// knot32f.fe

// 3,2 torus knot with soap film fully touching boundary

parameter maj_r = 2
parameter min_r = 0.5
parameter height = 1

boundary 1 parameter 1 convex
x1:  cos(2*p1)*(maj_r + min_r*cos(3*p1))
x2:  sin(2*p1)*(maj_r + min_r*cos(3*p1))
x3:  height*min_r*sin(3*p1)

vertices
1    -pi/12 boundary 1 fixed
2    pi/12  boundary 1  fixed
3    3*pi/12  boundary 1  
4    5*pi/12  boundary 1
5    7*pi/12  boundary 1 fixed
6    9*pi/12  boundary 1 fixed
7    11*pi/12  boundary 1
8    13*pi/12  boundary 1
9    15*pi/12  boundary 1  fixed
10   17*pi/12  boundary 1  fixed
11   19*pi/12  boundary 1
12   21*pi/12  boundary 1

edges
1     1 2 boundary 1 fixed
2     2 3 boundary 1 fixed
3     3 4 boundary 1
4     4 5 boundary 1 fixed
5     5 6 boundary 1 fixed
6     6 7 boundary 1 fixed
7     7 8 boundary 1
8     8 9 boundary 1 fixed
9     9 10 boundary 1 fixed
10    10 11 boundary 1 fixed
11    11 12 boundary 1
12    12 1 boundary 1 fixed
13   1 7
14   2 8
15   3 9
16   4 10
17   5 11
18   6 12
19   8 3  // triple line
20   4 11 // triple line
21   12 7 // triple line

faces
1    7 19 3 20 11 21 // center
2    4 17 -20
3    5 18 -11 -17
4    6 -21 -18
5    12 13 -21
6    1 14 -7 -13
7    2 -19 -14
8    8 -15 -19
9    15 9 -16 -3
10   10 -20 16



read
hessian_normal

// Fix vertices on wire except those where wire leaves film.
fixer := { fix vertex where on_boundary 1 and id !=3 and id !=6 }

// Typical evolution
gogo := { g 20; U; r; g 20; V;V;V;V; u; g 20; r; g 20; V; V; g 20;
	  r; g 20; V; V;
	  fix vertex where on_boundary 1; k 0;  // so can use Hessian
	  fix edge where on_boundary 1;
	  hessian; hessian;
	}