// Created on: 1993-03-24 // Created by: JCV // Copyright (c) 1993-1999 Matra Datavision // Copyright (c) 1999-2014 OPEN CASCADE SAS // // This file is part of Open CASCADE Technology software library. // // This library is free software; you can redistribute it and/or modify it under // the terms of the GNU Lesser General Public License version 2.1 as published // by the Free Software Foundation, with special exception defined in the file // OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT // distribution for complete text of the license and disclaimer of any warranty. // // Alternatively, this file may be used under the terms of Open CASCADE // commercial license or contractual agreement. #ifndef _Geom2d_BezierCurve_HeaderFile #define _Geom2d_BezierCurve_HeaderFile #include #include #include #include #include #include #include #include class gp_Pnt2d; class gp_Vec2d; class gp_Trsf2d; class Geom2d_Geometry; class Geom2d_BezierCurve; DEFINE_STANDARD_HANDLE(Geom2d_BezierCurve, Geom2d_BoundedCurve) //! 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() Standard_OVERRIDE; //! 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 Standard_OVERRIDE; //! 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 Standard_OVERRIDE; //! Continuity of the curve, returns True. Standard_EXPORT Standard_Boolean IsCN (const Standard_Integer N) const Standard_OVERRIDE; //! Returns False. A BezierCurve cannot be periodic in this //! package Standard_EXPORT Standard_Boolean IsPeriodic() const Standard_OVERRIDE; //! 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 Standard_OVERRIDE; //! 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_OVERRIDE; Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1) const Standard_OVERRIDE; Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2) const Standard_OVERRIDE; Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt2d& P, gp_Vec2d& V1, gp_Vec2d& V2, gp_Vec2d& V3) const Standard_OVERRIDE; //! 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 Standard_OVERRIDE; //! Returns the end point or start point of this Bezier curve. Standard_EXPORT gp_Pnt2d EndPoint() const Standard_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. Standard_EXPORT Standard_Real FirstParameter() const Standard_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. Standard_EXPORT Standard_Real LastParameter() const Standard_OVERRIDE; //! 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 const 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 all the poles of the curve. const TColgp_Array1OfPnt2d& Poles() const { return poles->Array1(); } //! Returns Value (U=1), it is the first control point //! of the curve. Standard_EXPORT gp_Pnt2d StartPoint() const Standard_OVERRIDE; //! 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; //! Returns all the weights of the curve. const TColStd_Array1OfReal* Weights() const { if (!weights.IsNull()) return &weights->Array1(); return BSplCLib::NoWeights(); } //! Applies the transformation T to this Bezier curve. Standard_EXPORT void Transform (const gp_Trsf2d& T) Standard_OVERRIDE; //! 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 Standard_OVERRIDE; //! Dumps the content of me into the stream Standard_EXPORT virtual void DumpJson (Standard_OStream& theOStream, Standard_Integer theDepth = -1) const Standard_OVERRIDE; DEFINE_STANDARD_RTTIEXT(Geom2d_BezierCurve,Geom2d_BoundedCurve) 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 void Init (const Handle(TColgp_HArray1OfPnt2d)& Poles, const Handle(TColStd_HArray1OfReal)& Weights); Standard_Boolean rational; Standard_Boolean closed; Handle(TColgp_HArray1OfPnt2d) poles; Handle(TColStd_HArray1OfReal) weights; Standard_Real maxderivinv; Standard_Boolean maxderivinvok; }; #endif // _Geom2d_BezierCurve_HeaderFile