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// quadtbox.cmd
// finds bounding box for quadratic facets
// Suitable for torus model.
// Tricky to define a bounding box in a torus, with the wraps.
// So the bounding box is based on unwrapped edges and facets
// relative to the first vertex.;
// Bounding box calculations are done in normalized unit cell
// coordinates, so bounding box is really parallelogram
// parallel to unit cell.
// Programmer: Ken Brakke, brakke@susqu.edu www.susqu.edu/brakke
// xmin,xmax,ymin,ymax,zmin,zmax
define edge attribute ebox real [3][2]
define facet attribute fbox real [3][2]
eboxes := {
local ii,v0,v1,v2,v4,uopt,denom;
local u0,u1,u2;
define u0 real[space_dimension];
define u1 real[space_dimension];
define u2 real[space_dimension];
if ( !quadratic ) then
{ errprintf "eboxes: Must be in quadratic mode.\n";
abort;
};
if ( !torus ) then
{ errprintf "eboxes: Must be in torus model.\n";
abort;
};
foreach edge ee do
{
u0 := ee.vertex[1].__x * inverse_periods;
u1 := ee.edge_vector * inverse_periods;
u2 := ee.vertex[3].__x * inverse_periods;
for ( ii := 1; ii <= space_dimension; ii++ )
{
// get normalized vertex coordinates, recalling midv is third vertex
// of the edge, and on the same wrap as the tail.
v0 := u0[ii];
v1 := v0 + u1[ii];
v2 := u2[ii];
// now set bounding boxes
if ( v0 > v1 )
then { ee.ebox[ii][1] := v1; ee.ebox[ii][2] := v0; }
else { ee.ebox[ii][1] := v0; ee.ebox[ii][2] := v1; };
if ( v2 < ee.ebox[ii][1] ) then ee.ebox[ii][1] := v2;
if ( v2 > ee.ebox[ii][2] ) then ee.ebox[ii][2] := v2;
denom := v0 - 2*v1 + v2;
if ( denom == 0.0 ) then continue;
uopt := (-1.5*v0 + 2*v1 - .5*v2)/denom;
if ( uopt <= 0.0 or uopt >= 1.0 )
then continue;
v4 := 0.5*(1-uopt)*(2-uopt)*v0 + uopt*(2-uopt)*v1
+ 0.5*uopt*(uopt-1)*v2;
if ( v4 < ee.ebox[ii][1] ) then ee.ebox[ii][1] := v4;
if ( v4 > ee.ebox[ii][2] ) then ee.ebox[ii][2] := v4;
}
}
} // end eboxes
fboxes := {
local ewraps,ii,ww,jj,www,tempbox,vwrap,v0,v1,v2,v3,v4,v5;
local a11,a12,b1,a21,a22,b2,denom,uopt,vopt,vcrit;
define ewraps integer[3][space_dimension];
local u0,u1,u2,u3,u4,u5;
define u0 real[space_dimension];
define u1 real[space_dimension];
define u2 real[space_dimension];
define u3 real[space_dimension];
define u4 real[space_dimension];
define u5 real[space_dimension];
eboxes;
if ( ! quadratic ) then
{ print "fboxes: Must be in quadratic mode.\n";
abort;
};
foreach facet ff do
{ // extract wraps on edges
for ( ii := 1; ii <= 3 ; ii++ )
{ ww := ff.edge[ii].wrap;
for ( jj := 1 ; jj <= space_dimension ; jj++ )
{ www := ww imod 64;
if www == 0 then ewraps[ii][jj] := 0
else if www < 16 then ewraps[ii][jj] := www
else ewraps[ii][jj] := www-32;
ww /= 64;
}
};
u0 := ff.edge[1].vertex[1].__x * inverse_periods;
u1 := ff.edge[1].vertex[3].__x * inverse_periods;
u2 := ff.edge[1].edge_vector * inverse_periods;
u3 := ff.edge[3].vertex[3].__x * inverse_periods;
u4 := ff.edge[2].vertex[3].__x * inverse_periods;
u5 := ff.edge[2].edge_vector * inverse_periods;
for ( ii := 1; ii <= space_dimension ; ii++ )
{ define tempbox real[2];
/* first, edge boxes */
ff.fbox[ii] := ff.edge[1].ebox[ii];
if ff.edge[1].oid < 0 then
ff.fbox[ii] += ewraps[1][ii];
vwrap := ewraps[1][ii];
for ( jj := 2 ; jj <= 3; jj++ )
{ tempbox := ff.edge[jj].ebox[ii];
tempbox += vwrap;
if ff.edge[jj].oid < 0 then
tempbox += ewraps[jj][ii];
if ( tempbox[1] < ff.fbox[ii][1] )
then ff.fbox[ii][1] := tempbox[1];
if ( tempbox[2] > ff.fbox[ii][2] )
then ff.fbox[ii][2] := tempbox[2];
vwrap += ewraps[jj][ii];
};
v0 := u0[ii];
v1 := u1[ii];
v2 := v0 + u2[ii];
v3 := u3[ii];
v4 := u4[ii];
v5 := v2 + u5[ii];
// fix up midpoint to be near endpoints, since don't have edge vector to midpoint
v1 := ((7+v1-(v0+v2-1)/2) mod 1) + (v0+v2-1)/2;
v3 := ((7+v3-(v0+v5-1)/2) mod 1) + (v0+v5-1)/2;
v4 := ((7+v4-(v5+v2-1)/2) mod 1) + (v5+v2-1)/2;
// x_u coeff of u
a11 := v0 - 2*v1 + v2;
// x_u coeff of v
a12 := v0 - v1 - v3 + v4;
// x_u rhs
b1 := -(-1.5*v0 + 2*v1 - .5*v2);
// x_v coeff of u
a21 := v0 - v1 - v3 + v4;
// x_v coeff of v
a22 := v0 - 2*v3 + v5;
// x_v rhs
b2 := -(-1.5*v0 + 2*v3 - 0.5*v5);
// solve for critical point
denom := a11*a22 - a12*a21;
if ( denom == 0.0 ) then continue;
uopt := (b1*a22 - b2*a12)/denom;
vopt := (a11*b2 - a21*b1)/denom;
if ( uopt <= 0.0 ) then continue;
if ( vopt <= 0.0 ) then continue;
if ( uopt+vopt >= 2.0 ) then continue;
vcrit := 0.5*(uopt+vopt-1)*(uopt+vopt-2)*v0
+ uopt*(2-uopt-vopt)*v1
+ 0.5*uopt*(uopt-1)*v2
+ vopt*(2-uopt-vopt)*v3
+ uopt*vopt*v4
+ 0.5*vopt*(vopt-1)*v5;
if ( vcrit < ff.fbox[ii][1] ) then ff.fbox[ii][1] := vcrit;
if ( vcrit > ff.fbox[ii][2] ) then ff.fbox[ii][2] := vcrit;
}
}
}
// End quadtbox.cmd
// Usage: fboxes
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