// t2.fe
// Test of facet_2form_sq_integral method, with corrected symplectic area form
//  Andrew Hanson, Indiana University,  September 2001
// Experiment with s1 x s1 torus embedding
// using (1  0),
//  a = (-0.5   0.866025), b = (-0.5 -0.866025) in each complex plane


space_dimension 4

quantity  mycurv  ENERGY modulus 0 global_method star_sq_mean_curvature

// symplectic area
// Correspondence: z1 = (x1,x2)  z2 = (x3,x4)
#define DENOM ((x1^2+x2^2+x3^2+x4^2)^2)
quantity symplectic_sq energy method facet_2form_sq_integral global
form_integrand:
q1: -2*(x3^2 + x4^2)/DENOM    // dx1 wedge dx2 term
q2:  2*(x2*x3-x1*x4)/DENOM    // dx1 wedge dx3 term
q3:  2*(x1*x3+x2*x4)/DENOM    // dx1 wedge dx4 term
q4: -2*(x1*x3+x2*x4)/DENOM    // dx2 wedge dx3 term
q5:  2*(x2*x3-x1*x4)/DENOM    // dx2 wedge dx4 term
q6: -2*(x1^2 + x2^2)/DENOM    // dx3 wedge dx4 term


vertices


1  -0.5   0.866025   -0.5 -0.866025   // a,b
2    -0.5 -0.866025   1  0            //  b,1
3      1  0       -0.5   0.866025      // 1,a
4   -0.5 -0.866025  -0.5 -0.866025   //   b,b
5     1  0   1  0                      // 1,1
6  -0.5   0.866025  -0.5   0.866025    // a,a
7  -0.5   0.866025   1  0             // a,1
8   1  0  -0.5 -0.866025             // 1,b
9    -0.5 -0.866025  -0.5   0.866025     // b,a


edges

1   1 4  
2   1 5
3   1 6
4   2 4
5   2 5
6   2 6
7   3 4
8   3 5
9   3 6
10  4 7
11  4 8
12  4 9
13  5 7
14  5 8
15  5 9
16  6 7
17  6 8
18  6 9
19  7 1
20  7 2
21  7 3
22  8 1
23  8 2
24  8 3
25  9 1
26  9 2
27  9 3

faces
1  22 2 14     
2  -2 -19 -13  
3  1  10 19     
4  -4 -20 -10    
5  23 4 11      
6  -14 -5  -23   
7  17 24 9      
8  -3 -22 -17    
9  25 3 18      
10  -12 -1 -25    
11   7 12 27    
12  -24 -11 -7    
13  21 8 13    
14  -16 -9 -21    
15  6 16 20    
16  -26 -18 -6    
17  15 26 5    
18  -8 -27 -15    

read
set facet tension 0

gogo := { r; g 10; r; g 10; r; g 10 }

// to see it evolve by square curvature
go_curv := { mycurv.modulus := 1; symplectic_sq.modulus := 0; recalc; gogo; 
             symplectic_sq.modulus := 1; recalc; v; }

// to see it evolve by symplectic_sq
go_symp := { mycurv.modulus := 0; symplectic_sq.modulus := 1; recalc; 
             scale_limit := 10;
             r; g 10; r; g 10; conj_grad; g 100; r; g 100;
             mycurv.modulus := 1; recalc; v;
           }