Open CASCADE Technology  7.6.0.dev
Public Member Functions | Static Public Member Functions
Geom2d_BezierCurve Class Reference

Describes a rational or non-rational Bezier curve. More...

#include <Geom2d_BezierCurve.hxx>

Inheritance diagram for Geom2d_BezierCurve:
Inheritance graph
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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 () override
 Reverses the direction of parametrization of <me> Value (NewU) = Value (1 - OldU) More...
 
Standard_Real ReversedParameter (const Standard_Real U) const override
 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 override
 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 override
 Continuity of the curve, returns True. More...
 
Standard_Boolean IsPeriodic () const override
 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 override
 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 override
 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 override
 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 override
 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 override
 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 override
 For this Bezier curve, computes. More...
 
gp_Pnt2d EndPoint () const override
 Returns the end point or start point of this Bezier curve. More...
 
Standard_Real FirstParameter () const override
 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 override
 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...
 
const gp_Pnt2dPole (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...
 
const TColgp_Array1OfPnt2dPoles () const
 Returns all the poles of the curve. More...
 
gp_Pnt2d StartPoint () const override
 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...
 
const TColStd_Array1OfRealWeights () const
 Returns all the weights of the curve. More...
 
void Transform (const gp_Trsf2d &T) override
 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_GeometryCopy () const override
 Creates a new object which is a copy of this Bezier curve. More...
 
virtual void DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const override
 Dumps the content of me into the stream. 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_CurveReversed () 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_GeometryMirrored (const gp_Pnt2d &P) const
 
Handle< Geom2d_GeometryMirrored (const gp_Ax2d &A) const
 
Handle< Geom2d_GeometryRotated (const gp_Pnt2d &P, const Standard_Real Ang) const
 
Handle< Geom2d_GeometryScaled (const gp_Pnt2d &P, const Standard_Real S) const
 
Handle< Geom2d_GeometryTransformed (const gp_Trsf2d &T) const
 
Handle< Geom2d_GeometryTranslated (const gp_Vec2d &V) const
 
Handle< Geom2d_GeometryTranslated (const gp_Pnt2d &P1, const gp_Pnt2d &P2) const
 
- Public Member Functions inherited from Standard_Transient
 Standard_Transient ()
 Empty constructor. More...
 
 Standard_Transient (const Standard_Transient &)
 Copy constructor – does nothing. More...
 
Standard_Transientoperator= (const Standard_Transient &)
 Assignment operator, needed to avoid copying reference counter. More...
 
virtual ~Standard_Transient ()
 Destructor must be virtual. More...
 
virtual void Delete () const
 Memory deallocator for transient classes. More...
 
virtual const opencascade::handle< Standard_Type > & DynamicType () const
 Returns a type descriptor about this object. More...
 
Standard_Boolean IsInstance (const opencascade::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 opencascade::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...
 
Standard_TransientThis () const
 Returns non-const pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero. More...
 
Standard_Integer GetRefCount () const
 Get the reference counter of this object. More...
 
void IncrementRefCounter () const
 Increments the reference counter of this object. More...
 
Standard_Integer DecrementRefCounter () const
 Decrements the reference counter of this object; returns the decremented value. 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...
 
- Static Public Member Functions inherited from Standard_Transient
static const char * get_type_name ()
 Returns a type descriptor about this object. More...
 
static const opencascade::handle< Standard_Type > & get_type_descriptor ()
 Returns type descriptor of Standard_Transient class. More...
 

Additional Inherited Members

- Public Types inherited from Standard_Transient
typedef void base_type
 Returns a type descriptor about this object. More...
 

Detailed Description

Describes a rational or non-rational Bezier curve.

Constructor & Destructor Documentation

◆ Geom2d_BezierCurve() [1/2]

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() [2/2]

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.

Member Function Documentation

◆ Continuity()

GeomAbs_Shape Geom2d_BezierCurve::Continuity ( ) const
overridevirtual

Returns GeomAbs_CN, which is the continuity of any Bezier curve.

Implements Geom2d_Curve.

◆ Copy()

Handle< Geom2d_Geometry > Geom2d_BezierCurve::Copy ( ) const
overridevirtual

Creates a new object which is a copy of this Bezier curve.

Implements Geom2d_Geometry.

◆ D0()

void Geom2d_BezierCurve::D0 ( const Standard_Real  U,
gp_Pnt2d P 
) const
overridevirtual

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.

◆ D1()

void Geom2d_BezierCurve::D1 ( const Standard_Real  U,
gp_Pnt2d P,
gp_Vec2d V1 
) const
overridevirtual

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.

◆ D2()

void Geom2d_BezierCurve::D2 ( const Standard_Real  U,
gp_Pnt2d P,
gp_Vec2d V1,
gp_Vec2d V2 
) const
overridevirtual

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.

◆ D3()

void Geom2d_BezierCurve::D3 ( const Standard_Real  U,
gp_Pnt2d P,
gp_Vec2d V1,
gp_Vec2d V2,
gp_Vec2d V3 
) const
overridevirtual

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.

◆ Degree()

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".

◆ DN()

gp_Vec2d Geom2d_BezierCurve::DN ( const Standard_Real  U,
const Standard_Integer  N 
) const
overridevirtual

For this Bezier curve, computes.

  • the point P of parameter U, or
  • the point P and one or more of the following values:
  • V1, the first derivative vector,
  • V2, the second derivative vector,
  • V3, the third derivative vector. Note: the parameter U can be outside the bounds of the curve. Raises RangeError if N < 1.

Implements Geom2d_Curve.

◆ DumpJson()

virtual void Geom2d_BezierCurve::DumpJson ( Standard_OStream theOStream,
Standard_Integer  theDepth = -1 
) const
overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom2d_BoundedCurve.

◆ EndPoint()

gp_Pnt2d Geom2d_BezierCurve::EndPoint ( ) const
overridevirtual

Returns the end point or start point of this Bezier curve.

Implements Geom2d_BoundedCurve.

◆ FirstParameter()

Standard_Real Geom2d_BezierCurve::FirstParameter ( ) const
overridevirtual

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.

◆ Increase()

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>.

◆ InsertPoleAfter()

void Geom2d_BezierCurve::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.

◆ InsertPoleBefore()

void Geom2d_BezierCurve::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.

◆ IsClosed()

Standard_Boolean Geom2d_BezierCurve::IsClosed ( ) const
overridevirtual

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.

◆ IsCN()

Standard_Boolean Geom2d_BezierCurve::IsCN ( const Standard_Integer  N) const
overridevirtual

Continuity of the curve, returns True.

Implements Geom2d_Curve.

◆ IsPeriodic()

Standard_Boolean Geom2d_BezierCurve::IsPeriodic ( ) const
overridevirtual

Returns False. A BezierCurve cannot be periodic in this package.

Implements Geom2d_Curve.

◆ IsRational()

Standard_Boolean Geom2d_BezierCurve::IsRational ( ) const

Returns false if all the weights are identical. The tolerance criterion is Resolution from package gp.

◆ LastParameter()

Standard_Real Geom2d_BezierCurve::LastParameter ( ) const
overridevirtual

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.

◆ MaxDegree()

static Standard_Integer Geom2d_BezierCurve::MaxDegree ( )
static

Returns the value of the maximum polynomial degree of a BezierCurve. This value is 25.

◆ NbPoles()

Standard_Integer Geom2d_BezierCurve::NbPoles ( ) const

Returns the number of poles for this Bezier curve.

◆ Pole()

const 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].

◆ Poles() [1/2]

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.

◆ Poles() [2/2]

const TColgp_Array1OfPnt2d& Geom2d_BezierCurve::Poles ( ) const
inline

Returns all the poles of the curve.

◆ RemovePole()

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].

◆ Resolution()

void Geom2d_BezierCurve::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.

◆ Reverse()

void Geom2d_BezierCurve::Reverse ( )
overridevirtual

Reverses the direction of parametrization of <me> Value (NewU) = Value (1 - OldU)

Implements Geom2d_Curve.

◆ ReversedParameter()

Standard_Real Geom2d_BezierCurve::ReversedParameter ( const Standard_Real  U) const
overridevirtual

Returns the parameter on the reversed curve for the point of parameter U on <me>.

returns 1-U

Implements Geom2d_Curve.

◆ Segment()

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.

◆ SetPole() [1/2]

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].

◆ SetPole() [2/2]

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.

◆ SetWeight()

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.

◆ StartPoint()

gp_Pnt2d Geom2d_BezierCurve::StartPoint ( ) const
overridevirtual

Returns Value (U=1), it is the first control point of the curve.

Implements Geom2d_BoundedCurve.

◆ Transform()

void Geom2d_BezierCurve::Transform ( const gp_Trsf2d T)
overridevirtual

Applies the transformation T to this Bezier curve.

Implements Geom2d_Geometry.

◆ Weight()

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].

◆ Weights() [1/2]

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.

◆ Weights() [2/2]

const TColStd_Array1OfReal* Geom2d_BezierCurve::Weights ( ) const
inline

Returns all the weights of the curve.


The documentation for this class was generated from the following file: