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

#include <Geom2d_BezierCurve.hxx>

Inheritance diagram for Geom2d_BezierCurve:

[legend]

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...

Detailed Description

Describes a rational or non-rational Bezier curve.

a non-rational Bezier curve is defined by a table of poles (also called control points),
a rational Bezier curve is defined by a table of poles with varying weights. These data are manipulated by two parallel arrays:
the poles table, which is an array of gp_Pnt2d points, and
the weights table, which is an array of reals. The bounds of these arrays are 1 and "the number of poles" of the curve. The poles of the curve are "control points" used to deform the curve. The first pole is the start point of the curve, and the last pole is the end point of the curve. The segment which joins the first pole to the second pole is the tangent to the curve at its start point, and the segment which joins the last pole to the second-from-last pole is the tangent to the curve at its end point. It is more difficult to give a geometric signification to the weights but they are useful for providing exact representations of the arcs of a circle or ellipse. Moreover, if the weights of all the poles are equal, the curve is polynomial; it is therefore a non-rational curve. The non-rational curve is a special and frequently used case. The weights are defined and used only in case of a rational curve. The degree of a Bezier curve is equal to the number of poles, minus 1. It must be greater than or equal to 1. However, the degree of a Geom2d_BezierCurve curve is limited to a value (25) which is defined and controlled by the system. This value is returned by the function MaxDegree. The parameter range for a Bezier curve is [ 0, 1 ]. If the first and last control points of the Bezier curve are the same point then the curve is closed. For example, to create a closed Bezier curve with four control points, you have to give a set of control points P1, P2, P3 and P1. The continuity of a Bezier curve is infinite. It is not possible to build a Bezier curve with negative weights. We consider that a weight value is zero if it is less than or equal to gp::Resolution(). We also consider that two weight values W1 and W2 are equal if: |W2 - W1| <= gp::Resolution(). Warning
When considering the continuity of a closed Bezier curve at the junction point, remember that a curve of this type is never periodic. This means that the derivatives for the parameter u = 0 have no reason to be the same as the derivatives for the parameter u = 1 even if the curve is closed.
The length of a Bezier curve can be null.

Constructor & Destructor Documentation

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.

Member Function Documentation

GeomAbs_Shape Geom2d_BezierCurve::Continuity ( ) const

virtual

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

Implements Geom2d_Curve.

Handle< Geom2d_Geometry > Geom2d_BezierCurve::Copy ( ) const

virtual

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

Implements Geom2d_Geometry.

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

virtual

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.

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

virtual

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.

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

virtual

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.

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

virtual

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".

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

virtual

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.

gp_Pnt2d Geom2d_BezierCurve::EndPoint ( ) const

virtual

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

Implements Geom2d_BoundedCurve.

Standard_Real Geom2d_BezierCurve::FirstParameter ( ) const

virtual

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`
	)

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`
	)

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.

Standard_Boolean Geom2d_BezierCurve::IsClosed ( ) const

virtual

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.

Standard_Boolean Geom2d_BezierCurve::IsCN ( const Standard_Integer N ) const

virtual

Continuity of the curve, returns True.

Implements Geom2d_Curve.

Standard_Boolean Geom2d_BezierCurve::IsPeriodic ( ) const

virtual

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.

Standard_Real Geom2d_BezierCurve::LastParameter ( ) const

virtual

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.

static Standard_Integer Geom2d_BezierCurve::MaxDegree ( )

static

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
	)

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.

void Geom2d_BezierCurve::Reverse ( )

virtual

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

Implements Geom2d_Curve.

Standard_Real Geom2d_BezierCurve::ReversedParameter ( const Standard_Real U ) const

virtual

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.

gp_Pnt2d Geom2d_BezierCurve::StartPoint ( ) const

virtual

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

Implements Geom2d_BoundedCurve.

void Geom2d_BezierCurve::Transform ( const gp_Trsf2d & T )

virtual

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.