// This file is generated by WOK (CPPExt). // Please do not edit this file; modify original file instead. // The copyright and license terms as defined for the original file apply to // this header file considered to be the "object code" form of the original source. #ifndef _Geom2d_BezierCurve_HeaderFile #define _Geom2d_BezierCurve_HeaderFile #ifndef _Standard_HeaderFile #include #endif #ifndef _Standard_DefineHandle_HeaderFile #include #endif #ifndef _Handle_Geom2d_BezierCurve_HeaderFile #include #endif #ifndef _Standard_Boolean_HeaderFile #include #endif #ifndef _Handle_TColgp_HArray1OfPnt2d_HeaderFile #include #endif #ifndef _Handle_TColStd_HArray1OfReal_HeaderFile #include #endif #ifndef _Standard_Integer_HeaderFile #include #endif #ifndef _Standard_Real_HeaderFile #include #endif #ifndef _Geom2d_BoundedCurve_HeaderFile #include #endif #ifndef _GeomAbs_Shape_HeaderFile #include #endif #ifndef _Handle_Geom2d_Geometry_HeaderFile #include #endif class TColgp_HArray1OfPnt2d; class TColStd_HArray1OfReal; class Standard_ConstructionError; class Standard_DimensionError; class Standard_RangeError; class Standard_OutOfRange; class TColgp_Array1OfPnt2d; class TColStd_Array1OfReal; class gp_Pnt2d; class gp_Vec2d; class gp_Trsf2d; class Geom2d_Geometry; //! 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.
class Geom2d_BezierCurve : public Geom2d_BoundedCurve { public: //! 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.
Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles); //! 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.
Standard_EXPORT Geom2d_BezierCurve(const TColgp_Array1OfPnt2d& CurvePoles,const TColStd_Array1OfReal& PoleWeights); //! Increases the degree of a bezier curve. Degree is the new
//! degree of .
//! raises ConstructionError if Degree is greater than MaxDegree or lower than 2
//! or lower than the initial degree of .
Standard_EXPORT void Increase(const Standard_Integer Degree) ; //! 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.
Standard_EXPORT 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 [1, NbPoles+1]
//! Raised if the resulting number of poles is greater than
//! MaxDegree + 1.
Standard_EXPORT void InsertPoleBefore(const Standard_Integer Index,const gp_Pnt2d& P,const Standard_Real Weight = 1.0) ; //! 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]
Standard_EXPORT void RemovePole(const Standard_Integer Index) ; //! Reverses the direction of parametrization of
//! Value (NewU) = Value (1 - OldU)
Standard_EXPORT void Reverse() ; //! Returns the parameter on the reversed curve for
//! the point of parameter U on .
//!
//! returns 1-U
Standard_EXPORT Standard_Real ReversedParameter(const Standard_Real U) const; //! 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 is not closed it can become closed after the
//! segmentation for example if U1 or U2 are out of the bounds
//! of the curve or if the curve makes loop.
//! After the segmentation the length of a curve can be null.
Standard_EXPORT void Segment(const Standard_Real U1,const Standard_Real U2) ; //! Substitutes the pole of range index with P.
//! If the curve is rational the weight of range Index
//! is not modified.
//! raiseD if Index is not in the range [1, NbPoles]
Standard_EXPORT void SetPole(const Standard_Integer Index,const gp_Pnt2d& P) ; //! Substitutes the pole and the weights of range Index.
//! If the curve is not rational it can become rational
//! if all the weights are not identical.
//! If the curve was rational it can become non rational if
//! all the weights are identical.
//! Raised if Index is not in the range [1, NbPoles]
//! Raised if Weight <= Resolution from package gp
Standard_EXPORT void SetPole(const Standard_Integer Index,const gp_Pnt2d& P,const Standard_Real Weight) ; //! Changes the weight of the pole of range Index.
//! If the curve is not rational it can become rational
//! if all the weights are not identical.
//! If the curve was rational it can become non rational if
//! all the weights are identical.
//! Raised if Index is not in the range [1, NbPoles]
//! Raised if Weight <= Resolution from package gp
Standard_EXPORT void SetWeight(const Standard_Integer Index,const Standard_Real Weight) ; //! Returns True if the distance between the first point
//! and the last point of the curve is lower or equal to
//! the Resolution from package gp.
Standard_EXPORT Standard_Boolean IsClosed() const; //! Continuity of the curve, returns True.
Standard_EXPORT Standard_Boolean IsCN(const Standard_Integer N) const; //! Returns False. A BezierCurve cannot be periodic in this
//! package
Standard_EXPORT Standard_Boolean IsPeriodic() const; //! Returns false if all the weights are identical. The tolerance
//! criterion is Resolution from package gp.
Standard_EXPORT Standard_Boolean IsRational() const; //! Returns GeomAbs_CN, which is the continuity of any Bezier curve.
Standard_EXPORT GeomAbs_Shape Continuity() 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".
Standard_EXPORT Standard_Integer Degree() const; Standard_EXPORT void D0(const Standard_Real U,gp_Pnt2d& P) const; Standard_EXPORT void D1(const Standard_Real U,gp_Pnt2d& P,gp_Vec2d& V1) const; Standard_EXPORT void D2(const Standard_Real U,gp_Pnt2d& P,gp_Vec2d& V1,gp_Vec2d& V2) const; Standard_EXPORT void D3(const Standard_Real U,gp_Pnt2d& P,gp_Vec2d& V1,gp_Vec2d& V2,gp_Vec2d& V3) const; //! 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.
Standard_EXPORT gp_Vec2d DN(const Standard_Real U,const Standard_Integer N) const; //! Returns the end point or start point of this Bezier curve.
Standard_EXPORT gp_Pnt2d EndPoint() const; //! Returns the value of the first parameter of this
//! Bezier curve. This is 0.0, which gives the start point of this Bezier curve.
Standard_EXPORT Standard_Real FirstParameter() const; //! Returns the value of the last parameter of this
//! Bezier curve. This is 1.0, which gives the end point of this Bezier curve.
Standard_EXPORT Standard_Real LastParameter() const; //! Returns the number of poles for this Bezier curve.
Standard_EXPORT Standard_Integer NbPoles() const; //! Returns the pole of range Index.
//! Raised if Index is not in the range [1, NbPoles]
Standard_EXPORT gp_Pnt2d Pole(const Standard_Integer Index) const; //! Returns all the poles of the curve.
//! Raised if the length of P is not equal to the number of poles.
Standard_EXPORT void Poles(TColgp_Array1OfPnt2d& P) const; //! Returns Value (U=1), it is the first control point
//! of the curve.
Standard_EXPORT gp_Pnt2d StartPoint() const; //! Returns the weight of range Index.
//! Raised if Index is not in the range [1, NbPoles]
Standard_EXPORT Standard_Real Weight(const Standard_Integer Index) const; //! Returns all the weights of the curve.
//! Raised if the length of W is not equal to the number of poles.
Standard_EXPORT void Weights(TColStd_Array1OfReal& W) const; //! Applies the transformation T to this Bezier curve.
Standard_EXPORT void Transform(const gp_Trsf2d& T) ; //! Returns the value of the maximum polynomial degree of a
//! BezierCurve. This value is 25.
Standard_EXPORT static Standard_Integer MaxDegree() ; //! 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
Standard_EXPORT void Resolution(const Standard_Real ToleranceUV,Standard_Real& UTolerance) ; //! Creates a new object which is a copy of this Bezier curve.
Standard_EXPORT Handle_Geom2d_Geometry Copy() const; DEFINE_STANDARD_RTTI(Geom2d_BezierCurve) protected: private: //! Set poles to Poles, weights to Weights (not
//! copied). If Weights is null the curve is non
//! rational. Create the arrays of coefficients. Poles
//! and Weights are assumed to have the first
//! coefficient 1.
//!
//! Update rational and closed.
//!
//! if nbpoles < 2 or nbboles > MaDegree + 1
Standard_EXPORT void Init(const Handle(TColgp_HArray1OfPnt2d)& Poles,const Handle(TColStd_HArray1OfReal)& Weights) ; //! returns true if the coefficients have been
//! computed with the right value of cacheparameter
//! for the given U value.
//!
Standard_EXPORT Standard_Boolean CoefficientsOK(const Standard_Real U) const; //! Recompute the coeficients.
Standard_EXPORT void UpdateCoefficients(const Standard_Real U = 0.0) ; Standard_Boolean rational; Standard_Boolean closed; Handle_TColgp_HArray1OfPnt2d poles; Handle_TColStd_HArray1OfReal weights; Handle_TColgp_HArray1OfPnt2d coeffs; Handle_TColStd_HArray1OfReal wcoeffs; Standard_Integer validcache; Standard_Real parametercache; Standard_Real spanlenghtcache; Standard_Real maxderivinv; Standard_Boolean maxderivinvok; }; // other Inline functions and methods (like "C++: function call" methods) #endif