// Created on: 1991-06-25 // Created by: JCV // 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. // modified by Edward AGAPOV (eap) Jan 28 2002 --- DN(), occ143(BUC60654) #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include typedef Geom2d_OffsetCurve OffsetCurve; typedef Geom2d_Curve Curve; typedef gp_Dir2d Dir2d; typedef gp_Pnt2d Pnt2d; typedef gp_Vec2d Vec2d; typedef gp_Trsf2d Trsf2d; typedef gp_XY XY; //ordre de derivation maximum pour la recherche de la premiere //derivee non nulle static const int maxDerivOrder = 3; static const Standard_Real MinStep = 1e-7; static const Standard_Real MyAngularToleranceForG1 = Precision::Angular(); static gp_Vec2d dummyDerivative; // used as empty value for unused derivatives in AdjustDerivative // Recalculate derivatives in the singular point // Returns true if the direction of derivatives is changed static Standard_Boolean AdjustDerivative(const Handle(Geom2d_Curve)& theCurve, Standard_Integer theMaxDerivative, Standard_Real theU, gp_Vec2d& theD1, gp_Vec2d& theD2 = dummyDerivative, gp_Vec2d& theD3 = dummyDerivative, gp_Vec2d& theD4 = dummyDerivative); //======================================================================= //function : Copy //purpose : //======================================================================= Handle(Geom2d_Geometry) Geom2d_OffsetCurve::Copy () const { Handle(Geom2d_OffsetCurve) C; C = new OffsetCurve (basisCurve, offsetValue); return C; } //======================================================================= //function : Geom2d_OffsetCurve //purpose : Basis curve cannot be an Offset curve or trimmed from // offset curve. //======================================================================= Geom2d_OffsetCurve::Geom2d_OffsetCurve (const Handle(Geom2d_Curve)& theCurve, const Standard_Real theOffset, const Standard_Boolean isTheNotCheckC0) : offsetValue (theOffset) { SetBasisCurve (theCurve, isTheNotCheckC0); } //======================================================================= //function : Reverse //purpose : //======================================================================= void Geom2d_OffsetCurve::Reverse () { basisCurve->Reverse(); offsetValue = -offsetValue; } //======================================================================= //function : ReversedParameter //purpose : //======================================================================= Standard_Real Geom2d_OffsetCurve::ReversedParameter( const Standard_Real U) const { return basisCurve->ReversedParameter( U); } //======================================================================= //function : SetBasisCurve //purpose : //======================================================================= void Geom2d_OffsetCurve::SetBasisCurve (const Handle(Geom2d_Curve)& C, const Standard_Boolean isNotCheckC0) { const Standard_Real aUf = C->FirstParameter(), aUl = C->LastParameter(); Handle(Geom2d_Curve) aCheckingCurve = C; Standard_Boolean isTrimmed = Standard_False; while(aCheckingCurve->IsKind(STANDARD_TYPE(Geom2d_TrimmedCurve)) || aCheckingCurve->IsKind(STANDARD_TYPE(Geom2d_OffsetCurve))) { if (aCheckingCurve->IsKind(STANDARD_TYPE(Geom2d_TrimmedCurve))) { Handle(Geom2d_TrimmedCurve) aTrimC = Handle(Geom2d_TrimmedCurve)::DownCast(aCheckingCurve); aCheckingCurve = aTrimC->BasisCurve(); isTrimmed = Standard_True; } if (aCheckingCurve->IsKind(STANDARD_TYPE(Geom2d_OffsetCurve))) { Handle(Geom2d_OffsetCurve) aOC = Handle(Geom2d_OffsetCurve)::DownCast(aCheckingCurve); aCheckingCurve = aOC->BasisCurve(); offsetValue += aOC->Offset(); } } myBasisCurveContinuity = aCheckingCurve->Continuity(); Standard_Boolean isC0 = !isNotCheckC0 && (myBasisCurveContinuity == GeomAbs_C0); // Basis curve must be at least C1 if (isC0 && aCheckingCurve->IsKind(STANDARD_TYPE(Geom2d_BSplineCurve))) { Handle(Geom2d_BSplineCurve) aBC = Handle(Geom2d_BSplineCurve)::DownCast(aCheckingCurve); if(aBC->IsG1(aUf, aUl, MyAngularToleranceForG1)) { //Checking if basis curve has more smooth (C1, G2 and above) is not done. //It can be done in case of need. myBasisCurveContinuity = GeomAbs_G1; isC0 = Standard_False; } // Raise exception if still C0 if (isC0) Standard_ConstructionError::Raise("Offset on C0 curve"); } // if(isTrimmed) { basisCurve = new Geom2d_TrimmedCurve(aCheckingCurve, aUf, aUl); } else { basisCurve = aCheckingCurve; } } //======================================================================= //function : SetOffsetValue //purpose : //======================================================================= void Geom2d_OffsetCurve::SetOffsetValue (const Standard_Real D) { offsetValue = D; } //======================================================================= //function : BasisCurve //purpose : //======================================================================= Handle(Geom2d_Curve) Geom2d_OffsetCurve::BasisCurve () const { return basisCurve; } //======================================================================= //function : Continuity //purpose : //======================================================================= GeomAbs_Shape Geom2d_OffsetCurve::Continuity () const { GeomAbs_Shape OffsetShape=GeomAbs_C0; switch (myBasisCurveContinuity) { case GeomAbs_C0 : OffsetShape = GeomAbs_C0; break; case GeomAbs_C1 : OffsetShape = GeomAbs_C0; break; case GeomAbs_C2 : OffsetShape = GeomAbs_C1; break; case GeomAbs_C3 : OffsetShape = GeomAbs_C2; break; case GeomAbs_CN : OffsetShape = GeomAbs_CN; break; case GeomAbs_G1 : OffsetShape = GeomAbs_G1; break; case GeomAbs_G2 : OffsetShape = GeomAbs_G2; break; } return OffsetShape; } //======================================================================= //function : D0 //purpose : //======================================================================= void Geom2d_OffsetCurve::D0 (const Standard_Real theU, Pnt2d& theP) const { Vec2d vD1; basisCurve->D1 (theU, theP, vD1); Standard_Boolean IsDirectionChange = Standard_False; if(vD1.SquareMagnitude() <= gp::Resolution()) IsDirectionChange = AdjustDerivative(basisCurve, 1, theU, vD1); CSLib_Offset::D0(theP, vD1, offsetValue, IsDirectionChange, theP); } //======================================================================= //function : D1 //purpose : //======================================================================= void Geom2d_OffsetCurve::D1 (const Standard_Real theU, Pnt2d& theP, Vec2d& theV1) const { // P(u) = p(u) + Offset * Ndir / R // with R = || p' ^ Z|| and Ndir = P' ^ Z // P'(u) = p'(u) + (Offset / R**2) * (DNdir/DU * R - Ndir * (DR/R)) Vec2d V2; basisCurve->D2 (theU, theP, theV1, V2); Standard_Boolean IsDirectionChange = Standard_False; if(theV1.SquareMagnitude() <= gp::Resolution()) IsDirectionChange = AdjustDerivative(basisCurve, 2, theU, theV1, V2); CSLib_Offset::D1(theP, theV1, V2, offsetValue, IsDirectionChange, theP, theV1); } //======================================================================= //function : D2 //purpose : //======================================================================= void Geom2d_OffsetCurve::D2 (const Standard_Real theU, Pnt2d& theP, Vec2d& theV1, Vec2d& theV2) const { // P(u) = p(u) + Offset * Ndir / R // with R = || p' ^ Z|| and Ndir = P' ^ Z // P'(u) = p'(u) + (Offset / R**2) * (DNdir/DU * R - Ndir * (DR/R)) // P"(u) = p"(u) + (Offset / R) * (D2Ndir/DU - DNdir * (2.0 * Dr/ R**2) + // Ndir * ( (3.0 * Dr**2 / R**4) - (D2r / R**2))) Vec2d V3; basisCurve->D3 (theU, theP, theV1, theV2, V3); Standard_Boolean IsDirectionChange = Standard_False; if(theV1.SquareMagnitude() <= gp::Resolution()) IsDirectionChange = AdjustDerivative(basisCurve, 3, theU, theV1, theV2, V3); CSLib_Offset::D2(theP, theV1, theV2, V3, offsetValue, IsDirectionChange, theP, theV1, theV2); } //======================================================================= //function : D3 //purpose : //======================================================================= void Geom2d_OffsetCurve::D3 (const Standard_Real theU, Pnt2d& theP, Vec2d& theV1, Vec2d& theV2, Vec2d& theV3) const { // P(u) = p(u) + Offset * Ndir / R // with R = || p' ^ Z|| and Ndir = P' ^ Z // P'(u) = p'(u) + (Offset / R**2) * (DNdir/DU * R - Ndir * (DR/R)) // P"(u) = p"(u) + (Offset / R) * (D2Ndir/DU - DNdir * (2.0 * Dr/ R**2) + // Ndir * ( (3.0 * Dr**2 / R**4) - (D2r / R**2))) //P"'(u) = p"'(u) + (Offset / R) * (D3Ndir - (3.0 * Dr/R**2 ) * D2Ndir - // (3.0 * D2r / R2) * DNdir) + (3.0 * Dr * Dr / R4) * DNdir - // (D3r/R2) * Ndir + (6.0 * Dr * Dr / R4) * Ndir + // (6.0 * Dr * D2r / R4) * Ndir - (15.0 * Dr* Dr* Dr /R6) * Ndir basisCurve->D3 (theU, theP, theV1, theV2, theV3); Vec2d V4 = basisCurve->DN (theU, 4); Standard_Boolean IsDirectionChange = Standard_False; if(theV1.SquareMagnitude() <= gp::Resolution()) IsDirectionChange = AdjustDerivative(basisCurve, 4, theU, theV1, theV2, theV3, V4); CSLib_Offset::D3(theP, theV1, theV2, theV3, V4, offsetValue, IsDirectionChange, theP, theV1, theV2, theV3); } //======================================================================= //function : DN //purpose : //======================================================================= Vec2d Geom2d_OffsetCurve::DN (const Standard_Real U, const Standard_Integer N) const { Standard_RangeError_Raise_if (N < 1, "Exception: Geom2d_OffsetCurve::DN(). N<1."); gp_Vec2d VN, VBidon; gp_Pnt2d PBidon; switch (N) { case 1: D1( U, PBidon, VN); break; case 2: D2( U, PBidon, VBidon, VN); break; case 3: D3( U, PBidon, VBidon, VBidon, VN); break; default: Standard_NotImplemented::Raise("Exception: Derivative order is greater than 3. " "Cannot compute of derivative."); } return VN; } //======================================================================= //function : Value //purpose : //======================================================================= void Geom2d_OffsetCurve::Value (const Standard_Real theU, Pnt2d& theP, Pnt2d& thePbasis, Vec2d& theV1basis ) const { basisCurve->D1(theU, thePbasis, theV1basis); D0(theU,theP); } //======================================================================= //function : D1 //purpose : //======================================================================= void Geom2d_OffsetCurve::D1 (const Standard_Real U, Pnt2d& P, Pnt2d& Pbasis, Vec2d& V1, Vec2d& V1basis, Vec2d& V2basis ) const { // P(u) = p(u) + Offset * Ndir / R // with R = || p' ^ Z|| and Ndir = P' ^ Z // P'(u) = p'(u) + (Offset / R**2) * (DNdir/DU * R - Ndir * (DR/R)) basisCurve->D2 (U, Pbasis, V1basis, V2basis); V1 = V1basis; Vec2d V2 = V2basis; Standard_Integer Index = 2; while (V1.Magnitude() <= gp::Resolution() && Index <= maxDerivOrder) { V1 = basisCurve->DN (U, Index); Index++; } if (Index != 2) { V2 = basisCurve->DN (U, Index); } CSLib_Offset::D1(P, V1, V2, offsetValue, Standard_False, P, V1); } //======================================================================= //function : D2 //purpose : //======================================================================= void Geom2d_OffsetCurve::D2 (const Standard_Real U, Pnt2d& P, Pnt2d& Pbasis, Vec2d& V1, Vec2d& V2, Vec2d& V1basis, Vec2d& V2basis, Vec2d& V3basis ) const { // P(u) = p(u) + Offset * Ndir / R // with R = || p' ^ Z|| and Ndir = P' ^ Z // P'(u) = p'(u) + (Offset / R**2) * (DNdir/DU * R - Ndir * (DR/R)) // P"(u) = p"(u) + (Offset / R) * (D2Ndir/DU - DNdir * (2.0 * Dr/ R**2) + // Ndir * ( (3.0 * Dr**2 / R**4) - (D2r / R**2))) basisCurve->D3 (U, Pbasis, V1basis, V2basis, V3basis); Standard_Integer Index = 2; V1 = V1basis; V2 = V2basis; Vec2d V3 = V3basis; while (V1.Magnitude() <= gp::Resolution() && Index <= maxDerivOrder) { V1 = basisCurve->DN (U, Index); Index++; } if (Index != 2) { V2 = basisCurve->DN (U, Index); V3 = basisCurve->DN (U, Index + 1); } CSLib_Offset::D2(P, V1, V2, V3, offsetValue, Standard_False, P, V1, V2); } //======================================================================= //function : FirstParameter //purpose : //======================================================================= Standard_Real Geom2d_OffsetCurve::FirstParameter () const { return basisCurve->FirstParameter(); } //======================================================================= //function : LastParameter //purpose : //======================================================================= Standard_Real Geom2d_OffsetCurve::LastParameter () const { return basisCurve->LastParameter(); } //======================================================================= //function : Offset //purpose : //======================================================================= Standard_Real Geom2d_OffsetCurve::Offset () const { return offsetValue; } //======================================================================= //function : IsClosed //purpose : //======================================================================= Standard_Boolean Geom2d_OffsetCurve::IsClosed () const { gp_Pnt2d PF, PL; D0(FirstParameter(),PF); D0(LastParameter(),PL); return ( PF.Distance(PL) <= gp::Resolution()); } //======================================================================= //function : IsCN //purpose : //======================================================================= Standard_Boolean Geom2d_OffsetCurve::IsCN (const Standard_Integer N) const { Standard_RangeError_Raise_if (N < 0, " " ); return basisCurve->IsCN (N + 1); } //======================================================================= //function : IsPeriodic //purpose : //======================================================================= Standard_Boolean Geom2d_OffsetCurve::IsPeriodic () const { return basisCurve->IsPeriodic(); } //======================================================================= //function : Period //purpose : //======================================================================= Standard_Real Geom2d_OffsetCurve::Period() const { return basisCurve->Period(); } //======================================================================= //function : Transform //purpose : //======================================================================= void Geom2d_OffsetCurve::Transform (const Trsf2d& T) { basisCurve->Transform (T); offsetValue *= Abs(T.ScaleFactor()); } //======================================================================= //function : TransformedParameter //purpose : //======================================================================= Standard_Real Geom2d_OffsetCurve::TransformedParameter(const Standard_Real U, const gp_Trsf2d& T) const { return basisCurve->TransformedParameter(U,T); } //======================================================================= //function : ParametricTransformation //purpose : //======================================================================= Standard_Real Geom2d_OffsetCurve::ParametricTransformation(const gp_Trsf2d& T) const { return basisCurve->ParametricTransformation(T); } //======================================================================= //function : GetBasisCurveContinuity //purpose : //======================================================================= GeomAbs_Shape Geom2d_OffsetCurve::GetBasisCurveContinuity() const { return myBasisCurveContinuity; } // ============= Auxiliary functions =================== Standard_Boolean AdjustDerivative(const Handle(Geom2d_Curve)& theCurve, Standard_Integer theMaxDerivative, Standard_Real theU, gp_Vec2d& theD1, gp_Vec2d& theD2, gp_Vec2d& theD3, gp_Vec2d& theD4) { static const Standard_Real aTol = gp::Resolution(); Standard_Boolean IsDirectionChange = Standard_False; const Standard_Real anUinfium = theCurve->FirstParameter(); const Standard_Real anUsupremum = theCurve->LastParameter(); const Standard_Real DivisionFactor = 1.e-3; Standard_Real du; if((anUsupremum >= RealLast()) || (anUinfium <= RealFirst())) du = 0.0; else du = anUsupremum - anUinfium; const Standard_Real aDelta = Max(du * DivisionFactor, MinStep); //Derivative is approximated by Taylor-series Standard_Integer anIndex = 1; //Derivative order Vec2d V; do { V = theCurve->DN(theU, ++anIndex); } while((V.SquareMagnitude() <= aTol) && anIndex < maxDerivOrder); Standard_Real u; if(theU-anUinfium < aDelta) u = theU+aDelta; else u = theU-aDelta; Pnt2d P1, P2; theCurve->D0(Min(theU, u),P1); theCurve->D0(Max(theU, u),P2); Vec2d V1(P1,P2); IsDirectionChange = V.Dot(V1) < 0.0; Standard_Real aSign = IsDirectionChange ? -1.0 : 1.0; theD1 = V * aSign; gp_Vec2d* aDeriv[3] = {&theD2, &theD3, &theD4}; for (Standard_Integer i = 1; i < theMaxDerivative; i++) *(aDeriv[i-1]) = theCurve->DN(theU, anIndex + i) * aSign; return IsDirectionChange; }