// iwp.fe

// fundamental cell for Schoen's IW-P minimal surface

// Programmer: Ken Brakke, brakke@susqu.edu, http://www.susqu.edu

/* Commands:
   gogo - typical evolution
   showcube - show one unit cell, as on web page
   showcubelet - show 1/8 of unit cell
   transforms off - show just single fundamental region
   setcolor - to color one side yellow, as in my web page.

   To turn off showing all the edges in the graphics display,
      hit the "e" key in the graphics window.
*/

// from Alan Mackay UBCG04M@CCS.BBK.AC.UK Sat Jul  2 06:23:56 1994:
// My colleague Cvijovic has proved that the area of surface is exactly
// two time root three (in unit cube)  and the space is divided in the 
// ratio of root three over two to one.

// So area here (in 2x2x2 cube with 48-fold symmetry) should be 
//  2*sqrt(3)/12 = 0.288675134594813

// square_curvature 0

CONSTRAINT 1   // top
FUNCTION:  z  = 1  
CONTENT 
C1: 0.5*(y-1)  
C2: -0.5*(x-1)  
C3: 0  

CONSTRAINT 2  // right side
FUNCTION:  y - x  = 0  

CONSTRAINT 3  // left  side
FUNCTION:  -y  = 0  

CONSTRAINT 4  // front bottom
FUNCTION:  x - z  = 0  
CONTENT 
C1: (2*x+1)*y/6
C2: -(2*x+1)*(x-1)/6
C3: 0  


view_transform_generators 4
1,0,0,0  0,1,0,0   0,0,-1,2  0,0,0,1  // a: z=1 mirror
0,1,0,0  1,0,0,0   0,0,1,0   0,0,0,1  // b: x=y mirror
1,0,0,0  0,-1,0,0  0,0,1,0   0,0,0,1  // c: y=0 mirror
0,0,1,0  0,1,0,0   1,0,0,0   0,0,0,1  // d: x=z mirror


vertices         
  1  1   0.5   1   constraints 1 4 
  2  0.5 0.5   1   constraints 1 2 
  3  0.0 0.0 0.5   constraints 2 3 
  4  0.5 0 0.5   constraints 3 4 
  5                  0                 0                 0  fixed  bare
  6                  0                 0                 1  fixed  bare
  7                  1                 0                 1  fixed  bare
  8                  1                 1                 1  fixed  bare

edges
1   1 2 constraint 1
2   2 3 constraint 2
3   3 4 constraint 3
4   4 1 constraint 4
5   5 6 fixed bare no_refine // for tetrahedron display
6   5 7 fixed bare no_refine
7   5 8 fixed bare no_refine
8   6 7 fixed bare no_refine
9   6 8 fixed bare no_refine
10  7 8 fixed bare no_refine

facets
1  1 2 3 4

bodies 
1  1 volume  1/(1+sqrt(.75))/6  volconst -1/3

read
hessian_normal

// to display cubical cell
showcube := {
  set edge color clear where bare;
  transform_expr "3(bcd)";
  show_trans "R";
}

// show 1/8 of unit cell
showcubelet := {
  set edge color clear where bare;
  transform_expr "bdb";
  show_trans "R";
}

// Set inside color to yellow
setcolor := { set facet frontcolor yellow }

// typical evolution
gogo := { r; u; g 5; refine edge where valence==1;
          u; V; g 5; r; g 12; u; V;
          convert_to_quantities; hessian; hessian;
          r; hessian; hessian;
}

/* Commands:
   gogo - typical evolution
   showcube - show one unit cell, as on web page
   showcubelet - show 1/8 of unit cell
   transforms off - show just single fundamental region
   setcolor - to color one side yellow, as in my web page.

   To turn off showing all the edges in the graphics display,
      hit the "e" key in the graphics window.
*/

// from Alan Mackay UBCG04M@CCS.BBK.AC.UK Sat Jul  2 06:23:56 1994: