// 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 typedef Handle(Geom2d_OffsetCurve) Handle(OffsetCurve); typedef Geom2d_OffsetCurve OffsetCurve; typedef Handle(Geom2d_Geometry) Handle(Geometry); typedef Handle(Geom2d_Curve) Handle(Curve); 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(); //======================================================================= //function : Copy //purpose : //======================================================================= Handle(Geom2d_Geometry) Geom2d_OffsetCurve::Copy () const { Handle(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(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(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 { const Standard_Real aTol = gp::Resolution(); Vec2d vD1; basisCurve->D1 (theU, theP, vD1); Standard_Real Ndu = vD1.Magnitude(); if(Ndu <= aTol) { const Standard_Real anUinfium = basisCurve->FirstParameter(); const Standard_Real anUsupremum = basisCurve->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 = basisCurve->DN(theU,++anIndex); Ndu = V.Magnitude(); } while((Ndu <= aTol) && anIndex < maxDerivOrder); Standard_Real u; if(theU-anUinfium < aDelta) u = theU+aDelta; else u = theU-aDelta; Pnt2d P1, P2; basisCurve->D0(Min(theU, u),P1); basisCurve->D0(Max(theU, u),P2); Vec2d V1(P1,P2); Standard_Real aDirFactor = V.Dot(V1); if(aDirFactor < 0.0) vD1 = -V; else vD1 = V; Ndu = vD1.Magnitude(); }//if(Ndu <= aTol) if (Ndu <= aTol) Geom2d_UndefinedValue::Raise("Exception: Undefined normal vector " "because tangent vector has zero-magnitude!"); Standard_Real A = vD1.Y(); Standard_Real B = - vD1.X(); A = A * offsetValue/Ndu; B = B * offsetValue/Ndu; theP.SetCoord(theP.X() + A, theP.Y() + B); } //======================================================================= //function : D1 //purpose : //======================================================================= void Geom2d_OffsetCurve::D1 (const Standard_Real theU, Pnt2d& P, 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)) const Standard_Real aTol = gp::Resolution(); Vec2d V2; basisCurve->D2 (theU, P, theV1, V2); if(theV1.Magnitude() <= aTol) { const Standard_Real anUinfium = basisCurve->FirstParameter(); const Standard_Real anUsupremum = basisCurve->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 = basisCurve->DN(theU,++anIndex); } while((V.Magnitude() <= aTol) && anIndex < maxDerivOrder); Standard_Real u; if(theU-anUinfium < aDelta) u = theU+aDelta; else u = theU-aDelta; Pnt2d P1, P2; basisCurve->D0(Min(theU, u),P1); basisCurve->D0(Max(theU, u),P2); Vec2d V1(P1,P2); Standard_Real aDirFactor = V.Dot(V1); if(aDirFactor < 0.0) { theV1 = -V; V2 = - basisCurve->DN (theU, anIndex+1); } else { theV1 = V; V2 = basisCurve->DN (theU, anIndex+1); } }//if(theV1.Magnitude() <= aTol) XY Ndir (theV1.Y(), -theV1.X()); XY DNdir (V2.Y(), -V2.X()); Standard_Real R2 = Ndir.SquareModulus(); Standard_Real R = Sqrt (R2); Standard_Real R3 = R * R2; Standard_Real Dr = Ndir.Dot (DNdir); if (R3 <= gp::Resolution()) { //We try another computation but the stability is not very good. if (R2 <= gp::Resolution()) Geom2d_UndefinedDerivative::Raise(); DNdir.Multiply(R); DNdir.Subtract (Ndir.Multiplied (Dr/R)); DNdir.Multiply (offsetValue/R2); theV1.Add (Vec2d(DNdir)); } else { // Same computation as IICURV in EUCLID-IS because the stability is // better DNdir.Multiply (offsetValue/R); DNdir.Subtract (Ndir.Multiplied (offsetValue*Dr/R3)); theV1.Add (Vec2d(DNdir)); } D0(theU, P); } //======================================================================= //function : D2 //purpose : //======================================================================= void Geom2d_OffsetCurve::D2 (const Standard_Real theU, Pnt2d& P, Vec2d& theV1, Vec2d& V2) 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, P, theV1, V2, V3); const Standard_Real aTol = gp::Resolution(); Standard_Boolean IsDirectionChange = Standard_False; if(theV1.Magnitude() <= aTol) { const Standard_Real anUinfium = basisCurve->FirstParameter(); const Standard_Real anUsupremum = basisCurve->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 = basisCurve->DN(theU,++anIndex); } while((V.Magnitude() <= aTol) && anIndex < maxDerivOrder); Standard_Real u; if(theU-anUinfium < aDelta) u = theU+aDelta; else u = theU-aDelta; Pnt2d P1, P2; basisCurve->D0(Min(theU, u),P1); basisCurve->D0(Max(theU, u),P2); Vec2d V1(P1,P2); Standard_Real aDirFactor = V.Dot(V1); if(aDirFactor < 0.0) { theV1 = -V; V2 = -basisCurve->DN (theU, anIndex+1); V3 = -basisCurve->DN (theU, anIndex + 2); IsDirectionChange = Standard_True; } else { theV1 = V; V2 = basisCurve->DN (theU, anIndex+1); V3 = basisCurve->DN (theU, anIndex + 2); } }//if(V1.Magnitude() <= aTol) XY Ndir (theV1.Y(), -theV1.X()); XY DNdir (V2.Y(), -V2.X()); XY D2Ndir (V3.Y(), -V3.X()); Standard_Real R2 = Ndir.SquareModulus(); Standard_Real R = Sqrt (R2); Standard_Real R3 = R2 * R; Standard_Real R4 = R2 * R2; Standard_Real R5 = R3 * R2; Standard_Real Dr = Ndir.Dot (DNdir); Standard_Real D2r = Ndir.Dot (D2Ndir) + DNdir.Dot (DNdir); if (R5 <= gp::Resolution()) { //We try another computation but the stability is not very good //dixit ISG. if (R4 <= gp::Resolution()) { Geom2d_UndefinedDerivative::Raise(); } // V2 = P" (U) : Standard_Real R4 = R2 * R2; D2Ndir.Subtract (DNdir.Multiplied (2.0 * Dr / R2)); D2Ndir.Add (Ndir.Multiplied (((3.0 * Dr * Dr)/R4) - (D2r/R2))); D2Ndir.Multiply (offsetValue / R); if(IsDirectionChange) V2=-V2; V2.Add (Vec2d(D2Ndir)); // V1 = P' (U) : DNdir.Multiply(R); DNdir.Subtract (Ndir.Multiplied (Dr/R)); DNdir.Multiply (offsetValue/R2); theV1.Add (Vec2d(DNdir)); } else { // Same computation as IICURV in EUCLID-IS because the stability is // better. // V2 = P" (U) : D2Ndir.Multiply (offsetValue/R); D2Ndir.Subtract (DNdir.Multiplied (2.0 * offsetValue * Dr / R3)); D2Ndir.Add (Ndir.Multiplied (offsetValue * (((3.0 * Dr * Dr) / R5) - (D2r / R3)))); if(IsDirectionChange) V2=-V2; V2.Add (Vec2d(D2Ndir)); // V1 = P' (U) DNdir.Multiply (offsetValue/R); DNdir.Subtract (Ndir.Multiplied (offsetValue*Dr/R3)); theV1.Add (Vec2d(DNdir)); } //P (U) : D0(theU, P); } //======================================================================= //function : D3 //purpose : //======================================================================= void Geom2d_OffsetCurve::D3 (const Standard_Real theU, Pnt2d& P, Vec2d& theV1, Vec2d& V2, Vec2d& V3) 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 const Standard_Real aTol = gp::Resolution(); Standard_Boolean IsDirectionChange = Standard_False; basisCurve->D3 (theU, P, theV1, V2, V3); Vec2d V4 = basisCurve->DN (theU, 4); if(theV1.Magnitude() <= aTol) { const Standard_Real anUinfium = basisCurve->FirstParameter(); const Standard_Real anUsupremum = basisCurve->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 = basisCurve->DN(theU,++anIndex); } while((V.Magnitude() <= aTol) && anIndex < maxDerivOrder); Standard_Real u; if(theU-anUinfium < aDelta) u = theU+aDelta; else u = theU-aDelta; Pnt2d P1, P2; basisCurve->D0(Min(theU, u),P1); basisCurve->D0(Max(theU, u),P2); Vec2d V1(P1,P2); Standard_Real aDirFactor = V.Dot(V1); if(aDirFactor < 0.0) { theV1 = -V; V2 = -basisCurve->DN (theU, anIndex + 1); V3 = -basisCurve->DN (theU, anIndex + 2); V4 = -basisCurve->DN (theU, anIndex + 3); IsDirectionChange = Standard_True; } else { theV1 = V; V2 = basisCurve->DN (theU, anIndex + 1); V3 = basisCurve->DN (theU, anIndex + 2); V4 = basisCurve->DN (theU, anIndex + 3); } }//if(V1.Magnitude() <= aTol) XY Ndir (theV1.Y(), -theV1.X()); XY DNdir (V2.Y(), -V2.X()); XY D2Ndir (V3.Y(), -V3.X()); XY D3Ndir (V4.Y(), -V4.X()); Standard_Real R2 = Ndir.SquareModulus(); Standard_Real R = Sqrt (R2); Standard_Real R3 = R2 * R; Standard_Real R4 = R2 * R2; Standard_Real R5 = R3 * R2; Standard_Real R6 = R3 * R3; Standard_Real R7 = R5 * R2; Standard_Real Dr = Ndir.Dot (DNdir); Standard_Real D2r = Ndir.Dot (D2Ndir) + DNdir.Dot (DNdir); Standard_Real D3r = Ndir.Dot (D3Ndir) + 3.0 * DNdir.Dot (D2Ndir); if (R7 <= gp::Resolution()) { //We try another computation but the stability is not very good //dixit ISG. if (R6 <= gp::Resolution()) Geom2d_UndefinedDerivative::Raise(); // V3 = P"' (U) : D3Ndir.Subtract (D2Ndir.Multiplied (3.0 * offsetValue * Dr / R2)); D3Ndir.Subtract ( (DNdir.Multiplied ((3.0 * offsetValue) * ((D2r/R2) + (Dr*Dr)/R4)))); D3Ndir.Add (Ndir.Multiplied ( (offsetValue * (6.0*Dr*Dr/R4 + 6.0*Dr*D2r/R4 - 15.0*Dr*Dr*Dr/R6 - D3r)))); D3Ndir.Multiply (offsetValue/R); if(IsDirectionChange) V3=-V3; V3.Add (Vec2d(D3Ndir)); // V2 = P" (U) : Standard_Real R4 = R2 * R2; D2Ndir.Subtract (DNdir.Multiplied (2.0 * Dr / R2)); D2Ndir.Subtract (Ndir.Multiplied (((3.0 * Dr * Dr)/R4) - (D2r/R2))); D2Ndir.Multiply (offsetValue / R); V2.Add (Vec2d(D2Ndir)); // V1 = P' (U) : DNdir.Multiply(R); DNdir.Subtract (Ndir.Multiplied (Dr/R)); DNdir.Multiply (offsetValue/R2); theV1.Add (Vec2d(DNdir)); } else { // Same computation as IICURV in EUCLID-IS because the stability is // better. // V3 = P"' (U) : D3Ndir.Multiply (offsetValue/R); D3Ndir.Subtract (D2Ndir.Multiplied (3.0 * offsetValue * Dr / R3)); D3Ndir.Subtract (DNdir.Multiplied ( ((3.0 * offsetValue) * ((D2r/R3) + (Dr*Dr)/R5))) ); D3Ndir.Add (Ndir.Multiplied ( (offsetValue * (6.0*Dr*Dr/R5 + 6.0*Dr*D2r/R5 - 15.0*Dr*Dr*Dr/R7 - D3r)))); if(IsDirectionChange) V3=-V3; V3.Add (Vec2d(D3Ndir)); // V2 = P" (U) : D2Ndir.Multiply (offsetValue/R); D2Ndir.Subtract (DNdir.Multiplied (2.0 * offsetValue * Dr / R3)); D2Ndir.Subtract (Ndir.Multiplied ( offsetValue * (((3.0 * Dr * Dr) / R5) - (D2r / R3)))); V2.Add (Vec2d(D2Ndir)); // V1 = P' (U) : DNdir.Multiply (offsetValue/R); DNdir.Subtract (Ndir.Multiplied (offsetValue*Dr/R3)); theV1.Add (Vec2d(DNdir)); } //P (U) : D0(theU, P); } //======================================================================= //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); } XY Ndir (V1.Y(), -V1.X()); XY DNdir (V2.Y(), -V2.X()); Standard_Real R2 = Ndir.SquareModulus(); Standard_Real R = Sqrt (R2); Standard_Real R3 = R * R2; Standard_Real Dr = Ndir.Dot (DNdir); if (R3 <= gp::Resolution()) { //We try another computation but the stability is not very good. if (R2 <= gp::Resolution()) { Geom2d_UndefinedDerivative::Raise(); } DNdir.Multiply(R); DNdir.Subtract (Ndir.Multiplied (Dr/R)); DNdir.Multiply (offsetValue / R2); V1.Add (Vec2d(DNdir)); } else { // Same computation as IICURV in EUCLID-IS because the stability is // better DNdir.Multiply (offsetValue/R); DNdir.Subtract (Ndir.Multiplied (offsetValue*Dr/R3)); V1.Add (Vec2d(DNdir)); } Ndir.Multiply (offsetValue/R); Ndir.Add (Pbasis.XY()); P.SetXY (Ndir); } //======================================================================= //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); } XY Ndir (V1.Y(), -V1.X()); XY DNdir (V2.Y(), -V2.X()); XY D2Ndir (V3.Y(), -V3.X()); Standard_Real R2 = Ndir.SquareModulus(); Standard_Real R = Sqrt (R2); Standard_Real R3 = R2 * R; Standard_Real R4 = R2 * R2; Standard_Real R5 = R3 * R2; Standard_Real Dr = Ndir.Dot (DNdir); Standard_Real D2r = Ndir.Dot (D2Ndir) + DNdir.Dot (DNdir); if (R5 <= gp::Resolution()) { //We try another computation but the stability is not very good //dixit ISG. if (R4 <= gp::Resolution()) { Geom2d_UndefinedDerivative::Raise(); } // V2 = P" (U) : Standard_Real R4 = R2 * R2; D2Ndir.Subtract (DNdir.Multiplied (2.0 * Dr / R2)); D2Ndir.Subtract (Ndir.Multiplied (((3.0 * Dr * Dr)/R4) - (D2r/R2))); D2Ndir.Multiply (offsetValue / R); V2.Add (Vec2d(D2Ndir)); // V1 = P' (U) : DNdir.Multiply(R); DNdir.Subtract (Ndir.Multiplied (Dr/R)); DNdir.Multiply (offsetValue/R2); V1.Add (Vec2d(DNdir)); } else { // Same computation as IICURV in EUCLID-IS because the stability is // better. // V2 = P" (U) : D2Ndir.Multiply (offsetValue/R); D2Ndir.Subtract (DNdir.Multiplied (2.0 * offsetValue * Dr / R3)); D2Ndir.Subtract (Ndir.Multiplied ( offsetValue * (((3.0 * Dr * Dr) / R5) - (D2r / R3)) ) ); V2.Add (Vec2d(D2Ndir)); // V1 = P' (U) : DNdir.Multiply (offsetValue/R); DNdir.Subtract (Ndir.Multiplied (offsetValue*Dr/R3)); V1.Add (Vec2d(DNdir)); } //P (U) : Ndir.Multiply (offsetValue/R); Ndir.Add (Pbasis.XY()); P.SetXY (Ndir); } //======================================================================= //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; }