Open CASCADE Technology 6.6.0
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Describes a rational or non-rational Bezier curve
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#include <Geom2d_BezierCurve.hxx>
Public Member Functions | |
Geom2d_BezierCurve (const TColgp_Array1OfPnt2d &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. | |
Geom2d_BezierCurve (const TColgp_Array1OfPnt2d &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_Pnt2d &P, const Standard_Real Weight=1.0) |
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 [0, NbPoles] Raised if the resulting number of poles is greater than MaxDegree + 1. | |
void | InsertPoleBefore (const Standard_Integer Index, const gp_Pnt2d &P, const Standard_Real Weight=1.0) |
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+1] Raised if the resulting number of poles is greater than MaxDegree + 1. | |
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] | |
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_Pnt2d &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_Pnt2d &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 False. A BezierCurve cannot be periodic in this package | |
Standard_Boolean | IsRational () const |
Returns false if all the weights are identical. The tolerance criterion is Resolution from package gp. | |
GeomAbs_Shape | Continuity () const |
Returns GeomAbs_CN, which is the continuity of any Bezier curve. | |
Standard_Integer | Degree () const |
Returns the polynomial degree of the curve. It is the number of poles less one. In this package the Degree of a Bezier curve cannot be greater than "MaxDegree". | |
void | D0 (const Standard_Real U, gp_Pnt2d &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_Pnt2d &P, gp_Vec2d &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_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &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_Pnt2d &P, gp_Vec2d &V1, gp_Vec2d &V2, gp_Vec2d &V3) const |
Returns the point P of parameter U, the first, the second and the third derivative. //! Raised if the continuity of the curve is not C3. | |
gp_Vec2d | DN (const Standard_Real U, const Standard_Integer N) const |
For this Bezier curve, computes | |
gp_Pnt2d | EndPoint () const |
Returns the end point or start point of this 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 for this Bezier curve. | |
gp_Pnt2d | 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_Array1OfPnt2d &P) const |
Returns all the poles of the curve. Raised if the length of P is not equal to the number of poles. | |
gp_Pnt2d | StartPoint () const |
Returns Value (U=1), it is the first control point of the curve. | |
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_Trsf2d &T) |
Applies the transformation T to this Bezier curve. | |
void | Resolution (const Standard_Real ToleranceUV, Standard_Real &UTolerance) |
Computes for this Bezier curve the parametric tolerance UTolerance for a given tolerance Tolerance3D (relative to dimensions in the plane). If f(t) is the equation of this Bezier curve, UTolerance ensures that | t1 - t0| < Utolerance ===> |f(t1) - f(t0)| < ToleranceUV | |
Handle_Geom2d_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 a BezierCurve. This value is 25. |
Geom2d_BezierCurve::Geom2d_BezierCurve | ( | const TColgp_Array1OfPnt2d & | CurvePoles | ) |
Geom2d_BezierCurve::Geom2d_BezierCurve | ( | const TColgp_Array1OfPnt2d & | CurvePoles, |
const TColStd_Array1OfReal & | PoleWeights | ||
) |
GeomAbs_Shape Geom2d_BezierCurve::Continuity | ( | ) | const [virtual] |
Implements Geom2d_Curve.
Handle_Geom2d_Geometry Geom2d_BezierCurve::Copy | ( | ) | const [virtual] |
Implements Geom2d_Geometry.
void Geom2d_BezierCurve::D0 | ( | const Standard_Real | U, |
gp_Pnt2d & | P | ||
) | const [virtual] |
Implements Geom2d_Curve.
void Geom2d_BezierCurve::D1 | ( | const Standard_Real | U, |
gp_Pnt2d & | P, | ||
gp_Vec2d & | V1 | ||
) | const [virtual] |
Implements Geom2d_Curve.
void Geom2d_BezierCurve::D2 | ( | const Standard_Real | U, |
gp_Pnt2d & | P, | ||
gp_Vec2d & | V1, | ||
gp_Vec2d & | V2 | ||
) | const [virtual] |
Implements Geom2d_Curve.
void Geom2d_BezierCurve::D3 | ( | const Standard_Real | U, |
gp_Pnt2d & | P, | ||
gp_Vec2d & | V1, | ||
gp_Vec2d & | V2, | ||
gp_Vec2d & | V3 | ||
) | const [virtual] |
Implements Geom2d_Curve.
Standard_Integer Geom2d_BezierCurve::Degree | ( | ) | const |
gp_Vec2d Geom2d_BezierCurve::DN | ( | const Standard_Real | U, |
const Standard_Integer | N | ||
) | const [virtual] |
Implements Geom2d_Curve.
gp_Pnt2d Geom2d_BezierCurve::EndPoint | ( | ) | const [virtual] |
Implements Geom2d_BoundedCurve.
Standard_Real Geom2d_BezierCurve::FirstParameter | ( | ) | const [virtual] |
Implements Geom2d_Curve.
void Geom2d_BezierCurve::Increase | ( | const Standard_Integer | Degree | ) |
void Geom2d_BezierCurve::InsertPoleAfter | ( | const Standard_Integer | Index, |
const gp_Pnt2d & | P, | ||
const Standard_Real | Weight = 1.0 |
||
) |
void Geom2d_BezierCurve::InsertPoleBefore | ( | const Standard_Integer | Index, |
const gp_Pnt2d & | P, | ||
const Standard_Real | Weight = 1.0 |
||
) |
Standard_Boolean Geom2d_BezierCurve::IsClosed | ( | ) | const [virtual] |
Implements Geom2d_Curve.
Standard_Boolean Geom2d_BezierCurve::IsCN | ( | const Standard_Integer | N | ) | const [virtual] |
Implements Geom2d_Curve.
Standard_Boolean Geom2d_BezierCurve::IsPeriodic | ( | ) | const [virtual] |
Implements Geom2d_Curve.
Standard_Boolean Geom2d_BezierCurve::IsRational | ( | ) | const |
Standard_Real Geom2d_BezierCurve::LastParameter | ( | ) | const [virtual] |
Implements Geom2d_Curve.
static Standard_Integer Geom2d_BezierCurve::MaxDegree | ( | ) | [static] |
Standard_Integer Geom2d_BezierCurve::NbPoles | ( | ) | const |
gp_Pnt2d Geom2d_BezierCurve::Pole | ( | const Standard_Integer | Index | ) | const |
void Geom2d_BezierCurve::Poles | ( | TColgp_Array1OfPnt2d & | P | ) | const |
void Geom2d_BezierCurve::RemovePole | ( | const Standard_Integer | Index | ) |
void Geom2d_BezierCurve::Resolution | ( | const Standard_Real | ToleranceUV, |
Standard_Real & | UTolerance | ||
) |
void Geom2d_BezierCurve::Reverse | ( | ) | [virtual] |
Implements Geom2d_Curve.
Standard_Real Geom2d_BezierCurve::ReversedParameter | ( | const Standard_Real | U | ) | const [virtual] |
Implements Geom2d_Curve.
void Geom2d_BezierCurve::Segment | ( | const Standard_Real | U1, |
const Standard_Real | U2 | ||
) |
void Geom2d_BezierCurve::SetPole | ( | const Standard_Integer | Index, |
const gp_Pnt2d & | P | ||
) |
void Geom2d_BezierCurve::SetPole | ( | const Standard_Integer | Index, |
const gp_Pnt2d & | P, | ||
const Standard_Real | Weight | ||
) |
void Geom2d_BezierCurve::SetWeight | ( | const Standard_Integer | Index, |
const Standard_Real | Weight | ||
) |
gp_Pnt2d Geom2d_BezierCurve::StartPoint | ( | ) | const [virtual] |
Implements Geom2d_BoundedCurve.
void Geom2d_BezierCurve::Transform | ( | const gp_Trsf2d & | T | ) | [virtual] |
Implements Geom2d_Geometry.
Standard_Real Geom2d_BezierCurve::Weight | ( | const Standard_Integer | Index | ) | const |
void Geom2d_BezierCurve::Weights | ( | TColStd_Array1OfReal & | W | ) | const |