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0027895: Correction in the constructor Extrema_ExtElC::Extrema_ExtElC (const gp_Lin&,const gp_Lin&,const Standard_Real)
Computation algorithm is made more simple. Adjusting some test cases according to their new behavior.
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@ -233,8 +233,8 @@ Extrema_ExtElC::Extrema_ExtElC ()
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//function : Extrema_ExtElC
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//purpose :
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//=======================================================================
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Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& C1,
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const gp_Lin& C2,
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Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& theC1,
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const gp_Lin& theC2,
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const Standard_Real)
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// Function:
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// Find min distance between 2 straight lines.
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@ -245,71 +245,82 @@ Extrema_ExtElC::Extrema_ExtElC (const gp_Lin& C1,
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// 1- if Angle(D1,D2) < AngTol, straight lines are parallel.
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// The distance is the distance between a point of C1 and the straight line C2.
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// 2- if Angle(D1,D2) > AngTol:
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// Let P1=C1(u1) and P2=C2(u2) be 2 solution points:
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// Then, ( P1P2.D1 = 0. (1)
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// ( P1P2.D2 = 0. (2)
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// Let O1 and O2 be the origins of C1 and C2;
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// THen, (1) <=> (O1P2-u1*D1).D1 = 0. as O1P1 = u1*D1
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// <=> u1 = O1P2.D1 as D1.D1 = 1.
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// (2) <=> (P1O2+u2*D2).D2 = 0. as O2P2 = u2*D2
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// <=> u2 = O2P1.D2 as D2.D2 = 1.
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// <=> u2 = (O2O1+O1P1).D2
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// <=> u2 = O2O1.D2+((O1P2.T1)T1).T2) as O1P1 = u1*T1 = (O1P2.T1)T1
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// <=> u2 = O2O1.D2+(((O1O2+O2P2).D1)D1).D2)
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// <=> u2 = O2O1.D2+((O1O2.D1)D1).D2)+(O2P2.D1)(D1.D2)
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// <=> u2 = ((O1O2.D1)D1-O1O2).D2 + u2*(D2.D1)(D1.D2)
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// <=> u2 = (((O1O2.D1)D1-O1O2).D2) / 1.-(D1.D2)**2
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// Let P1=C1(u1) and P2=C2(u2).
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// Then we must find u1 and u2 such as the distance P1P2 is minimal.
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// Target function is:
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// F(u1, u2) = ((L1x+D1x*u1)-(L2x+D2x*u2))^2 +
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// ((L1y+D1y*u1)-(L2y+D2y*u2))^2 +
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// ((L1z+D1z*u1)-(L2z+D2z*u2))^2 --> min,
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// where L1 and L2 are lines locations, D1 and D2 are lines directions.
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// Let simplify the function F
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// F(u1, u2) = (D1x*u1-D2x*u2-Lx)^2 + (D1y*u1-D2y*u2-Ly)^2 + (D1z*u1-D2z*u2-Lz)^2,
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// where L is a vector L1L2.
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// In point of minimum, the condition
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// {dF/du1 = 0
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// {dF/du2 = 0
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// must be satisfied.
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// dF/du1 = 2*D1x*(D1x*u1-D2x*u2-Lx) +
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// 2*D1y*(D1y*u1-D2y*u2-Ly) +
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// 2*D1z*(D1z*u1-D2z*u2-Lz) =
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// = 2*((D1^2)*u1-(D1.D2)*u2-L.D1) =
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// = 2*(u1-(D1.D2)*u2-L.D1)
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// dF/du2 = -2*D2x*(D1x*u1-D2x*u2-Lx) -
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// 2*D2y*(D1y*u1-D2y*u2-Ly) -
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// 2*D2z*(D1z*u1-D2z*u2-Lz)=
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// = -2*((D2.D1)*u1-(D2^2)*u2-(D2.L)) =
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// = -2*((D2.D1)*u1-u2-(D2.L))
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// Consequently, we have two-equation system with two variables:
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// {u1 - (D1.D2)*u2 = L.D1
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// {(D1.D2)*u1 - u2 = L.D2
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// This system has one solution if (D1.D2)^2 != 1
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// (if straight lines are not parallel).
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{
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myDone = Standard_False;
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myNbExt = 0;
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myIsPar = Standard_False;
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gp_Dir D1 = C1.Position().Direction();
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gp_Dir D2 = C2.Position().Direction();
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// MSV 16/01/2000: avoid "divide by zero"
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Standard_Real D1DotD2 = D1.Dot(D2);
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Standard_Real aSin = 1.-D1DotD2*D1DotD2;
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if (aSin < gp::Resolution() ||
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D1.IsParallel(D2, Precision::Angular())) {
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const gp_Dir &aD1 = theC1.Position().Direction(),
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&aD2 = theC2.Position().Direction();
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const Standard_Real aCosA = aD1.Dot(aD2);
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const Standard_Real aSqSinA = 1.0 - aCosA * aCosA;
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Standard_Real aU1 = 0.0, aU2 = 0.0;
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if (aSqSinA < gp::Resolution() || aD1.IsParallel(aD2, Precision::Angular()))
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{
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myIsPar = Standard_True;
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mySqDist[0] = C2.SquareDistance(C1.Location());
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mySqDist[1] = mySqDist[0];
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}
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else {
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myIsPar = Standard_False;
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gp_Pnt O1 = C1.Location();
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gp_Pnt O2 = C2.Location();
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gp_Vec O1O2 (O1,O2);
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Standard_Real U2 = (D1.XYZ()*(O1O2.Dot(D1))-(O1O2.XYZ())).Dot(D2.XYZ());
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if( Precision::IsInfinite(U2) ) {
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myIsPar = Standard_True;
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mySqDist[0] = C2.SquareDistance(C1.Location());
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mySqDist[1] = mySqDist[0];
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}
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else {
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U2 /= aSin;
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if( Precision::IsInfinite(U2) ) {
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myIsPar = Standard_True;
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mySqDist[0] = C2.SquareDistance(C1.Location());
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mySqDist[1] = mySqDist[0];
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}
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else {
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gp_Pnt P2(ElCLib::Value(U2,C2));
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Standard_Real U1 = (gp_Vec(O1,P2)).Dot(D1);
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if( Precision::IsInfinite(U1) ) {
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myIsPar = Standard_True;
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mySqDist[0] = C2.SquareDistance(C1.Location());
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mySqDist[1] = mySqDist[0];
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}
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else {
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gp_Pnt P1(ElCLib::Value(U1,C1));
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mySqDist[myNbExt] = P1.SquareDistance(P2);
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myPoint[myNbExt][0] = Extrema_POnCurv(U1,P1);
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myPoint[myNbExt][1] = Extrema_POnCurv(U2,P2);
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myNbExt = 1;
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}
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}
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}
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else
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{
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const gp_XYZ aL1L2 = theC2.Location().XYZ() - theC1.Location().XYZ();
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const Standard_Real aD1L = aD1.XYZ().Dot(aL1L2),
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aD2L = aD2.XYZ().Dot(aL1L2);
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aU1 = (aD1L - aCosA * aD2L) / aSqSinA;
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aU2 = (aCosA * aD1L - aD2L) / aSqSinA;
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myIsPar = Precision::IsInfinite(aU1) || Precision::IsInfinite(aU2);
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}
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if (myIsPar)
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{
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mySqDist[0] = mySqDist[1] = theC2.SquareDistance(theC1.Location());
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myDone = Standard_True;
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return;
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}
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// Here myIsPar == Standard_False;
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const gp_Pnt aP1(ElCLib::Value(aU1, theC1)),
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aP2(ElCLib::Value(aU2, theC2));
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mySqDist[myNbExt] = aP1.SquareDistance(aP2);
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myPoint[myNbExt][0] = Extrema_POnCurv(aU1, aP1);
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myPoint[myNbExt][1] = Extrema_POnCurv(aU2, aP2);
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myNbExt = 1;
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myDone = Standard_True;
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}
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//=======================================================================
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@ -14,5 +14,5 @@ bcommon result b1 b2
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checkprops result -s 1690.81
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checkshape result
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checknbshapes result -vertex 20 -edge 31 -wire 13 -face 13 -shell 1 -solid 1 -compsolid 0 -compound 1 -shape 80
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checknbshapes result -vertex 19 -edge 30 -wire 13 -face 13 -shell 1 -solid 1 -compsolid 0 -compound 1 -shape 78
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checkview -display result -2d -path ${imagedir}/${test_image}.png
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@ -17,5 +17,5 @@ bcommon result b1 b2
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checkprops result -s 1690.81
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checkshape result
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checknbshapes result -vertex 20 -edge 31 -wire 13 -face 13 -shell 1 -solid 1 -compsolid 0 -compound 1 -shape 80
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checknbshapes result -vertex 19 -edge 30 -wire 13 -face 13 -shell 1 -solid 1 -compsolid 0 -compound 1 -shape 78
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checkview -display result -2d -path ${imagedir}/${test_image}.png
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