M_Rectangle3
M_RectangleFromPts3(M_Vector3 a, M_Vector3 b, M_Vector3 c)
{
M_Rectangle3 R;
M_Vector3 d;
M_Plane3 P;
P = M_PlaneFromPts3(a, b, c);
d.x = a.x;
d.y = c.y;
d.z = -(P.a*d.x + P.b*d.y + P.d)/P.d;
R.a = M_LineFromPts3(a, b);
R.b = M_LineFromPts3(b, c);
R.c = M_LineFromPts3(c, d);
R.d = M_LineFromPts3(d, a);
return (R);
}
/*
* Compute a new line parallel to the given line, with perpendicular
* endpoints. XXX this is a circle of solutions in R3
*/
M_Line3
M_LineParallel3(M_Line3 L, M_Real dist)
{
M_Vector3 p1, p2, pd;
M_LineToPts3(L, &p1, &p2);
pd.x = L.d.y;
pd.y = -L.d.x;
M_VecScale3v(&pd, dist);
M_VecAdd3v(&p1, &pd);
M_VecAdd3v(&p2, &pd);
return M_LineFromPts3(p1, p2);
}
/*
* Compute the shortest line segment connecting two lines in R^3.
* Adapted from Paul Bourke's example code:
* http://paulbourke.net/geometry/lineline3d
*/
int
M_LineLineShortest3(M_Line3 L1, M_Line3 L2, M_Line3 *Ls)
{
M_Vector3 p1 = M_LineInitPt3(L1);
M_Vector3 p2 = M_LineTermPt3(L1);
M_Vector3 p3 = M_LineInitPt3(L2);
M_Vector3 p4 = M_LineTermPt3(L2);
M_Vector3 p13, p43, p21;
M_Real d1343, d4321, d1321, d4343, d2121;
M_Real numer, denom;
M_Real muA, muB;
p13 = M_VecSub3(p1, p3);
p43 = M_VecSub3(p4, p3);
if (Fabs(p43.x) < M_MACHEP &&
Fabs(p43.y) < M_MACHEP &&
Fabs(p43.z) < M_MACHEP)
return (0);
p21 = M_VecSub3(p2, p1);
if (Fabs(p21.x) < M_MACHEP &&
Fabs(p21.y) < M_MACHEP &&
Fabs(p21.z) < M_MACHEP)
return (0);
d1343 = M_VecDot3p(&p13, &p43);
d4321 = M_VecDot3p(&p43, &p21);
d4343 = M_VecDot3p(&p43, &p43);
d2121 = M_VecDot3p(&p21, &p21);
denom = d2121*d4343 - d4321*d4321;
if (Fabs(denom) < M_MACHEP) {
return (0);
}
numer = d1343*d4321 - d1321*d4343;
muA = numer/denom;
muB = (d1343 + d4321*muA) / d4343;
if (Ls != NULL) {
*Ls = M_LineFromPts3(
M_VecAdd3(p1, M_VecScale3(p21,muA)),
M_VecAdd3(p3, M_VecScale3(p43,muB)));
}
return (1);
}
