standard_Real | ReversedParameter (const Standard_Real U) const |
Returns the parameter on the reversed curve for the point of parameter U on <me>. returns 1-U | |
void | Segment (const Standard_Real U1, const Standard_Real U2) |
Segments the curve between U1 and U2 which can be out of the bounds of the curve. The curve is oriented from U1 to U2. The control points are modified, the first and the last point are not the same but the parametrization range is [0, 1] else it could not be a Bezier curve. Warnings : Even if <me> is not closed it can become closed after the segmentation for example if U1 or U2 are out of the bounds of the curve <me> or if the curve makes loop. After the segmentation the length of a curve can be null. | |
void | SetPole (const Standard_Integer Index, const gp_Pnt &P) |
Substitutes the pole of range index with P. If the curve <me> is rational the weight of range Index is not modified. //! raiseD if Index is not in the range [1, NbPoles] | |
void | SetPole (const Standard_Integer Index, const gp_Pnt &P, const Standard_Real Weight) |
Substitutes the pole and the weights of range Index. If the curve <me> is not rational it can become rational if all the weights are not identical. If the curve was rational it can become non rational if all the weights are identical. //! Raised if Index is not in the range [1, NbPoles] //! Raised if Weight <= Resolution from package gp | |
void | SetWeight (const Standard_Integer Index, const Standard_Real Weight) |
Changes the weight of the pole of range Index. If the curve <me> is not rational it can become rational if all the weights are not identical. If the curve was rational it can become non rational if all the weights are identical. //! Raised if Index is not in the range [1, NbPoles] //! Raised if Weight <= Resolution from package gp | |
Standard_Boolean | IsClosed () const |
Returns True if the distance between the first point and the last point of the curve is lower or equal to the Resolution from package gp. | |
Standard_Boolean | IsCN (const Standard_Integer N) const |
Continuity of the curve, returns True. | |
Standard_Boolean | IsPeriodic () const |
Returns True if the parametrization of a curve is periodic. (P(u) = P(u + T) T = constante) | |
Standard_Boolean | IsRational () const |
Returns false if all the weights are identical. The tolerance criterion is Resolution from package gp. | |
GeomAbs_Shape | Continuity () const |
a Bezier curve is CN | |
Standard_Integer | Degree () const |
Returns the polynomial degree of the curve. it is the number of poles - 1 //! point P and derivatives (V1, V2, V3) computation The Bezier Curve has a Polynomial representation so the parameter U can be out of the bounds of the curve. | |
void | D0 (const Standard_Real U, gp_Pnt &P) const |
Returns in P the point of parameter U. If the curve is periodic then the returned point is P(U) with U = Ustart + (U - Uend) where Ustart and Uend are the parametric bounds of the curve. Raised only for the "OffsetCurve" if it is not possible to compute the current point. For example when the first derivative on the basis curve and the offset direction are parallel. | |
void | D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const |
Returns the point P of parameter U and the first derivative V1. //! Raised if the continuity of the curve is not C1. | |
void | D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const |
Returns the point P of parameter U, the first and second derivatives V1 and V2. //! Raised if the continuity of the curve is not C2. | |
void | D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const |
For this Bezier curve, computes | |
gp_Vec | DN (const Standard_Real U, const Standard_Integer N) const |
For the point of parameter U of this Bezier curve, computes the vector corresponding to the Nth derivative. Note: the parameter U can be outside the bounds of the curve. Exceptions Standard_RangeError if N is less than 1. | |
gp_Pnt | StartPoint () const |
Returns Value (U=0.), it is the first control point of the curve. | |
gp_Pnt | EndPoint () const |
Returns Value (U=1.), it is the last control point of the Bezier curve. | |
Standard_Real | FirstParameter () const |
Returns the value of the first parameter of this Bezier curve. This is 0.0, which gives the start point of this Bezier curve | |
Standard_Real | LastParameter () const |
Returns the value of the last parameter of this Bezier curve. This is 1.0, which gives the end point of this Bezier curve. | |
Standard_Integer | NbPoles () const |
Returns the number of poles of this Bezier curve. | |
gp_Pnt | Pole (const Standard_Integer Index) const |
Returns the pole of range Index. //! Raised if Index is not in the range [1, NbPoles] | |
void | Poles (TColgp_Array1OfPnt &P) const |
Returns all the poles of the curve. Raised if the length of P is not equal to the number of poles. | |
Standard_Real | Weight (const Standard_Integer Index) const |
Returns the weight of range Index. //! Raised if Index is not in the range [1, NbPoles] | |
void | Weights (TColStd_Array1OfReal &W) const |
Returns all the weights of the curve. Raised if the length of W is not equal to the number of poles. | |
void | Transform (const gp_Trsf &T) |
Applies the transformation T to this Bezier curve. | |
void | Resolution (const Standard_Real Tolerance3D, Standard_Real &UTolerance) |
Computes for this Bezier curve the parametric tolerance UTolerance for a given 3D tolerance Tolerance3D. If f(t) is the equation of this Bezier curve, UTolerance ensures that: |t1-t0| < UTolerance ===> |f(t1)-f(t0)| < Tolerance3D | |
Handle_Geom_Geometry | Copy () const |
Creates a new object which is a copy of this Bezier curve. | |
Static Public Member Functions | |
static Standard_Integer | MaxDegree () |
Returns the value of the maximum polynomial degree of any Geom_BezierCurve curve. This value is 25. |
Geom_BezierCurve::Geom_BezierCurve | ( | const TColgp_Array1OfPnt & | CurvePoles | ) |
Geom_BezierCurve::Geom_BezierCurve | ( | const TColgp_Array1OfPnt & | CurvePoles, |
const TColStd_Array1OfReal & | PoleWeights | ||
) |
GeomAbs_Shape Geom_BezierCurve::Continuity | ( | ) | const [virtual] |
Implements Geom_Curve.
Handle_Geom_Geometry Geom_BezierCurve::Copy | ( | ) | const [virtual] |
Implements Geom_Geometry.
void Geom_BezierCurve::D0 | ( | const Standard_Real | U, |
gp_Pnt & | P | ||
) | const [virtual] |
Implements Geom_Curve.
void Geom_BezierCurve::D1 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Vec & | V1 | ||
) | const [virtual] |
Implements Geom_Curve.
void Geom_BezierCurve::D2 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Vec & | V1, | ||
gp_Vec & | V2 | ||
) | const [virtual] |
Implements Geom_Curve.
void Geom_BezierCurve::D3 | ( | const Standard_Real | U, |
gp_Pnt & | P, | ||
gp_Vec & | V1, | ||
gp_Vec & | V2, | ||
gp_Vec & | V3 | ||
) | const [virtual] |
Implements Geom_Curve.
Standard_Integer Geom_BezierCurve::Degree | ( | ) | const |
gp_Vec Geom_BezierCurve::DN | ( | const Standard_Real | U, |
const Standard_Integer | N | ||
) | const [virtual] |
Implements Geom_Curve.
gp_Pnt Geom_BezierCurve::EndPoint | ( | ) | const [virtual] |
Implements Geom_BoundedCurve.
Standard_Real Geom_BezierCurve::FirstParameter | ( | ) | const [virtual] |
Implements Geom_Curve.
void Geom_BezierCurve::Increase | ( | const Standard_Integer | Degree | ) |
void Geom_BezierCurve::InsertPoleAfter | ( | const Standard_Integer | Index, |
const gp_Pnt & | P | ||
) |
void Geom_BezierCurve::InsertPoleAfter | ( | const Standard_Integer | Index, |
const gp_Pnt & | P, | ||
const Standard_Real | Weight | ||
) |
void Geom_BezierCurve::InsertPoleBefore | ( | const Standard_Integer | Index, |
const gp_Pnt & | P | ||
) |
void Geom_BezierCurve::InsertPoleBefore | ( | const Standard_Integer | Index, |
const gp_Pnt & | P, | ||
const Standard_Real | Weight | ||
) |
Standard_Boolean Geom_BezierCurve::IsClosed | ( | ) | const [virtual] |
Implements Geom_Curve.
Standard_Boolean Geom_BezierCurve::IsCN | ( | const Standard_Integer | N | ) | const [virtual] |
Implements Geom_Curve.
Standard_Boolean Geom_BezierCurve::IsPeriodic | ( | ) | const [virtual] |
Implements Geom_Curve.
Standard_Boolean Geom_BezierCurve::IsRational | ( | ) | const |
Standard_Real Geom_BezierCurve::LastParameter | ( | ) | const [virtual] |
Implements Geom_Curve.
static Standard_Integer Geom_BezierCurve::MaxDegree | ( | ) | [static] |
Standard_Integer Geom_BezierCurve::NbPoles | ( | ) | const |
gp_Pnt Geom_BezierCurve::Pole | ( | const Standard_Integer | Index | ) | const |
void Geom_BezierCurve::Poles | ( | TColgp_Array1OfPnt & | P | ) | const |
void Geom_BezierCurve::RemovePole | ( | const Standard_Integer | Index | ) |
void Geom_BezierCurve::Resolution | ( | const Standard_Real | Tolerance3D, |
Standard_Real & | UTolerance | ||
) |
void Geom_BezierCurve::Reverse | ( | ) | [virtual] |
Implements Geom_Curve.
Standard_Real Geom_BezierCurve::ReversedParameter | ( | const Standard_Real | U | ) | const [virtual] |
Implements Geom_Curve.
void Geom_BezierCurve::Segment | ( | const Standard_Real | U1, |
const Standard_Real | U2 | ||
) |
void Geom_BezierCurve::SetPole | ( | const Standard_Integer | Index, |
const gp_Pnt & | P | ||
) |
void Geom_BezierCurve::SetPole | ( | const Standard_Integer | Index, |
const gp_Pnt & | P, | ||
const Standard_Real | Weight | ||
) |
void Geom_BezierCurve::SetWeight | ( | const Standard_Integer | Index, |
const Standard_Real | Weight | ||
) |
gp_Pnt Geom_BezierCurve::StartPoint | ( | ) | const [virtual] |
Implements Geom_BoundedCurve.
void Geom_BezierCurve::Transform | ( | const gp_Trsf & | T | ) | [virtual] |
Implements Geom_Geometry.
Standard_Real Geom_BezierCurve::Weight | ( | const Standard_Integer | Index | ) | const |
void Geom_BezierCurve::Weights | ( | TColStd_Array1OfReal & | W | ) | const |