// Created on: 1994-01-04 // Created by: Christophe MARION // Copyright (c) 1994-1999 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. #include #include #include #include #include #include #include #include #include #include #include #include #include #include //======================================================================= //function : Extrema_ExtElC2d //purpose : //======================================================================= Extrema_ExtElC2d::Extrema_ExtElC2d() { myDone = Standard_False; myIsPar = Standard_False; myNbExt = 0; for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++) { mySqDist[anIdx] = RealLast(); } } //======================================================================= //function : Extrema_ExtElC2d //purpose : //======================================================================= Extrema_ExtElC2d::Extrema_ExtElC2d (const gp_Lin2d& C1, const gp_Lin2d& C2, const Standard_Real) /*----------------------------------------------------------------------------- Function: Find min distance between 2 straight lines. Method: Let D1 and D2 be 2 directions of straight lines C1 and C2. 2 cases are considered: 1- if Angle(D1,D2) < AngTol, the straight lines are parallel. The distance is the distance between any point of C1 and straight line C2. 2- if Angle(D1,D2) > AngTol: Let P = C1(u1) and P =C2(u2) the point intersection: -----------------------------------------------------------------------------*/ { myDone = Standard_False; myIsPar = Standard_False; myNbExt = 0; for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++) { mySqDist[anIdx] = RealLast(); } gp_Vec2d D1(C1.Direction()); gp_Vec2d D2(C2.Direction()); if (D1.IsParallel(D2, Precision::Angular())) { myIsPar = Standard_True; mySqDist[0] = C2.SquareDistance(C1.Location()); myNbExt = 1; } else { // Vector from P1 to P2 (P2 - P1). gp_Vec2d aP1P2(C1.Location(), C2.Location()); // Solve linear system using Cramer's rule: // D1.X * t1 + D2.X * (-t2) = P2.X - P1.X // D1.Y * t1 + D2.Y * (-t2) = P2.Y - P1.Y // There is no division by zero since lines are not parallel. Standard_Real aDelim = 1 / (D1^D2); Standard_Real aParam1 = (aP1P2 ^ D2) * aDelim; Standard_Real aParam2 = -(D1 ^ aP1P2) * aDelim; // -1.0 coefficient before t2. gp_Pnt2d P1 = ElCLib::Value(aParam1, C1); gp_Pnt2d P2 = ElCLib::Value(aParam2, C2); mySqDist[myNbExt] = 0.0; myPoint[myNbExt][0] = Extrema_POnCurv2d(aParam1,P1); myPoint[myNbExt][1] = Extrema_POnCurv2d(aParam2,P2); myNbExt = 1; } myDone = Standard_True; } //============================================================================= Extrema_ExtElC2d::Extrema_ExtElC2d (const gp_Lin2d& C1, const gp_Circ2d& C2, const Standard_Real) /*----------------------------------------------------------------------------- Function: Find extreme distances between straight line C1 and circle C2. Method: Let P1=C1(u1) and P2=C2(u2) be two solution points D the direction of straight line C1 T the tangent at point P2; Then, ( P1P2.D = 0. (1) ( P1P2.T = 0. (2) -----------------------------------------------------------------------------*/ { myIsPar = Standard_False; myDone = Standard_False; myNbExt = 0; for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++) { mySqDist[anIdx] = RealLast(); } // Calculate T1 in the reference of the circle ... gp_Dir2d D = C1.Direction(); gp_Dir2d x2, y2; x2 = C2.XAxis().Direction(); y2 = C2.YAxis().Direction(); Standard_Real Dx = D.Dot(x2); Standard_Real Dy = D.Dot(y2); Standard_Real U1, teta[2]; gp_Pnt2d O1=C1.Location(); gp_Pnt2d P1, P2; if (Abs(Dy) <= RealEpsilon()) { teta[0] = M_PI/2.0; } else teta[0] = ATan(-Dx/Dy); teta[1] = teta[0]+ M_PI; if (teta[0] < 0.0) teta[0] = teta[0] + 2.0*M_PI; P2 = ElCLib::Value(teta[0], C2); U1 = (gp_Vec2d(O1, P2)).Dot(D); P1 = ElCLib::Value(U1, C1); mySqDist[myNbExt] = P1.SquareDistance(P2); myPoint[myNbExt][0] = Extrema_POnCurv2d(U1,P1); myPoint[myNbExt][1] = Extrema_POnCurv2d(teta[0],P2); myNbExt++; P2 = ElCLib::Value(teta[1], C2); U1 = (gp_Vec2d(O1, P2)).Dot(D); P1 = ElCLib::Value(U1, C1); mySqDist[myNbExt] = P1.SquareDistance(P2); myPoint[myNbExt][0] = Extrema_POnCurv2d(U1,P1); myPoint[myNbExt][1] = Extrema_POnCurv2d(teta[1],P2); myNbExt++; myDone = Standard_True; } // ============================================================================= Extrema_ExtElC2d::Extrema_ExtElC2d (const gp_Lin2d& C1, const gp_Elips2d& C2) { myDone = Standard_True; myIsPar = Standard_False; myDone = Standard_False; myNbExt = 0; for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++) { mySqDist[anIdx] = RealLast(); } // Calculate T1 in the reference of the ellipse ... gp_Dir2d D = C1.Direction(); gp_Dir2d x2, y2; x2 = C2.XAxis().Direction(); y2 = C2.YAxis().Direction(); Standard_Real Dx = D.Dot(x2); Standard_Real Dy = D.Dot(y2); Standard_Real U1, teta[2], r1 = C2.MajorRadius(), r2 = C2.MinorRadius(); gp_Pnt2d O1=C1.Location(), P1, P2; if (Abs(Dy) <= RealEpsilon()) { teta[0] = M_PI/2.0; } else teta[0] = ATan(-Dx*r2/(Dy*r1)); teta[1] = teta[0] + M_PI; if (teta[0] < 0.0) teta[0] += 2.0*M_PI; P2 = ElCLib::Value(teta[0], C2); U1 = (gp_Vec2d(O1, P2)).Dot(D); P1 = ElCLib::Value(U1, C1); mySqDist[myNbExt] = P1.SquareDistance(P2); myPoint[myNbExt][0] = Extrema_POnCurv2d(U1,P1); myPoint[myNbExt][1] = Extrema_POnCurv2d(teta[0],P2); myNbExt++; P2 = ElCLib::Value(teta[1], C2); U1 = (gp_Vec2d(O1, P2)).Dot(D); P1 = ElCLib::Value(U1, C1); mySqDist[myNbExt] = P1.SquareDistance(P2); myPoint[myNbExt][0] = Extrema_POnCurv2d(U1,P1); myPoint[myNbExt][1] = Extrema_POnCurv2d(teta[1],P2); myNbExt++; myDone = Standard_True; } //============================================================================= Extrema_ExtElC2d::Extrema_ExtElC2d (const gp_Lin2d& C1, const gp_Hypr2d& C2) { myIsPar = Standard_False; myDone = Standard_False; myNbExt = 0; for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++) { mySqDist[anIdx] = RealLast(); } // Calculate T1 in the reference of the parabole ... gp_Dir2d D = C1.Direction(); gp_Dir2d x2, y2; x2 = C2.XAxis().Direction(); y2 = C2.YAxis().Direction(); Standard_Real Dx = D.Dot(x2); Standard_Real Dy = D.Dot(y2); Standard_Real U1, v2, U2=0, R = C2.MajorRadius(), r = C2.MinorRadius(); gp_Pnt2d P1, P2; if (Abs(Dy) < RealEpsilon()) { return;} if (Abs(R - r*Dx/Dy) < RealEpsilon()) return; v2 = (R + r*Dx/Dy)/(R - r*Dx/Dy); if (v2 > 0.0) U2 = Log(Sqrt(v2)); P2 = ElCLib::Value(U2, C2); U1 = (gp_Vec2d(C1.Location(), P2)).Dot(D); P1 = ElCLib::Value(U1, C1); mySqDist[myNbExt] = P1.SquareDistance(P2); myPoint[myNbExt][0] = Extrema_POnCurv2d(U1,P1); myPoint[myNbExt][1] = Extrema_POnCurv2d(U2,P2); myNbExt++; myDone = Standard_True; } //============================================================================ Extrema_ExtElC2d::Extrema_ExtElC2d (const gp_Lin2d& C1, const gp_Parab2d& C2) { myIsPar = Standard_False; myDone = Standard_False; myNbExt = 0; for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++) { mySqDist[anIdx] = RealLast(); } // Calculate T1 in the reference of the parabole ... gp_Dir2d D = C1.Direction(); gp_Dir2d x2, y2; x2 = C2.MirrorAxis().Direction(); y2 = C2.Axis().YAxis().Direction(); Standard_Real Dx = D.Dot(x2); Standard_Real Dy = D.Dot(y2); Standard_Real U1, U2, P = C2.Parameter(); gp_Pnt2d P1, P2; if (Abs(Dy) < RealEpsilon()) { return; } U2 = Dx*P/Dy; P2 = ElCLib::Value(U2, C2); U1 = (gp_Vec2d(C1.Location(), P2)).Dot(D); P1 = ElCLib::Value(U1, C1); mySqDist[myNbExt] = P1.SquareDistance(P2); myPoint[myNbExt][0] = Extrema_POnCurv2d(U1,P1); myPoint[myNbExt][1] = Extrema_POnCurv2d(U2,P2); myNbExt++; myDone = Standard_True; } //============================================================================ Extrema_ExtElC2d::Extrema_ExtElC2d (const gp_Circ2d& C1, const gp_Circ2d& C2) { myIsPar = Standard_False; myDone = Standard_False; myNbExt = 0; myDone = Standard_True; for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++) { mySqDist[anIdx] = RealLast(); } gp_Pnt2d O1 = C1.Location(); gp_Pnt2d O2 = C2.Location(); gp_Vec2d DO1O2 (O1, O2); const Standard_Real aSqDCenters = DO1O2.SquareMagnitude(); if (aSqDCenters < Precision::SquareConfusion()) { myIsPar = Standard_True; myNbExt = 1; myDone = Standard_True; const Standard_Real aDR = C1.Radius() - C2.Radius(); mySqDist[0] = aDR*aDR; return; } Standard_Integer NoSol, kk; Standard_Real U1, U2; Standard_Real r1 = C1.Radius(), r2 = C2.Radius(); Standard_Real Usol2[2], Usol1[2]; gp_Pnt2d P1[2], P2[2]; gp_Vec2d O1O2(DO1O2/Sqrt(aSqDCenters)); P1[0] = O1.Translated(r1*O1O2); Usol1[0] = ElCLib::Parameter(C1, P1[0]); P1[1] = O1.Translated(-r1*O1O2); Usol1[1] = ElCLib::Parameter(C1, P1[1]); P2[0] = O2.Translated(r2*O1O2); Usol2[0] = ElCLib::Parameter(C2, P2[0]); P2[1] = O2.Translated(-r2*O1O2); Usol2[1] = ElCLib::Parameter(C2, P2[1]); for (NoSol = 0; NoSol <= 1; NoSol++) { U1 = Usol1[NoSol]; for (kk = 0; kk <= 1; kk++) { U2 = Usol2[kk]; mySqDist[myNbExt] = P2[kk].SquareDistance(P1[NoSol]); myPoint[myNbExt][0] = Extrema_POnCurv2d(U1, P1[NoSol]); myPoint[myNbExt][1] = Extrema_POnCurv2d(U2, P2[kk]); myNbExt++; } } } //=========================================================================== Extrema_ExtElC2d::Extrema_ExtElC2d (const gp_Circ2d& C1, const gp_Elips2d& C2) { myIsPar = Standard_False; myDone = Standard_False; myNbExt = 0; for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++) { mySqDist[anIdx] = RealLast(); } Standard_Integer i, j; Extrema_ExtPElC2d ExtElip(C1.Location(), C2, Precision::Confusion(), 0.0, 2.0*M_PI); if (ExtElip.IsDone()) { for (i = 1; i <= ExtElip.NbExt(); i++) { Extrema_ExtPElC2d ExtCirc(ExtElip.Point(i).Value(), C1, Precision::Confusion(), 0.0, 2.0*M_PI); if (ExtCirc.IsDone()) { for (j = 1; j <= ExtCirc.NbExt(); j++) { mySqDist[myNbExt] = ExtCirc.SquareDistance(j); myPoint[myNbExt][0] = ExtCirc.Point(j); myPoint[myNbExt][1] = ExtElip.Point(i); myNbExt++; } } myDone = Standard_True; } } } //============================================================================ Extrema_ExtElC2d::Extrema_ExtElC2d (const gp_Circ2d& C1, const gp_Hypr2d& C2) { myIsPar = Standard_False; myDone = Standard_False; myNbExt = 0; for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++) { mySqDist[anIdx] = RealLast(); } Standard_Integer i, j; Extrema_ExtPElC2d ExtHyp(C1.Location(), C2, Precision::Confusion(), RealFirst(), RealLast()); if (ExtHyp.IsDone()) { for (i = 1; i <= ExtHyp.NbExt(); i++) { Extrema_ExtPElC2d ExtCirc(ExtHyp.Point(i).Value(), C1, Precision::Confusion(), 0.0, 2.0*M_PI); if (ExtCirc.IsDone()) { for (j = 1; j <= ExtCirc.NbExt(); j++) { mySqDist[myNbExt] = ExtCirc.SquareDistance(j); myPoint[myNbExt][0] = ExtCirc.Point(j); myPoint[myNbExt][1] = ExtHyp.Point(i); myNbExt++; } } myDone = Standard_True; } } } //============================================================================ Extrema_ExtElC2d::Extrema_ExtElC2d (const gp_Circ2d& C1, const gp_Parab2d& C2) { myIsPar = Standard_False; myDone = Standard_False; myNbExt = 0; for (size_t anIdx = 0; anIdx < sizeof (mySqDist) / sizeof (mySqDist[0]); anIdx++) { mySqDist[anIdx] = RealLast(); } Standard_Integer i, j; Extrema_ExtPElC2d ExtParab(C1.Location(), C2, Precision::Confusion(), RealFirst(), RealLast()); if (ExtParab.IsDone()) { for (i = 1; i <= ExtParab.NbExt(); i++) { Extrema_ExtPElC2d ExtCirc(ExtParab.Point(i).Value(), C1, Precision::Confusion(), 0.0, 2.0*M_PI); if (ExtCirc.IsDone()) { for (j = 1; j <= ExtCirc.NbExt(); j++) { mySqDist[myNbExt] = ExtCirc.SquareDistance(j); myPoint[myNbExt][0] = ExtCirc.Point(j); myPoint[myNbExt][1] = ExtParab.Point(i); myNbExt++; } } myDone = Standard_True; } } } //============================================================================ Standard_Boolean Extrema_ExtElC2d::IsDone () const { return myDone; } //============================================================================ Standard_Boolean Extrema_ExtElC2d::IsParallel () const { if (!IsDone()) { throw StdFail_NotDone(); } return myIsPar; } //============================================================================ Standard_Integer Extrema_ExtElC2d::NbExt () const { if (!IsDone()) { throw StdFail_NotDone(); } return myNbExt; } //============================================================================ Standard_Real Extrema_ExtElC2d::SquareDistance (const Standard_Integer N) const { if (N < 1 || N > NbExt()) { throw Standard_OutOfRange(); } return mySqDist[N - 1]; } //============================================================================ void Extrema_ExtElC2d::Points (const Standard_Integer N, Extrema_POnCurv2d& P1, Extrema_POnCurv2d& P2) const { if (N < 1 || N > NbExt()) { throw Standard_OutOfRange(); } P1 = myPoint[N-1][0]; P2 = myPoint[N-1][1]; } //============================================================================