// Created on: 1993-03-09 // Created by: Philippe DAUTRY // 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 _Geom_BezierCurve_HeaderFile #define _Geom_BezierCurve_HeaderFile #include #include #include #include #include #include #include #include #include #include #include #include class gp_Pnt; class gp_Vec; class gp_Trsf; class Geom_Geometry; class Geom_BezierCurve; DEFINE_STANDARD_HANDLE(Geom_BezierCurve, Geom_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_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 //! 1. 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. class Geom_BezierCurve : public Geom_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 Geom_BezierCurve(const TColgp_Array1OfPnt& 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 Geom_BezierCurve(const TColgp_Array1OfPnt& 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 P after the pole of range Index. //! If the curve 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. Standard_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt& P); //! 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_EXPORT void InsertPoleAfter (const Standard_Integer Index, const gp_Pnt& P, const Standard_Real Weight); //! Inserts a pole P before the pole of range Index. //! If the curve 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. Standard_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt& P); //! 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_EXPORT void InsertPoleBefore (const Standard_Integer Index, const gp_Pnt& P, const Standard_Real Weight); //! 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. 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_Pnt& 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_Pnt& 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 True if the parametrization of a curve is periodic. //! (P(u) = P(u + T) T = constante) 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; //! a Bezier curve is CN Standard_EXPORT GeomAbs_Shape Continuity() const Standard_OVERRIDE; //! 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. Standard_EXPORT Standard_Integer Degree() const; Standard_EXPORT void D0 (const Standard_Real U, gp_Pnt& P) const Standard_OVERRIDE; Standard_EXPORT void D1 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1) const Standard_OVERRIDE; Standard_EXPORT void D2 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2) 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. Standard_EXPORT void D3 (const Standard_Real U, gp_Pnt& P, gp_Vec& V1, gp_Vec& V2, gp_Vec& V3) const Standard_OVERRIDE; //! 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. Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Integer N) const Standard_OVERRIDE; //! Returns Value (U=0.), it is the first control point of the curve. Standard_EXPORT gp_Pnt StartPoint() const Standard_OVERRIDE; //! Returns Value (U=1.), it is the last control point of the Bezier curve. Standard_EXPORT gp_Pnt 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 of 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_Pnt& 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_Array1OfPnt& P) const; //! Returns all the poles of the curve. Standard_EXPORT const TColgp_Array1OfPnt& Poles () 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; //! 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_Trsf& T) Standard_OVERRIDE; //! Returns the value of the maximum polynomial degree //! of any Geom_BezierCurve curve. This value is 25. Standard_EXPORT static Standard_Integer MaxDegree(); //! 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 Standard_EXPORT void Resolution (const Standard_Real Tolerance3D, Standard_Real& UTolerance); //! Creates a new object which is a copy of this Bezier curve. Standard_EXPORT Handle(Geom_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(Geom_BezierCurve,Geom_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_HArray1OfPnt)& Poles, const Handle(TColStd_HArray1OfReal)& Weights); Standard_Boolean rational; Standard_Boolean closed; Handle(TColgp_HArray1OfPnt) poles; Handle(TColStd_HArray1OfReal) weights; Standard_Real maxderivinv; Standard_Boolean maxderivinvok; }; #endif // _Geom_BezierCurve_HeaderFile