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

#include <Geom_BezierCurve.hxx>

Inheritance diagram for Geom_BezierCurve:

[legend]

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. More...

	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. 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_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]. More...

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]. More...

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]. More...

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]. 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] Raised if Degree is lower than 2. 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_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]. More...

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. 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 True if the parametrization of a curve is periodic. (P(u) = P(u + T) T = constante) 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
	a Bezier curve is CN More...

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. More...

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. More...

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. More...

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. More...

void	D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const
	For this Bezier curve, computes. More...

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. More...

gp_Pnt	StartPoint () const
	Returns Value (U=0.), it is the first control point of the curve. More...

gp_Pnt	EndPoint () const
	Returns Value (U=1.), it is the last control point of the 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 of this Bezier curve. More...

gp_Pnt	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_Array1OfPnt &P) const
	Returns all the poles 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_Trsf &T)
	Applies the transformation T to this Bezier curve. More...

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. More...

Handle< Geom_Geometry >	Copy () const
	Creates a new object which is a copy of this Bezier curve. More...

Public Member Functions inherited from Geom_Curve
virtual Standard_Real	TransformedParameter (const Standard_Real U, const gp_Trsf &T) const
	Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>. More...

virtual Standard_Real	ParametricTransformation (const gp_Trsf &T) const
	Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>. More...

Handle< Geom_Curve >	Reversed () const
	Returns a copy of <me> reversed. More...

virtual Standard_Real	Period () const
	Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic. More...

gp_Pnt	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. it is implemented with D0. More...

Public Member Functions inherited from Geom_Geometry
void	Mirror (const gp_Pnt &P)
	Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry. More...

void	Mirror (const gp_Ax1 &A1)
	Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry. More...

void	Mirror (const gp_Ax2 &A2)
	Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection). More...

void	Rotate (const gp_Ax1 &A1, const Standard_Real Ang)
	Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians. More...

void	Scale (const gp_Pnt &P, const Standard_Real S)
	Scales a Geometry. S is the scaling value. More...

void	Translate (const gp_Vec &V)
	Translates a Geometry. V is the vector of the tanslation. More...

void	Translate (const gp_Pnt &P1, const gp_Pnt &P2)
	Translates a Geometry from the point P1 to the point P2. More...

Handle< Geom_Geometry >	Mirrored (const gp_Pnt &P) const

Handle< Geom_Geometry >	Mirrored (const gp_Ax1 &A1) const

Handle< Geom_Geometry >	Mirrored (const gp_Ax2 &A2) const

Handle< Geom_Geometry >	Rotated (const gp_Ax1 &A1, const Standard_Real Ang) const

Handle< Geom_Geometry >	Scaled (const gp_Pnt &P, const Standard_Real S) const

Handle< Geom_Geometry >	Transformed (const gp_Trsf &T) const

Handle< Geom_Geometry >	Translated (const gp_Vec &V) const

Handle< Geom_Geometry >	Translated (const gp_Pnt &P1, const gp_Pnt &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 any Geom_BezierCurve curve. 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_Pnt 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 that joins the first pole to the second pole is the tangent to the curve at its start point, and the segment that 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 the exact representations of arcs of a circle or ellipse. Moreover, if the weights of all 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 the 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

However, the degree of a Geom_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 the 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

Geom_BezierCurve::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::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.

Member Function Documentation

GeomAbs_Shape Geom_BezierCurve::Continuity ( ) const

virtual

a Bezier curve is CN

Implements Geom_Curve.

Handle< Geom_Geometry > Geom_BezierCurve::Copy ( ) const

virtual

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

Implements Geom_Geometry.

void Geom_BezierCurve::D0	(	const Standard_Real	U,
		gp_Pnt &	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 Geom_Curve.

void Geom_BezierCurve::D1	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	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 Geom_Curve.

void Geom_BezierCurve::D2	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	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 Geom_Curve.

void Geom_BezierCurve::D3	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2,
		gp_Vec &	V3
	)		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.

Implements Geom_Curve.

Standard_Integer Geom_BezierCurve::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.

gp_Vec Geom_BezierCurve::DN	(	const Standard_Real	U,
		const Standard_Integer	N
	)		const

virtual

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.

Implements Geom_Curve.

gp_Pnt Geom_BezierCurve::EndPoint ( ) const

virtual

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

Implements Geom_BoundedCurve.

Standard_Real Geom_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 Geom_Curve.

void Geom_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 Geom_BezierCurve::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 Geom_BezierCurve::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 Geom_BezierCurve::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 Geom_BezierCurve::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.

Standard_Boolean Geom_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 Geom_Curve.

Standard_Boolean Geom_BezierCurve::IsCN ( const Standard_Integer N ) const

virtual

Continuity of the curve, returns True.

Implements Geom_Curve.

Standard_Boolean Geom_BezierCurve::IsPeriodic ( ) const

virtual

Returns True if the parametrization of a curve is periodic. (P(u) = P(u + T) T = constante)

Implements Geom_Curve.

Standard_Boolean Geom_BezierCurve::IsRational ( ) const

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

Standard_Real Geom_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 Geom_Curve.

static Standard_Integer Geom_BezierCurve::MaxDegree ( )

static

Returns the value of the maximum polynomial degree of any Geom_BezierCurve curve. This value is 25.

Standard_Integer Geom_BezierCurve::NbPoles ( ) const

Returns the number of poles of this Bezier curve.

gp_Pnt Geom_BezierCurve::Pole ( const Standard_Integer Index ) const

Returns the pole of range Index. Raised if Index is not in the range [1, NbPoles].

void Geom_BezierCurve::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.

void Geom_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] Raised if Degree is lower than 2.

void Geom_BezierCurve::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.

void Geom_BezierCurve::Reverse ( )

virtual

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

Implements Geom_Curve.

Standard_Real Geom_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 Geom_Curve.

void Geom_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 Geom_BezierCurve::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 Geom_BezierCurve::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 Geom_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_Pnt Geom_BezierCurve::StartPoint ( ) const

virtual

Returns Value (U=0.), it is the first control point of the curve.

Implements Geom_BoundedCurve.

void Geom_BezierCurve::Transform ( const gp_Trsf & T )

virtual

Applies the transformation T to this Bezier curve.

Implements Geom_Geometry.

Standard_Real Geom_BezierCurve::Weight ( const Standard_Integer Index ) const

Returns the weight of range Index. Raised if Index is not in the range [1, NbPoles].

void Geom_BezierCurve::Weights ( TColStd_Array1OfReal & W ) const

Returns all the weights of the curve.