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// band.cmd
// Surface Evolver command to create triangulated band bordering
// deisgnated edges and vertices. Purpose is to make extremely
// accurate PostScript files without notching on thick edges.
// WARNING: This command modifies the surface by creating a lot of
// tiny facets. You should use only on a disposable copy of your surface.
/* Assumptions:
3D soapfilm model.
Linear model.
*/
// Usage: set bandcolor and bandwidth to desired values; bandwidth is
// the width of the band in surface coordinates on one
// side of an edge.
// set the edge attribute inband to nonzero for those edges
// to have band drawn along them.
// run makeband
/* To make PostScript file of the resulting surface, do like this:
Enter command: show edge where 0
Enter command: P 3
Show grid lines? n
Do colors? y
Do labels? (i for ids, o for originals) n
Enter file name (.ps will be added): xxx.ps
or in scripts:
show edge where 0;
ps_gridflag off;
ps_colorflag on;
ps_labelflag off;
postscript "xxx.ps"
*/
// IMPORTANT NOTE: The algorithm may have trouble where inband edges meet
// at an angle, since each vertex has a single band distance attribute
// and the vertex may be a neighbor to two different bands. This results
// in ragged bands near corners. A cure is to do banding in stages,
// doing one "original" edge at a time. But try banding all desired edges
// at once, since you may not have any trouble.
// Not wise to run more than once along a given edge. Numerical
// variations due to new vertices lead to a lot more unnecessary
// refinements.
define edge attribute inband integer // 1 if band center, 0 if not
define vertex attribute banddist real // distance from band center.
define facet attribute bandused integer // so use each facet at most once
define vertex attribute band_generation integer
bandcolor := black // Set this to desired color before makeband.
bandwidth := 0.010 // Set this to desired half-width before makeband.
init_bandcalc := {
// initialize vertex distances from band
maxbanddist := 100000*bandwidth;
set vertex banddist maxbanddist;
set vertex band_generation 100000;
foreach edge ee where inband do
{ set ee.vertex banddist 0;
set ee.vertex band_generation 0;
};
// Refine any edge whose endpoints are in band center but edge is not
foreach edge ee where (ee.inband==0) and (ee.vertex[1].banddist==0)
and (ee.vertex[2].banddist==0)
do { refine ee; ee.vertex[2].banddist := maxbanddist; } ;
}
function integer calc_v_banddist(integer vv_id)
{ local changed,ddiff,ss1,ss2,lambda1,lambda2;
local xx,yy,newd,ddd;
changed := 0;
foreach vertex[vv_id] vv do
{
foreach vv.edge ee where ee.vertex[2].banddist < bandwidth do
{ foreach ee.vertex[2].edge eee where eee.id != ee.id and
eee.vertex[2].banddist < maxbanddist do
{
ddiff := eee.vertex[2].banddist - eee.vertex[1].banddist;
ss1 := eee.length;
if abs(ddiff) > ss1*1.0000000001 then
{ // wrapping around something
if ddiff > 0 then
eee.vertex[2].banddist := eee.vertex[1].banddist + ss1
else
eee.vertex[1].banddist := eee.vertex[2].banddist + ss1;
changed += 1;
continue;
}
else if abs(ddiff) == ss1 then continue;
ss2 := ee.length;
lambda1 := -(ee.edge_vector * eee.edge_vector)/ss1^2;
lambda2 := sqrt(ss2^2 - lambda1^2*ss1^2);
xx := lambda1*ss1*sqrt(ss1^2 - ddiff^2)/ss1 - lambda2*ddiff/ss1;
yy := lambda1*ss1*ddiff/ss1 + lambda2*sqrt(ss1^2-ddiff^2)/ss1;
if xx < 0 then
{ // add radius from tail
newd := eee.vertex[1].banddist + ss2;
}
else if xx > sqrt(ss1^2 - ddiff^2) then
{ // add radius from head
ddd := (vv.__x - eee.vertex[2].__x)*(vv.__x - eee.vertex[2].__x);
newd := eee.vertex[2].banddist + sqrt(ddd);
}
else
{ // between endpoints
newd := eee.vertex[1].banddist + yy;
};
if newd < vv.banddist*0.99999999 then
{ vv.banddist := newd;
changed += 1;
}
};
}
};
return changed;
}
calc_banddist := {
local changed,this_generation;
init_bandcalc;
// Calculate vertex distances from band center, using
// only vertices of previous generation, to prevent using
// vertex distance value that is not finalized yet.
for ( this_generation := 1 ; ; this_generation += 1 )
{ changed := 0;
foreach vertex vv where banddist > 0 do
{
changed += calc_v_banddist(vv.id);
};
if not changed then break;
};
} // end calc_band_dist
makeband := {
local eps;
calc_banddist;
// Subdivide edges spanning band boundary
eps := 1e-4*bandwidth; // numerical margin for error
foreach edge ee do
{ local d1,d2;
local new_x,new_y,new_z;
local lambda;
d1 := ee.vertex[1].banddist;
d2 := ee.vertex[2].banddist;
if ( ((d1<=bandwidth+eps)&&(d2<=bandwidth+eps)) ||
((d1>=bandwidth-eps)&&(d2>=bandwidth-eps)))
then continue;
lambda := (d1 - bandwidth)/(d1 - d2);
if ( lambda < .00001 or lambda > .99999 ) then continue;
new_x := ee.vertex[1].x + lambda*ee.x; // suitable for torus model
new_y := ee.vertex[1].y + lambda*ee.y;
new_z := ee.vertex[1].z + lambda*ee.z;
refine ee;
ee.vertex[2].x := new_x;
ee.vertex[2].y := new_y;
ee.vertex[2].z := new_z;
ee.vertex[2].banddist := bandwidth;
};
// Color band triangles
foreach facet ff do
{ if avg(ff.vertex,banddist) < bandwidth then set ff color bandcolor; };
}
// to do edges on different constraints one constraint at a time.
cband := {
local connum;
for ( connum := 1 ; connum <= high_constraint ; connum += 1 )
{ if valid_constraint(connum) then
{ set edge inband on_constraint connum;
makeband;
}
};
}
// End band.cmd
// makeband usage:
// set bandwidth to desired half-width (in surface coordinates)
// set edge inband to 1 along band center, 0 elsewhere
// set bandcolor to desired color
// run makeband
// In making postscript, answer N to gridlines, and y to colors.
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