Open CASCADE Technology
6.9.1
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Describes a rational or non-rational Bezier curve. More...
#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. More... | |
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. More... | |
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>. More... | |
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]. More... | |
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]. More... | |
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]. More... | |
void | Reverse () |
Reverses the direction of parametrization of <me> Value (NewU) = Value (1 - OldU) More... | |
Standard_Real | ReversedParameter (const Standard_Real U) const |
Returns the parameter on the reversed curve for the point of parameter U on <me>. More... | |
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. More... | |
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]. More... | |
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. More... | |
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. More... | |
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. More... | |
Standard_Boolean | IsCN (const Standard_Integer N) const |
Continuity of the curve, returns True. More... | |
Standard_Boolean | IsPeriodic () const |
Returns False. A BezierCurve cannot be periodic in this package. More... | |
Standard_Boolean | IsRational () const |
Returns false if all the weights are identical. The tolerance criterion is Resolution from package gp. More... | |
GeomAbs_Shape | Continuity () const |
Returns GeomAbs_CN, which is the continuity of any Bezier curve. More... | |
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". More... | |
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. More... | |
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. More... | |
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. More... | |
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. More... | |
gp_Vec2d | DN (const Standard_Real U, const Standard_Integer N) const |
For this Bezier curve, computes. More... | |
gp_Pnt2d | EndPoint () const |
Returns the end point or start point of this Bezier curve. More... | |
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. More... | |
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. More... | |
Standard_Integer | NbPoles () const |
Returns the number of poles for this Bezier curve. More... | |
gp_Pnt2d | Pole (const Standard_Integer Index) const |
Returns the pole of range Index. Raised if Index is not in the range [1, NbPoles]. More... | |
void | Poles (TColgp_Array1OfPnt2d &P) const |
Returns all the poles of the curve. More... | |
gp_Pnt2d | StartPoint () const |
Returns Value (U=1), it is the first control point of the curve. More... | |
Standard_Real | Weight (const Standard_Integer Index) const |
Returns the weight of range Index. Raised if Index is not in the range [1, NbPoles]. More... | |
void | Weights (TColStd_Array1OfReal &W) const |
Returns all the weights of the curve. More... | |
void | Transform (const gp_Trsf2d &T) |
Applies the transformation T to this Bezier curve. More... | |
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. More... | |
Handle< Geom2d_Geometry > | Copy () const |
Creates a new object which is a copy of this Bezier curve. More... | |
Public Member Functions inherited from Geom2d_Curve | |
virtual Standard_Real | TransformedParameter (const Standard_Real U, const gp_Trsf2d &T) const |
Computes the parameter on the curve transformed by T for the point of parameter U on this curve. Note: this function generally returns U but it can be redefined (for example, on a line). More... | |
virtual Standard_Real | ParametricTransformation (const gp_Trsf2d &T) const |
Returns the coefficient required to compute the parametric transformation of this curve when transformation T is applied. This coefficient is the ratio between the parameter of a point on this curve and the parameter of the transformed point on the new curve transformed by T. Note: this function generally returns 1. but it can be redefined (for example, on a line). More... | |
Handle< Geom2d_Curve > | Reversed () const |
Creates a reversed duplicate Changes the orientation of this curve. The first and last parameters are not changed, but the parametric direction of the curve is reversed. If the curve is bounded: More... | |
virtual Standard_Real | Period () const |
Returns thne period of this curve. raises if the curve is not periodic. More... | |
gp_Pnt2d | Value (const Standard_Real U) const |
Computes the point of parameter U on <me>. 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. More... | |
Public Member Functions inherited from Geom2d_Geometry | |
void | Mirror (const gp_Pnt2d &P) |
Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry and assigns the result to this geometric object. More... | |
void | Mirror (const gp_Ax2d &A) |
Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More... | |
void | Rotate (const gp_Pnt2d &P, const Standard_Real Ang) |
Rotates a Geometry. P is the center of the rotation. Ang is the angular value of the rotation in radians. More... | |
void | Scale (const gp_Pnt2d &P, const Standard_Real S) |
Scales a Geometry. S is the scaling value. More... | |
void | Translate (const gp_Vec2d &V) |
Translates a Geometry. V is the vector of the tanslation. More... | |
void | Translate (const gp_Pnt2d &P1, const gp_Pnt2d &P2) |
Translates a Geometry from the point P1 to the point P2. More... | |
Handle< Geom2d_Geometry > | Mirrored (const gp_Pnt2d &P) const |
Handle< Geom2d_Geometry > | Mirrored (const gp_Ax2d &A) const |
Handle< Geom2d_Geometry > | Rotated (const gp_Pnt2d &P, const Standard_Real Ang) const |
Handle< Geom2d_Geometry > | Scaled (const gp_Pnt2d &P, const Standard_Real S) const |
Handle< Geom2d_Geometry > | Transformed (const gp_Trsf2d &T) const |
Handle< Geom2d_Geometry > | Translated (const gp_Vec2d &V) const |
Handle< Geom2d_Geometry > | Translated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const |
Public Member Functions inherited from MMgt_TShared | |
virtual void | Delete () const |
Memory deallocator for transient classes. More... | |
Public Member Functions inherited from Standard_Transient | |
Standard_Transient () | |
Empty constructor. More... | |
Standard_Transient (const Standard_Transient &) | |
Copy constructor – does nothing. More... | |
Standard_Transient & | operator= (const Standard_Transient &) |
Assignment operator, needed to avoid copying reference counter. More... | |
virtual | ~Standard_Transient () |
Destructor must be virtual. More... | |
virtual const Handle_Standard_Type & | DynamicType () const |
Returns a type information object about this object. More... | |
Standard_Boolean | IsInstance (const Handle_Standard_Type &theType) const |
Returns a true value if this is an instance of Type. More... | |
Standard_Boolean | IsInstance (const Standard_CString theTypeName) const |
Returns a true value if this is an instance of TypeName. More... | |
Standard_Boolean | IsKind (const Handle_Standard_Type &theType) const |
Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More... | |
Standard_Boolean | IsKind (const Standard_CString theTypeName) const |
Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism. More... | |
virtual Handle_Standard_Transient | This () const |
Returns a Handle which references this object. Must never be called to objects created in stack. More... | |
Standard_Integer | GetRefCount () const |
Get the reference counter of this object. More... | |
Static Public Member Functions | |
static Standard_Integer | MaxDegree () |
Returns the value of the maximum polynomial degree of a BezierCurve. This value is 25. More... | |
Describes a rational or non-rational Bezier curve.
Geom2d_BezierCurve::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::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.
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Returns GeomAbs_CN, which is the continuity of any Bezier curve.
Implements Geom2d_Curve.
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Creates a new object which is a copy of this Bezier curve.
Implements Geom2d_Geometry.
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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.
Implements Geom2d_Curve.
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Returns the point P of parameter U and the first derivative V1. Raised if the continuity of the curve is not C1.
Implements Geom2d_Curve.
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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.
Implements Geom2d_Curve.
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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.
Implements Geom2d_Curve.
Standard_Integer Geom2d_BezierCurve::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".
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For this Bezier curve, computes.
Implements Geom2d_Curve.
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Returns the end point or start point of this Bezier curve.
Implements Geom2d_BoundedCurve.
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Returns the value of the first parameter of this Bezier curve. This is 0.0, which gives the start point of this Bezier curve.
Implements Geom2d_Curve.
void Geom2d_BezierCurve::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 Geom2d_BezierCurve::InsertPoleAfter | ( | const Standard_Integer | Index, |
const gp_Pnt2d & | P, | ||
const Standard_Real | Weight = 1.0 |
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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 Geom2d_BezierCurve::InsertPoleBefore | ( | const Standard_Integer | Index, |
const gp_Pnt2d & | P, | ||
const Standard_Real | Weight = 1.0 |
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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.
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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.
Implements Geom2d_Curve.
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Continuity of the curve, returns True.
Implements Geom2d_Curve.
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Returns False. A BezierCurve cannot be periodic in this package.
Implements Geom2d_Curve.
Standard_Boolean Geom2d_BezierCurve::IsRational | ( | ) | const |
Returns false if all the weights are identical. The tolerance criterion is Resolution from package gp.
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Returns the value of the last parameter of this Bezier curve. This is 1.0, which gives the end point of this Bezier curve.
Implements Geom2d_Curve.
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Returns the value of the maximum polynomial degree of a BezierCurve. This value is 25.
Standard_Integer Geom2d_BezierCurve::NbPoles | ( | ) | const |
Returns the number of poles for this Bezier curve.
gp_Pnt2d Geom2d_BezierCurve::Pole | ( | const Standard_Integer | Index | ) | const |
Returns the pole of range Index. Raised if Index is not in the range [1, NbPoles].
void Geom2d_BezierCurve::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.
void Geom2d_BezierCurve::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 Geom2d_BezierCurve::Resolution | ( | const Standard_Real | ToleranceUV, |
Standard_Real & | UTolerance | ||
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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.
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Reverses the direction of parametrization of <me> Value (NewU) = Value (1 - OldU)
Implements Geom2d_Curve.
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Returns the parameter on the reversed curve for the point of parameter U on <me>.
returns 1-U
Implements Geom2d_Curve.
void Geom2d_BezierCurve::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 Geom2d_BezierCurve::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 Geom2d_BezierCurve::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 Geom2d_BezierCurve::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.
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Returns Value (U=1), it is the first control point of the curve.
Implements Geom2d_BoundedCurve.
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Applies the transformation T to this Bezier curve.
Implements Geom2d_Geometry.
Standard_Real Geom2d_BezierCurve::Weight | ( | const Standard_Integer | Index | ) | const |
Returns the weight of range Index. Raised if Index is not in the range [1, NbPoles].
void Geom2d_BezierCurve::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.