// Created on: 1991-10-03 // Created by: Jean Claude VAUTHIER // Copyright (c) 1991-1999 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 _Geom2dConvert_HeaderFile #define _Geom2dConvert_HeaderFile #include #include #include #include #include #include #include #include #include #include #include class Geom2d_BSplineCurve; class Geom2d_Curve; //! This package provides an implementation of algorithms to do //! the conversion between equivalent geometric entities from //! package Geom2d. //! It gives the possibility : //! . to obtain the B-spline representation of bounded curves. //! . to split a B-spline curve into several B-spline curves //! with some constraints of continuity, //! . to convert a B-spline curve into several Bezier curves //! or surfaces. //! All the geometric entities used in this package are bounded. //! References : //! . Generating the Bezier Points of B-spline curves and surfaces //! (Wolfgang Bohm) CAGD volume 13 number 6 november 1981 //! . On NURBS: A Survey (Leslie Piegl) IEEE Computer Graphics and //! Application January 1991 //! . Curve and surface construction using rational B-splines //! (Leslie Piegl and Wayne Tiller) CAD Volume 19 number 9 november //! 1987 //! . A survey of curve and surface methods in CAGD (Wolfgang BOHM) //! CAGD 1 1984 class Geom2dConvert { public: DEFINE_STANDARD_ALLOC //! -- Convert a curve to BSpline by Approximation //! //! This method computes the arc of B-spline curve between the two //! knots FromK1 and ToK2. If C is periodic the arc has the same //! orientation as C if SameOrientation = Standard_True. //! If C is not periodic SameOrientation is not used for the //! computation and C is oriented from the knot fromK1 to the //! knot toK2. //! We just keep the local definition of C between the knots //! FromK1 and ToK2. The returned B-spline curve has its first //! and last knots with a multiplicity equal to degree + 1, where //! degree is the polynomial degree of C. //! The indexes of the knots FromK1 and ToK2 doesn't include the //! repetition of multiple knots in their definition. //! //! Raised if FromK1 or ToK2 are out of the bounds //! [FirstUKnotIndex, LastUKnotIndex] //! Raised if FromK1 = ToK2 Standard_EXPORT static Handle(Geom2d_BSplineCurve) SplitBSplineCurve (const Handle(Geom2d_BSplineCurve)& C, const Standard_Integer FromK1, const Standard_Integer ToK2, const Standard_Boolean SameOrientation = Standard_True); //! This function computes the segment of B-spline curve between the //! parametric values FromU1, ToU2. //! If C is periodic the arc has the same orientation as C if //! SameOrientation = True. //! If C is not periodic SameOrientation is not used for the //! computation and C is oriented fromU1 toU2. //! If U1 and U2 and two parametric values we consider that //! U1 = U2 if Abs (U1 - U2) <= ParametricTolerance and //! ParametricTolerance must be greater or equal to Resolution //! from package gp. //! //! Raised if FromU1 or ToU2 are out of the parametric bounds of the //! curve (The tolerance criterion is ParametricTolerance). //! Raised if Abs (FromU1 - ToU2) <= ParametricTolerance //! Raised if ParametricTolerance < Resolution from gp. Standard_EXPORT static Handle(Geom2d_BSplineCurve) SplitBSplineCurve (const Handle(Geom2d_BSplineCurve)& C, const Standard_Real FromU1, const Standard_Real ToU2, const Standard_Real ParametricTolerance, const Standard_Boolean SameOrientation = Standard_True); //! This function converts a non infinite curve from //! Geom into a B-spline curve. C must be an ellipse or a //! circle or a trimmed conic or a trimmed line or a Bezier //! curve or a trimmed Bezier curve or a BSpline curve or a //! trimmed BSpline curve or an Offset curve or a trimmed //! Offset curve. //! The returned B-spline is not periodic except if C is a //! Circle or an Ellipse. //! ParameterisationType applies only if the curve is a Circle //! or an ellipse : //! TgtThetaOver2, //! TgtThetaOver2_1, //! TgtThetaOver2_2, //! TgtThetaOver2_3, //! TgtThetaOver2_4, //! Purpose: this is the classical rational parameterisation //! 2 //! 1 - t //! cos(theta) = ------ //! 2 //! 1 + t //! //! 2t //! sin(theta) = ------ //! 2 //! 1 + t //! //! t = tan (theta/2) //! //! with TgtThetaOver2 the routine will compute the number of spans //! using the rule num_spans = [ (ULast - UFirst) / 1.2 ] + 1 //! with TgtThetaOver2_N, N spans will be forced: an error will //! be raized if (ULast - UFirst) >= PI and N = 1, //! ULast - UFirst >= 2 PI and N = 2 //! //! QuasiAngular, //! here t is a rational function that approximates //! theta ----> tan(theta/2). //! Nevetheless the composing with above function yields exact //! functions whose square sum up to 1 //! RationalC1 ; //! t is replaced by a polynomial function of u so as to grant //! C1 contiuity across knots. //! Exceptions //! Standard_DomainError if the curve C is infinite. //! Standard_ConstructionError: //! - if C is a complete circle or ellipse, and if //! Parameterisation is not equal to //! Convert_TgtThetaOver2 or to Convert_RationalC1, or //! - if C is a trimmed circle or ellipse and if //! Parameterisation is equal to //! Convert_TgtThetaOver2_1 and if U2 - U1 > //! 0.9999 * Pi where U1 and U2 are //! respectively the first and the last parameters of the //! trimmed curve (this method of parameterization //! cannot be used to convert a half-circle or a //! half-ellipse, for example), or //! - if C is a trimmed circle or ellipse and //! Parameterisation is equal to //! Convert_TgtThetaOver2_2 and U2 - U1 > //! 1.9999 * Pi where U1 and U2 are //! respectively the first and the last parameters of the //! trimmed curve (this method of parameterization //! cannot be used to convert a quasi-complete circle or ellipse). Standard_EXPORT static Handle(Geom2d_BSplineCurve) CurveToBSplineCurve (const Handle(Geom2d_Curve)& C, const Convert_ParameterisationType Parameterisation = Convert_TgtThetaOver2); //! This Method concatenates G1 the ArrayOfCurves as far //! as it is possible. //! ArrayOfCurves[0..N-1] //! ArrayOfToler contains the biggest tolerance of the two //! points shared by two consecutives curves. //! Its dimension: [0..N-2] //! ClosedFlag indicates if the ArrayOfCurves is closed. //! In this case ClosedTolerance contains the biggest tolerance //! of the two points which are at the closure. //! Otherwise its value is 0.0 //! ClosedFlag becomes False on the output //! if it is impossible to build closed curve. Standard_EXPORT static void ConcatG1 (TColGeom2d_Array1OfBSplineCurve& ArrayOfCurves, const TColStd_Array1OfReal& ArrayOfToler, Handle(TColGeom2d_HArray1OfBSplineCurve)& ArrayOfConcatenated, Standard_Boolean& ClosedFlag, const Standard_Real ClosedTolerance); //! This Method concatenates C1 the ArrayOfCurves as far //! as it is possible. //! ArrayOfCurves[0..N-1] //! ArrayOfToler contains the biggest tolerance of the two //! points shared by two consecutives curves. //! Its dimension: [0..N-2] //! ClosedFlag indicates if the ArrayOfCurves is closed. //! In this case ClosedTolerance contains the biggest tolerance //! of the two points which are at the closure. //! Otherwise its value is 0.0 //! ClosedFlag becomes False on the output //! if it is impossible to build closed curve. Standard_EXPORT static void ConcatC1 (TColGeom2d_Array1OfBSplineCurve& ArrayOfCurves, const TColStd_Array1OfReal& ArrayOfToler, Handle(TColStd_HArray1OfInteger)& ArrayOfIndices, Handle(TColGeom2d_HArray1OfBSplineCurve)& ArrayOfConcatenated, Standard_Boolean& ClosedFlag, const Standard_Real ClosedTolerance); //! This Method concatenates C1 the ArrayOfCurves as far //! as it is possible. //! ArrayOfCurves[0..N-1] //! ArrayOfToler contains the biggest tolerance of the two //! points shared by two consecutives curves. //! Its dimension: [0..N-2] //! ClosedFlag indicates if the ArrayOfCurves is closed. //! In this case ClosedTolerance contains the biggest tolerance //! of the two points which are at the closure. //! Otherwise its value is 0.0 //! ClosedFlag becomes False on the output //! if it is impossible to build closed curve. Standard_EXPORT static void ConcatC1 (TColGeom2d_Array1OfBSplineCurve& ArrayOfCurves, const TColStd_Array1OfReal& ArrayOfToler, Handle(TColStd_HArray1OfInteger)& ArrayOfIndices, Handle(TColGeom2d_HArray1OfBSplineCurve)& ArrayOfConcatenated, Standard_Boolean& ClosedFlag, const Standard_Real ClosedTolerance, const Standard_Real AngularTolerance); //! This Method reduces as far as it is possible the //! multiplicities of the knots of the BSpline BS.(keeping the geometry). //! It returns a new BSpline which could still be C0. //! tolerance is a geometrical tolerance Standard_EXPORT static void C0BSplineToC1BSplineCurve (Handle(Geom2d_BSplineCurve)& BS, const Standard_Real Tolerance); //! This Method reduces as far as it is possible the //! multiplicities of the knots of the BSpline BS.(keeping the geometry). //! It returns an array of BSpline C1. //! Tolerance is a geometrical tolerance Standard_EXPORT static void C0BSplineToArrayOfC1BSplineCurve (const Handle(Geom2d_BSplineCurve)& BS, Handle(TColGeom2d_HArray1OfBSplineCurve)& tabBS, const Standard_Real Tolerance); //! This Method reduces as far as it is possible the //! multiplicities of the knots of the BSpline BS.(keeping the geometry). //! It returns an array of BSpline C1. //! tolerance is a geometrical tolerance Standard_EXPORT static void C0BSplineToArrayOfC1BSplineCurve (const Handle(Geom2d_BSplineCurve)& BS, Handle(TColGeom2d_HArray1OfBSplineCurve)& tabBS, const Standard_Real AngularTolerance, const Standard_Real Tolerance); protected: private: friend class Geom2dConvert_BSplineCurveKnotSplitting; friend class Geom2dConvert_BSplineCurveToBezierCurve; friend class Geom2dConvert_CompCurveToBSplineCurve; friend class Geom2dConvert_ApproxCurve; }; #endif // _Geom2dConvert_HeaderFile