// 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;
class Geom2dConvert_BSplineCurveKnotSplitting;
class Geom2dConvert_BSplineCurveToBezierCurve;
class Geom2dConvert_CompCurveToBSplineCurve;
class Geom2dConvert_ApproxCurve;
//! This package provides an implementation of algorithmes 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).
//! Neverthless 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