// sqcat.fe

// Catenoid between parallel squares.
// One fundamental region, bounded by mirror planes.

parameter height = 0.25   // half-distance between squares


// Mirror plane constraints
constraint z_mirror
formula: z = 0

constraint y_mirror
formula: y = 0

constraint xy_mirror
formula: x = y

// For viewing multiple copies of the fundamental region
view_transform_generators 3
// generator A: reflection in z_mirror
1 0 0 0
0 1 0 0
0 0 -1 0
0 0 0 1

// generator B: reflection in y_mirror
1  0 0 0 
0 -1 0 0
0  0 1 0
0  0 0 1

// generator C: reflection in xy_mirror
0 1 0 0 
1 0 0 0
0 0 1 0
0 0 0 1

vertices
1   1 0 height fixed // half-side of square frame
2   1 1 height fixed
3   1 0 0 constraints z_mirror,y_mirror // contact line on z_mirror
4   1 1 0 constraints z_mirror,xy_mirror
// Some coordinate axes, just to help viewer get oriented
5   0 0 0 fixed
6   1.2 0 0 fixed
7   0  1.2 0 fixed
8   0 0 0.5 fixed
9   1.2 1.2 0 fixed

edges
1  1 2 fixed  // half-side of square frame
2  1 3 constraint y_mirror   // contact line on y_mirror
3  3 4 constraint z_mirror   // contact line on z_mirror
4  4 2 constraint xy_mirror  // contact line on xy_mirror
// axes
5  5 6 fixed bare no_refine
6  5 7 fixed bare no_refine
7  5 8 fixed bare no_refine
8  5 9 fixed bare no_refine

faces
1  2 3 4 -1


read

// simple evolution
gogo := {  
 refine edge where length > .6;
 r;
 g 10;
 r;
 g 10;
 hessian;
 hessian;
}