// 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: