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516 lines
14 KiB
C++
516 lines
14 KiB
C++
// Copyright (c) 1995-1999 Matra Datavision
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// Copyright (c) 1999-2014 OPEN CASCADE SAS
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//
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// This file is part of Open CASCADE Technology software library.
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//
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// This library is free software; you can redistribute it and/or modify it under
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// the terms of the GNU Lesser General Public License version 2.1 as published
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// by the Free Software Foundation, with special exception defined in the file
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// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
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// distribution for complete text of the license and disclaimer of any warranty.
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//
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// Alternatively, this file may be used under the terms of Open CASCADE
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// commercial license or contractual agreement.
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#include <ElSLib.hxx>
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#include <Extrema_ExtPElS.hxx>
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#include <Extrema_POnSurf.hxx>
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#include <gp_Cone.hxx>
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#include <gp_Cylinder.hxx>
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#include <gp_Pln.hxx>
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#include <gp_Pnt.hxx>
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#include <gp_Sphere.hxx>
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#include <gp_Torus.hxx>
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#include <Standard_NotImplemented.hxx>
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#include <Standard_OutOfRange.hxx>
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#include <StdFail_NotDone.hxx>
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static const Standard_Real ExtPElS_MyEps = Epsilon(2. * M_PI);
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//=============================================================================
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Extrema_ExtPElS::Extrema_ExtPElS()
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{
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myDone = Standard_False;
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myNbExt = 0;
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for (Standard_Integer i = 0; i < 4; i++)
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{
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mySqDist[i] = RealLast();
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}
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}
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//=============================================================================
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Extrema_ExtPElS::Extrema_ExtPElS(const gp_Pnt& P, const gp_Cylinder& S, const Standard_Real Tol)
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{
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Perform(P, S, Tol);
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}
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/*-----------------------------------------------------------------------------
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Function:
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Find 2 extreme distances between point P and cylinder S.
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Method:
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Let Pp be the projection of P in plane XOY of the cylinder;
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2 cases are considered:
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1- distance(Pp,O) < Tol:
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There are infinite solutions; IsDone() = Standard_False.
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2- distance(Pp,O) > Tol:
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let V = OP.OZ,
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U1 = angle(OX,OPp) with 0 < U1 < 2.*M_PI
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U2 = U1 + M_PI with 0 < U2 < 2.*M_PI;
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then (U1,V) corresponds to the min distance.
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and (U2,V) corresponds to the max distance.
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-----------------------------------------------------------------------------*/
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void Extrema_ExtPElS::Perform(const gp_Pnt& P, const gp_Cylinder& S, const Standard_Real Tol)
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{
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myDone = Standard_False;
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myNbExt = 0;
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// Projection of point P in plane XOY of the cylinder ...
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gp_Ax3 Pos = S.Position();
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gp_Pnt O = Pos.Location();
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gp_Vec OZ(Pos.Direction());
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Standard_Real V = gp_Vec(O, P).Dot(OZ);
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gp_Pnt Pp = P.Translated(OZ.Multiplied(-V));
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// Calculation of extrema
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gp_Vec OPp(O, Pp);
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if (OPp.Magnitude() < Tol)
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{
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return;
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}
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gp_Vec myZ = Pos.XDirection() ^ Pos.YDirection();
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Standard_Real U1 = gp_Vec(Pos.XDirection()).AngleWithRef(OPp, myZ); //-M_PI<U1<M_PI
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if (U1 > -ExtPElS_MyEps && U1 < ExtPElS_MyEps)
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{
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U1 = 0.;
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}
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Standard_Real U2 = U1 + M_PI;
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if (U1 < 0.)
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{
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U1 += 2. * M_PI;
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}
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gp_Pnt Ps;
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Ps = ElSLib::Value(U1, V, S);
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mySqDist[0] = Ps.SquareDistance(P);
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myPoint[0] = Extrema_POnSurf(U1, V, Ps);
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Ps = ElSLib::Value(U2, V, S);
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mySqDist[1] = Ps.SquareDistance(P);
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myPoint[1] = Extrema_POnSurf(U2, V, Ps);
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myNbExt = 2;
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myDone = Standard_True;
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}
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//=============================================================================
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Extrema_ExtPElS::Extrema_ExtPElS(const gp_Pnt& P, const gp_Cone& S, const Standard_Real Tol)
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{
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Perform(P, S, Tol);
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}
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/*-----------------------------------------------------------------------------
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Function:
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Find 2 extreme distances between point P and cone S.
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Method:
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Let M the top of the cone.
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2 cases are considered:
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1- distance(P,M) < Tol:
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there is a minimum in M.
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2- distance(P,M) > Tol:
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Let Pp the projection of P in the plane XOY of the cone;
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2 cases are considered:
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1- distance(Pp,O) < Tol:
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There is an infinite number of solutions; IsDone() = Standard_False.
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2- distance(Pp,O) > Tol:
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There exist 2 extrema:
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Let Vm = value of v for point M,
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Vp = value of v for point P,
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U1 = angle(OX,OPp) if Vp > Vm )
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-angle(OX,OPp) otherwise ) with 0. < U1 < 2*M_PI,
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U2 = U1 + M_PI with 0. < U2 < 2*M_PI;
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We are in plane PpOZ.
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Let A the angle of the cone,
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B = angle(MP,MO) with 0. < B < M_PI,
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L = longueur(MP),
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V1 = (L * cos(B-A)) + Vm,
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V2 = (L * cos(B+A)) + Vm;
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then (U1,V1) and (U2,V2) correspond to min distances.
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-----------------------------------------------------------------------------*/
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void Extrema_ExtPElS::Perform(const gp_Pnt& P, const gp_Cone& S, const Standard_Real Tol)
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{
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myDone = Standard_False;
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myNbExt = 0;
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gp_Pnt M = S.Apex();
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gp_Ax3 Pos = S.Position();
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gp_Pnt O = Pos.Location();
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Standard_Real A = S.SemiAngle();
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gp_Vec OZ(Pos.Direction());
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gp_Vec myZ = Pos.XDirection() ^ Pos.YDirection();
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gp_Vec MP(M, P);
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Standard_Real L2 = MP.SquareMagnitude();
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Standard_Real Vm = -(S.RefRadius() / Sin(A));
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// Case when P is mixed with S ...
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if (L2 < Tol * Tol)
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{
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mySqDist[0] = L2;
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myPoint[0] = Extrema_POnSurf(0., Vm, M);
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myNbExt = 1;
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myDone = Standard_True;
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return;
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}
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gp_Vec DirZ;
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if (M.SquareDistance(O) < Tol * Tol)
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{
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DirZ = (A < 0 ? -OZ : OZ);
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}
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else
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DirZ = gp_Vec(M, O);
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// Projection of P in the reference plane of the cone ...
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Standard_Real Zp = gp_Vec(O, P).Dot(OZ);
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gp_Pnt Pp = P.Translated(OZ.Multiplied(-Zp));
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gp_Vec OPp(O, Pp);
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if (OPp.SquareMagnitude() < Tol * Tol)
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return;
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Standard_Real U1, V1, U2, V2;
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Standard_Boolean Same = DirZ.Dot(MP) >= 0.0;
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U1 = gp_Vec(Pos.XDirection()).AngleWithRef(OPp, myZ); //-M_PI<U1<M_PI
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if (U1 > -ExtPElS_MyEps && U1 < ExtPElS_MyEps)
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{
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U1 = 0.;
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}
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if (!Same)
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{
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U1 += M_PI;
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}
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U2 = U1 + M_PI;
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if (U1 < 0.)
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{
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U1 += 2. * M_PI;
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}
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if (U2 > 2. * M_PI)
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{
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U2 -= 2. * M_PI;
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}
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Standard_Real B = MP.Angle(DirZ);
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A = Abs(A);
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Standard_Real L = sqrt(L2);
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if (!Same)
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{
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B = M_PI - B;
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V1 = -L * cos(B - A);
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V2 = -L * cos(B + A);
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}
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else
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{
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V1 = L * cos(B - A);
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V2 = L * cos(B + A);
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}
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Standard_Real Sense = OZ.Dot(gp_Dir(DirZ));
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V1 *= Sense;
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V2 *= Sense;
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V1 += Vm;
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V2 += Vm;
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gp_Pnt Ps;
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Ps = ElSLib::Value(U1, V1, S);
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mySqDist[0] = Ps.SquareDistance(P);
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myPoint[0] = Extrema_POnSurf(U1, V1, Ps);
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Ps = ElSLib::Value(U2, V2, S);
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mySqDist[1] = Ps.SquareDistance(P);
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myPoint[1] = Extrema_POnSurf(U2, V2, Ps);
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myNbExt = 2;
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myDone = Standard_True;
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}
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//=============================================================================
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Extrema_ExtPElS::Extrema_ExtPElS(const gp_Pnt& P, const gp_Sphere& S, const Standard_Real Tol)
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{
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Perform(P, S, Tol);
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}
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/*-----------------------------------------------------------------------------
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Function:
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Find 2 extreme distances between point P and sphere S.
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Method:
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Let O be the origin of the sphere.
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2 cases are considered:
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1- distance(P,O) < Tol:
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There is an infinite number of solutions; IsDone() = Standard_False
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2- distance(P,O) > Tol:
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Let Pp be the projection of point P in the plane XOY of the sphere;
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2 cases are considered:
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1- distance(Pp,O) < Tol:
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2 solutions are: (0,-M_PI/2.) and (0.,M_PI/2.)
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2- distance(Pp,O) > Tol:
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Let U1 = angle(OX,OPp) with 0. < U1 < 2.*M_PI,
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U2 = U1 + M_PI avec 0. < U2 < 2*M_PI,
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V1 = angle(OPp,OP) with -M_PI/2. < V1 < M_PI/2. ,
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then (U1, V1) corresponds to the min distance
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and (U2,-V1) corresponds to the max distance.
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-----------------------------------------------------------------------------*/
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void Extrema_ExtPElS::Perform(const gp_Pnt& P, const gp_Sphere& S, const Standard_Real Tol)
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{
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myDone = Standard_False;
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myNbExt = 0;
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gp_Ax3 Pos = S.Position();
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gp_Vec OP(Pos.Location(), P);
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// Case when P is mixed with O ...
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if (OP.SquareMagnitude() < Tol * Tol)
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{
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return;
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}
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// Projection if P in plane XOY of the sphere ...
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gp_Pnt O = Pos.Location();
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gp_Vec OZ(Pos.Direction());
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Standard_Real Zp = OP.Dot(OZ);
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gp_Pnt Pp = P.Translated(OZ.Multiplied(-Zp));
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// Calculation of extrema ...
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gp_Vec OPp(O, Pp);
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Standard_Real U1, U2, V;
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if (OPp.SquareMagnitude() < Tol * Tol)
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{
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U1 = 0.;
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U2 = 0.;
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if (Zp < 0.)
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{
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V = -M_PI / 2.;
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}
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else
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{
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V = M_PI / 2.;
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}
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}
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else
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{
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gp_Vec myZ = Pos.XDirection() ^ Pos.YDirection();
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U1 = gp_Vec(Pos.XDirection()).AngleWithRef(OPp, myZ);
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if (U1 > -ExtPElS_MyEps && U1 < ExtPElS_MyEps)
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{
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U1 = 0.;
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}
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U2 = U1 + M_PI;
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if (U1 < 0.)
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{
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U1 += 2. * M_PI;
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}
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V = OP.Angle(OPp);
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if (Zp < 0.)
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{
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V = -V;
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}
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}
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gp_Pnt Ps;
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Ps = ElSLib::Value(U1, V, S);
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mySqDist[0] = Ps.SquareDistance(P);
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myPoint[0] = Extrema_POnSurf(U1, V, Ps);
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Ps = ElSLib::Value(U2, -V, S);
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mySqDist[1] = Ps.SquareDistance(P);
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myPoint[1] = Extrema_POnSurf(U2, -V, Ps);
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myNbExt = 2;
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myDone = Standard_True;
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}
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//=============================================================================
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Extrema_ExtPElS::Extrema_ExtPElS(const gp_Pnt& P, const gp_Torus& S, const Standard_Real Tol)
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{
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Perform(P, S, Tol);
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}
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/*-----------------------------------------------------------------------------
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Function:
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Find 2 extreme distances between point P and torus S.
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Method:
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Let Pp be the projection of point P in plane XOY of the torus;
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2 cases are considered:
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1- distance(Pp,O) < Tol:
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There is an infinite number of solutions; IsDone() = Standard_False.
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2- distance(Pp,O) > Tol:
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One is located in plane PpOZ;
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Let V1 = angle(OX,OPp) with 0. < V1 < 2.*M_PI,
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V2 = V1 + M_PI with 0. < V2 < 2.*M_PI,
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O1 and O2 centers of circles (O1 on coord. posit.)
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U1 = angle(OPp,O1P),
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U2 = angle(OPp,PO2);
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then (U1,V1) corresponds to the min distance
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and (U2,V2) corresponds to the max distance.
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-----------------------------------------------------------------------------*/
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void Extrema_ExtPElS::Perform(const gp_Pnt& P, const gp_Torus& S, const Standard_Real Tol)
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{
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const Standard_Real tol2 = Tol * Tol;
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myDone = Standard_False;
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myNbExt = 0;
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// Projection of P in plane XOY ...
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gp_Ax3 Pos = S.Position();
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gp_Pnt O = Pos.Location();
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gp_Vec OZ(Pos.Direction());
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gp_Pnt Pp = P.Translated(OZ.Multiplied(-(gp_Vec(O, P).Dot(Pos.Direction()))));
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// Calculation of extrema ...
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gp_Vec OPp(O, Pp);
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Standard_Real R2 = OPp.SquareMagnitude();
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if (R2 < tol2)
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{
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return;
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}
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gp_Vec myZ = Pos.XDirection() ^ Pos.YDirection();
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Standard_Real U1 = gp_Vec(Pos.XDirection()).AngleWithRef(OPp, myZ);
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if (U1 > -ExtPElS_MyEps && U1 < ExtPElS_MyEps)
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{
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U1 = 0.;
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}
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Standard_Real U2 = U1 + M_PI;
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if (U1 < 0.)
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{
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U1 += 2. * M_PI;
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}
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Standard_Real R = sqrt(R2);
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gp_Vec OO1 = OPp.Divided(R).Multiplied(S.MajorRadius());
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gp_Vec OO2 = OO1.Multiplied(-1.);
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gp_Pnt O1 = O.Translated(OO1);
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gp_Pnt O2 = O.Translated(OO2);
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if (O1.SquareDistance(P) < tol2)
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{
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return;
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}
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if (O2.SquareDistance(P) < tol2)
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{
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return;
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}
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Standard_Real V1 = OPp.AngleWithRef(gp_Vec(O1, P), OPp.Crossed(OZ));
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if (V1 > -ExtPElS_MyEps && V1 < ExtPElS_MyEps)
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{
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V1 = 0.;
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}
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OPp.Reverse();
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Standard_Real V2 = OPp.AngleWithRef(gp_Vec(P, O2), OPp.Crossed(OZ));
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if (V2 > -ExtPElS_MyEps && V2 < ExtPElS_MyEps)
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{
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V2 = 0.;
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}
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if (V1 < 0.)
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{
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V1 += 2. * M_PI;
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}
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if (V2 < 0.)
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{
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V2 += 2. * M_PI;
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}
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gp_Pnt Ps;
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Ps = ElSLib::Value(U1, V1, S);
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mySqDist[0] = Ps.SquareDistance(P);
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myPoint[0] = Extrema_POnSurf(U1, V1, Ps);
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Ps = ElSLib::Value(U1, V1 + M_PI, S);
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mySqDist[1] = Ps.SquareDistance(P);
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myPoint[1] = Extrema_POnSurf(U1, V1 + M_PI, Ps);
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Ps = ElSLib::Value(U2, V2, S);
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mySqDist[2] = Ps.SquareDistance(P);
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myPoint[2] = Extrema_POnSurf(U2, V2, Ps);
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Ps = ElSLib::Value(U2, V2 + M_PI, S);
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mySqDist[3] = Ps.SquareDistance(P);
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myPoint[3] = Extrema_POnSurf(U2, V2 + M_PI, Ps);
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myNbExt = 4;
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myDone = Standard_True;
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}
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Extrema_ExtPElS::Extrema_ExtPElS(const gp_Pnt& P, const gp_Pln& S, const Standard_Real Tol)
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{
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Perform(P, S, Tol);
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}
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void Extrema_ExtPElS::Perform(const gp_Pnt& P,
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const gp_Pln& S,
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// const Standard_Real Tol)
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const Standard_Real)
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{
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myDone = Standard_False;
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myNbExt = 0;
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// Projection of point P in plane XOY of the cylinder ...
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gp_Pnt O = S.Location();
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gp_Vec OZ(S.Axis().Direction());
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Standard_Real U, V = gp_Vec(O, P).Dot(OZ);
|
|
gp_Pnt Pp = P.Translated(OZ.Multiplied(-V));
|
|
|
|
ElSLib::Parameters(S, P, U, V);
|
|
mySqDist[0] = Pp.SquareDistance(P);
|
|
myPoint[0] = Extrema_POnSurf(U, V, Pp);
|
|
myNbExt = 1;
|
|
myDone = Standard_True;
|
|
}
|
|
|
|
//=============================================================================
|
|
|
|
Standard_Boolean Extrema_ExtPElS::IsDone() const
|
|
{
|
|
return myDone;
|
|
}
|
|
|
|
//=============================================================================
|
|
|
|
Standard_Integer Extrema_ExtPElS::NbExt() const
|
|
{
|
|
if (!IsDone())
|
|
{
|
|
throw StdFail_NotDone();
|
|
}
|
|
return myNbExt;
|
|
}
|
|
|
|
//=============================================================================
|
|
|
|
Standard_Real Extrema_ExtPElS::SquareDistance(const Standard_Integer N) const
|
|
{
|
|
if ((N < 1) || (N > NbExt()))
|
|
{
|
|
throw Standard_OutOfRange();
|
|
}
|
|
return mySqDist[N - 1];
|
|
}
|
|
|
|
//=============================================================================
|
|
|
|
const Extrema_POnSurf& Extrema_ExtPElS::Point(const Standard_Integer N) const
|
|
{
|
|
if ((N < 1) || (N > NbExt()))
|
|
{
|
|
throw Standard_OutOfRange();
|
|
}
|
|
return myPoint[N - 1];
|
|
}
|
|
|
|
//=============================================================================
|