// hexplane5adj.fe // Adjoint of 5th surface in hexplane series. // 5 crossings of z axis edge in fundamental tetrahedron // Four period to kill. // Programmer: Ken Brakke, brakke@susqu.edu, http://www.susqu.edu /* Commands: gogo - typical evolution; do before the following commands. showcube - display cubic unit cell showfour - show four cubic unit cells showrhombic - show rhombic dodecahedron unit cell rhombic_edges - create edges outlining rhombus 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. */ parameter asize = 2.000454320801075 // for period killing parameter bsize = 1.999278862181510 // for period killing parameter csize = 2.009939150687986 // for period killing parameter dsize = 1.862202905244816 // for period killing // Constraints for use after adjoint transformation constraint 3 formula: x = z constraint 4 formula: x + y = 0 constraint 5 formula: y = x constraint 6 formula: z = 1 constraint 7 formula: y = 0 view_transform_generators 8 0,1,0,0 1,0,0,0 0,0,1,0 0,0,0,1 // a: x,y swap 0,-1,0,0 -1,0,0,0 0,0,1,0 0,0,0,1 // b: x+y=0 mirror 0,0,1,0 0,1,0,0 1,0,0,0 0,0,0,1 // c: x,z swap swap_colors 1 0 0 2 , 0 1 0 0, 0 0 1 0, 0 0 0 1 // d: x translation swap_colors 1 0 0 0 , 0 1 0 2, 0 0 1 0, 0 0 0 1 // e: y translation swap_colors 1 0 0 0 , 0 1 0 0, 0 0 1 2, 0 0 0 1 // f: z translation swap_colors 1 0 0 0, 0 -1 0 0, 0 0 -1 2, 0 0 0 1 // g: C2 rotation 1 0 0 0 0 1 0 0 0 0 -1 2 0 0 0 1 // h: z=1 mirror vertices 1 0 0 0 fixed 2 -1 -1 0 fixed 3 -1-asize -1+asize 0 fixed 4 -1-asize-bsize -1+asize-bsize 0 fixed 5 -1-asize-bsize-csize -1+asize-bsize+csize 0 fixed 6 -1-asize-bsize-csize-dsize -1+asize-bsize+csize-dsize 0 fixed 7 -2-2*bsize-2*dsize 0 0 fixed 8 0 0 -2-2*bsize-2*dsize fixed edges 1 1 2 fixed 2 2 3 fixed 3 3 4 fixed 4 4 5 fixed 5 5 6 fixed 6 6 7 fixed 7 7 8 fixed 8 8 1 fixed faces 1 -8 -7 -6 -5 -4 -3 -2 -1 read hessian_normal // good evolution gg := { refine edge where valence == 1; g 5; r; g 10; u; V; g5; hessian;hessian; g 5; hessian; hessian; r; g 5; u; V; u; g 5; hessian; hessian; g5; hessian;hessian; r; g 5; u; V; u; g 5; hessian; hessian; g 5; V; u; V; hessian; hessian; r; refine edge where original==7 or original==8; // change with genus g 5; u; V; u; g 5; hessian; hessian; g 5; V; u; V; hessian; hessian; } // Some distances in the adjoint calc := { edge2dy := sum(edge ee where original==2, sum(ee.facet ff, (ff.z*ee.x-ff.x*ee.z)/sqrt(ff.x^2+ff.y^2+ff.z^2))); printf " edge2dy: %g \n",edge2dy; edge3dy := sum(edge ee where original==3, sum(ee.facet ff, (ff.z*ee.x-ff.x*ee.z)/sqrt(ff.x^2+ff.y^2+ff.z^2))); printf " edge3dy: %g \n",edge3dy; edge4dy := sum(edge ee where original==4, sum(ee.facet ff, (ff.z*ee.x-ff.x*ee.z)/sqrt(ff.x^2+ff.y^2+ff.z^2))); printf " edge4dy: %g \n",edge4dy; edge5dy := sum(edge ee where original==5, sum(ee.facet ff, (ff.z*ee.x-ff.x*ee.z)/sqrt(ff.x^2+ff.y^2+ff.z^2))); printf " edge5dy: %g \n",edge5dy; } read "adjoint.cmd" // Call this to do adjoint transformation! adj := { adjoint; } // Applying constraints after adjointing frame := { unfix vertices; unfix edges; aa := vertex[2].y; set vertex y y-aa; bb := minimum(min(vertex,x-y),min(vertex,x+y)); set vertex x x-bb; cc := min(vertex,z-x); set vertex z z-cc; mag := max(vertex,z); set vertex x x/mag; set vertex y y/mag; set vertex z z/mag; foreach edge ee where original==1 do { set ee.vertex constraint 4; set ee constraint 4; }; foreach edge ee where original==2 do { set ee constraint 5; set ee.vertex constraint 5; }; foreach edge ee where original==3 do { set ee constraint 4; set ee.vertex constraint 4; }; foreach edge ee where original==4 do { set ee constraint 5; set ee.vertex constraint 5; }; foreach edge ee where original==5 do { set ee constraint 4; set ee.vertex constraint 4; }; foreach edge ee where original==6 do { set ee constraint 5; set ee.vertex constraint 5; }; foreach edge ee where original==7 do { set ee constraint 3; set ee.vertex constraint 3; }; foreach edge ee where original==8 do { set ee constraint 6; set ee.vertex constraint 6; }; } // To get true asize after evolving after adjointing true_asize := { printf "True asize: %20.15f\n", sum(edge where original == 2,length)/sum(edge where original==1,length); } true_bsize := { printf "True bsize: %20.15f\n", sum(edge where original == 3,length)/sum(edge where original==1,length); } true_csize := { printf "True csize: %20.15f\n", sum(edge where original == 4,length)/sum(edge where original==1,length); } true_dsize := { printf "True dsize: %20.15f\n", sum(edge where original == 5,length)/sum(edge where original==1,length); } true := { true_asize; true_bsize; true_csize ; true_dsize } // command to show full cell in rhombic dodecahedron showrhombic := { transform_expr "abcabch"; transforms on; show edge where valence <= 1; show_trans "R"; } rhombic_edges := { va := new_vertex(0,0,0); vb := new_vertex(1,-1,1); newe1 := new_edge(va,vb); vc := new_vertex(1,1,1); newe2 := new_edge(va,vc); set edge[newe1] bare; set edge[newe1] fixed; set edge[newe1] no_refine; set edge[newe2] bare; set edge[newe2] fixed; set edge[newe2] no_refine; } // command to show full cell in cube showcube := { transform_expr "abcabc"; transforms on; set edge color black; show edge where valence == 1; show_trans "R"; } setcolor := { set facet frontcolor yellow } // To show just one fundamental region, do "transforms off". // To show tetrahedron outline again, do "show edges". // A typical evolution gogo := { gg; adj; frame; g 5; V; V; g 5; show_trans "R"; hessian; hessian; }