// 4.fe  Evolver initial data for 4 bubbles around two.
// The central film shrinks here, but unlike 3.fe, it does
// not collapse to a point.  See gogo for an evolution.

vertices //          coordinates
  1      1.000000  0.000000  1.000000
  2      1.000000  0.000000  0.000000
  3      1.000000  0.000000  -1.000000
  4      2.000000  0.000000  -1.000000
  5      2.000000  0.000000  1.000000
  6      -0.000002  -1.000000  1.000000
  7      -0.000002  -1.000000  0.000000
  8      -0.000002  -1.000000  -1.000000
  9      -0.000004  -2.000000  -1.000000
 10      -0.000004  -2.000000  1.000000
 11      -1.000000  0.000004  1.000000
 12      -1.000000  0.000004  0.000000
 13      -1.000000  0.000004  -1.000000
 14      -2.000000  0.000008  -1.000000
 15      -2.000000  0.000008  1.000000
 16      0.000006  1.000000  1.000000
 17      0.000006  1.000000  0.000000
 18      0.000006  1.000000  -1.000000
 19      0.000012  2.000000  -1.000000
 20      0.000012  2.000000  1.000000

edges // endpoints
  1       1    2
  2       2    3
  3       3    4
  4       4    5
  5       5    1
  6       1    6
  7       2    7
  8       3    8
  9       4    9
 10       5   10
 11       6    7
 12       7    8
 13       8    9
 14       9   10
 15      10    6
 16       6   11
 17       7   12
 18       8   13
 19       9   14
 20      10   15
 21      11   12
 22      12   13
 23      13   14
 24      14   15
 25      15   11
 26      11   16
 27      12   17
 28      13   18
 29      14   19
 30      15   20
 31      16   17
 32      17   18
 33      18   19
 34      19   20
 35      20   16
 36      16    1
 37      17    2
 38      18    3
 39      19    4
 40      20    5

faces  //  edges    
  1      1   2   3   4   5 
  2      6  11  -7  -1 
  3      7  12  -8  -2 
  4      8  13  -9  -3 
  5     10 -14  -9   4 
  6      6 -15 -10   5 
  7     11  12  13  14  15 
  8     16  21 -17 -11 
  9     17  22 -18 -12 
 10     18  23 -19 -13 
 11     20 -24 -19  14 
 12     16 -25 -20  15 
 13     21  22  23  24  25 
 14     26  31 -27 -21 
 15     27  32 -28 -22 
 16     28  33 -29 -23 
 17     30 -34 -29  24 
 18     26 -35 -30  25 
 19     31  32  33  34  35 
 20     36   1 -37 -31 
 21     37   2 -38 -32 
 22     38   3 -39 -33 
 23     40  -4 -39  34 
 24     36  -5 -40  35 
 25    -36  -26  -16   -6  
 26    -37  -27  -17   -7  
 27    -38  -28  -18   -8  

bodies   //      facets 
  1     -1   -2   -3   -4    5    6    7     volume  3.000000  
  2     -7   -8   -9  -10   11   12   13     volume  3.000000  
  3    -13  -14  -15  -16   17   18   19     volume  3.000000  
  4    -19  -20  -21  -22   23   24    1     volume  3.000000  
  5     25    2    8   14   20  -26     volume  2.000000
  6     26    3    9   15   21  -27     volume  2.000000

read

hessian_normal

// a quick way to color the bodies 
colorbodies := { set facet ff color max(ff.body,id); }

// to see inner surfaces
showinner := { show facets ff where sum(ff.body,1) == 2; }

// an evolution
gogo := { g; u; g 5; r; g 12; V 3; g 12;
          hessian_seek; hessian_seek;  // scale 1.06, pretty good
          V; V; g 5; hessian_seek; 
          hessian_seek; // scale very close to 1
          hessian; // fully converged
          r; g 5;
          hessian_seek; // scale .5
          V; V; g 5;
          hessian_seek; hessian_seek; // scale going down
          w .001; V; g 5;
          hessian_seek; hessian_seek; // scale near 1
          hessian; // converged
        }