// 3.fe   Evolver initial data for 3 bubbles around two.
// Main problem in evolving is that inner film between the
// axial bubbles shrinks to a point, and the resulting vertex
// needs to be popped.  See the gogo command below.

vertices //     coordinates
  1      0.877383  0.000000  1.000000
  2      0.877383  0.000000  0.000000
  3      0.877383  0.000000  -1.000000
  4      2.057645  0.000000  -1.000000
  5      2.057645  0.000000  1.000000
  6      -0.438691  -0.759836  1.000000
  7      -0.438691  -0.759836  0.000000
  8      -0.438691  -0.759836  -1.000000
  9      -1.028822  -1.781973  -1.000000
 10      -1.028822  -1.781973  1.000000
 11      -0.438691  0.759836  1.000000
 12      -0.438691  0.759836  0.000000
 13      -0.438691  0.759836  -1.000000
 14      -1.028822  1.781973  -1.000000
 15      -1.028822  1.781973  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    1
 27      12    2
 28      13    3
 29      14    4
 30      15    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   1 -27 -21 
 15     27   2 -28 -22 
 16     28   3 -29 -23 
 17     30  -4 -29  24 
 18     26  -5 -30  25 
 19    -26  -16   -6  
 20    -27  -17   -7  
 21    -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    1     volume  3.000000  
  4     19    2    8   14  -20     volume  1.000000
  5     20    3    9   15  -21     volume  1.000000

read

hessian_normal  // makes hessian work better

// prettify things, run once after loading
pretty := {
l 3;
refine edge where id==6 or id==16 or id==26 or id==8 or id==18 or id==28
  or id==7 or id==17 or id==27;  // around inner bubbles
u; // symmetrizes things
}

// 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, as run after loading 
gogo := { pretty; // improve the mesh
          g 5;   // just to get things started
          t 0.2; // get rid of some shrinking edges
	  showinner;  // where the action is
	  V; V;  // even out vertices
          g 10;
	  V; V; g 3;  // a couple of g's before hessian_seek
	  hessian_seek; hessian_seek;
          r;
          g 12;
          V; V; V; // scale was down; even out the vertices
          g 5;  // scale good again
          U; g 20; t .02; g 10; t .02; g 10; t .02; // collapse at center
	  o;   // pop center vertex
	  U;  // conj grad off
	  g 10; V 2;u;V;u;V;u; g 12; t .01;
	  refine edge[22]; refine edge[162]; // from picking
	  t .02; g 10 ; t .02; U; g 10 ; V 2; g 10;
	  hessian_seek; hessian_seek; t .02; t .03; t .04; t .05;
	  w .003; g 5; w .003; t .111; // now looking pretty good
	  g 10; hessian_seek; hessian_seek; // converged
	  r; g 10; hessian_seek; hessian_seek;  // converged

}