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// intersec.cmd
// Evolver command to detect intersection of linear edges and facets.
// For each facet, finds if any edge intersects in interior.
// Usage: read "intersec.cmd"
// detect
// Output: prints ids of facets and edges that intersect.
// Notes: In quadratic model, treats edges and facets as simply linear.
// Will not work in Lagrange model.
eps := 1e-10 // tolerance for being equal to zero
detect := {
local ax,ay,az,bx,by,bz,cx,cy,cz,acx,bcx,px,py,pz,qx,qy,qz,qpx,qcx;
local denom,lambda,mu,sigma;
local acy,acz,bcy,bcz,qpy,qpz,qcy,qcz;
if lagrange then
{ printf "intersect.cmd will not work in Lagrange model.\n";return;};
foreach facet ff do
{ ax := ff.vertex[1].x;
ay := ff.vertex[1].y;
az := ff.vertex[1].z;
bx := ff.vertex[2].x;
by := ff.vertex[2].y;
bz := ff.vertex[2].z;
cx := ff.vertex[3].x;
cy := ff.vertex[3].y;
cz := ff.vertex[3].z;
acx := ax-cx; acy := ay-cy; acz := az- cz;
bcx := bx-cx; bcy := by-cy; bcz := bz- cz;
foreach edge ee do
{ px := ee.vertex[1].x;
py := ee.vertex[1].y;
pz := ee.vertex[1].z;
qx := ee.vertex[2].x;
qy := ee.vertex[2].y;
qz := ee.vertex[2].z;
qpx := qx-px; qpy := qy-py; qpz := qz-pz;
qcx := qx-cx; qcy := qy-cy; qcz := qz-cz;
denom := qpx*(acy*bcz-acz*bcy) - qpy*(acx*bcz-acz*bcx)
+ qpz*(acx*bcy-acy*bcx);
if ( abs(denom) < eps ) then continue;
lambda := (qpx*(qcy*bcz-qcz*bcy) - qpy*(qcx*bcz-qcz*bcx)
+ qpz*(qcx*bcy-qcy*bcx))/denom;
if ( lambda <= eps ) then continue;
mu := (qpx*(acy*qcz-acz*qcy) - qpy*(acx*qcz-acz*qcx)
+ qpz*(acx*qcy-acy*qcx))/denom;
if ( mu <= eps ) then continue;
if ( lambda + mu > 1-eps ) then continue;
sigma := (qcx*(acy*bcz-acz*bcy) - qcy*(acx*bcz-acz*bcx)
+ qcz*(acx*bcy-acy*bcx))/denom;
if ( (sigma <= eps) or (sigma > 1-eps) ) then continue;
// now have intersection
printf "Facet %g and edge %g intersect.\n",ff.id,ee.id;
}
}
}
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