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// quadint2.cmd
// For detecting intersection of quadratic facets in 3D
// Not suitable for torus model.
// Needs quadbbox.cmd to be loaded first.
// Programmer: Ken Brakke, brakke@susqu.edu, http://www.susqu.edu/brakke
// Usage: quadmeet
// Prints id numbers of pairs of intersecting facets and colors them green.
a_refine_order := 4
b_refine_order := 5
eps := 1e-10 // tolerance for being equal to zero
ax := 0; bx := 0; cx := 0; ay := 0; by := 0; cy := 0; az := 0; bz := 0; cz := 0;
px := 0; py := 0; pz := 0; qx := 0; qy := 0; qz:= 0;
uuu := 0; vvv := 0;
xa1 := 0; xa2 := 0; xa3 := 0; xa4 := 0; xa5 := 0; xa6 := 0
ya1 := 0; ya2 := 0; ya3 := 0; ya4 := 0; ya5 := 0; ya6 := 0
za1 := 0; za2 := 0; za3 := 0; za4 := 0; za5 := 0; za6 := 0
intersection_found := 0;
// detection of triangle and edge intersection
detect := {
local acx,acy,acz,bcx,bcy,bcz,qpx,qpy,qpz,qcx,qcy,qcz;
local denom,lambda,mu,sigma;
do {
acx := ax-cx; acy := ay-cy; acz := az-cz;
bcx := bx-cx; bcy := by-cy; bcz := bz-cz;
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 break;
lambda := (qpx*(qcy*bcz-qcz*bcy) - qpy*(qcx*bcz-qcz*bcx)
+ qpz*(qcx*bcy-qcy*bcx))/denom;
if ( lambda <= eps ) then break;
mu := (qpx*(acy*qcz-acz*qcy) - qpy*(acx*qcz-acz*qcx)
+ qpz*(acx*qcy-acy*qcx))/denom;
if ( mu <= eps ) then break;
if ( lambda + mu > 1-eps ) then break;
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 break;
// now have intersection
intersection_found := 1;
} while 0; // so we could use break
} // end detect
calccoords := {
xx := 0.5*(uuu+vvv-1)*(uuu+vvv-2)*xa1 + uuu*(2-uuu-vvv)*xa2
+ 0.5*uuu*(uuu-1)*xa3 + vvv*(2-uuu-vvv)*xa4
+ uuu*vvv*xa5 + 0.5*vvv*(vvv-1)*xa6;
yy := 0.5*(uuu+vvv-1)*(uuu+vvv-2)*ya1 + uuu*(2-uuu-vvv)*ya2
+ 0.5*uuu*(uuu-1)*ya3 + vvv*(2-uuu-vvv)*ya4
+ uuu*vvv*ya5 + 0.5*vvv*(vvv-1)*ya6;
zz := 0.5*(uuu+vvv-1)*(uuu+vvv-2)*za1 + uuu*(2-uuu-vvv)*za2
+ 0.5*uuu*(uuu-1)*za3 + vvv*(2-uuu-vvv)*za4
+ uuu*vvv*za5 + 0.5*vvv*(vvv-1)*za6;
} // end calccoords
refine_and_test := {
// Test intersections of planar subtriangles and sub edges
adelta := 2/a_refine_order;
bdelta := 2/b_refine_order;
ua := 0;
while ( ua < 1.9999 ) do
{ va := 0;
while ( va < 1.9999 - ua ) do
{ uuu := ua; vvv := va; calccoords; ax := xx; ay := yy; az := zz;
uuu := ua+adelta; vvv := va; calccoords; bx := xx; by := yy; bz := zz;
uuu := ua; vvv := va+adelta; calccoords; cx := xx; cy := yy; cz := zz;
ub := 0;
while ( ub < 1.9999 ) do
{ vb := 0;
while ( vb < 1.9999 - ub ) do
{
uuu := ub; vvv := vb; calccoords; px := xx; py := yy; pz := zz;
uuu := ub+bdelta; vvv := vb; calccoords; qx := xx; qy := yy; qz := zz;
detect; if intersection_found then break;
uuu := ub; vvv := vb+bdelta; calccoords; px := xx; py := yy; pz := zz;
detect; if intersection_found then break;
uuu := ub; vvv := vb; calccoords; qx := xx; qy := yy; qz := zz;
detect; if intersection_found then break;
vb := vb + bdelta;
};
if intersection_found then break;
ub := ub + bdelta;
};
if intersection_found then break;
va := va + adelta;
};
if intersection_found then break;
ua := ua + adelta;
}
} // end refine_and_test
quadmeet := {
intersect_total := 0;
fboxes; // find facet bounding boxes
// test all facet pairs
foreach facet fa do
{ foreach facet fb where fb.id > fa.id do
{ // check adjacency
if ( fa.vertex[1].id == fb.vertex[1].id ) then continue;
if ( fa.vertex[2].id == fb.vertex[1].id ) then continue;
if ( fa.vertex[3].id == fb.vertex[1].id ) then continue;
if ( fa.vertex[1].id == fb.vertex[2].id ) then continue;
if ( fa.vertex[2].id == fb.vertex[2].id ) then continue;
if ( fa.vertex[3].id == fb.vertex[2].id ) then continue;
if ( fa.vertex[1].id == fb.vertex[3].id ) then continue;
if ( fa.vertex[2].id == fb.vertex[3].id ) then continue;
if ( fa.vertex[3].id == fb.vertex[3].id ) then continue;
// first, check bounding boxes
if ( fb.fbox[1] >= fa.fbox[2] or
fb.fbox[2] <= fa.fbox[1] or
fb.fbox[3] >= fa.fbox[4] or
fb.fbox[4] <= fa.fbox[3] or
fb.fbox[5] >= fa.fbox[6] or
fb.fbox[6] <= fa.fbox[5] ) then continue;
// extract coordinates
xa1 := fa.edge[1].vertex[1].x;
xa2 := fa.edge[1].vertex[3].x;
xa3 := fa.edge[1].vertex[2].x;
xa4 := fa.edge[3].vertex[3].x;
xa5 := fa.edge[2].vertex[3].x;
xa6 := fa.edge[2].vertex[2].x;
ya1 := fa.edge[1].vertex[1].y;
ya2 := fa.edge[1].vertex[3].y;
ya3 := fa.edge[1].vertex[2].y;
ya4 := fa.edge[3].vertex[3].y;
ya5 := fa.edge[2].vertex[3].y;
ya6 := fa.edge[2].vertex[2].y;
za1 := fa.edge[1].vertex[1].z;
za2 := fa.edge[1].vertex[3].z;
za3 := fa.edge[1].vertex[2].z;
za4 := fa.edge[3].vertex[3].z;
za5 := fa.edge[2].vertex[3].z;
za6 := fa.edge[2].vertex[2].z;
xb1 := fb.edge[1].vertex[1].x;
xb2 := fb.edge[1].vertex[3].x;
xb3 := fb.edge[1].vertex[2].x;
xb4 := fb.edge[3].vertex[3].x;
xb5 := fb.edge[2].vertex[3].x;
xb6 := fb.edge[2].vertex[2].x;
yb1 := fb.edge[1].vertex[1].y;
yb2 := fb.edge[1].vertex[3].y;
yb3 := fb.edge[1].vertex[2].y;
yb4 := fb.edge[3].vertex[3].y;
yb5 := fb.edge[2].vertex[3].y;
yb6 := fb.edge[2].vertex[2].y;
zb1 := fb.edge[1].vertex[1].z;
zb2 := fb.edge[1].vertex[3].z;
zb3 := fb.edge[1].vertex[2].z;
zb4 := fb.edge[3].vertex[3].z;
zb5 := fb.edge[2].vertex[3].z;
zb6 := fb.edge[2].vertex[2].z;
refine_and_test;
if intersection_found then
{ intersect_total := intersect_total + 1;
set fa color green; set fb color green;
printf "Facets %g and %g intersect.\n",fa.id,fb.id;
}
}
};
printf "Intersections found: %g\n",intersect_total;
} // end quadmeet
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