// batwingadj.fe // Adjoint of Schoen's batwing surface. // Programmer: Ken Brakke, brakke@susqu.edu, http://www.susqu.edu /* Commands: gogo - typical evolution showcubelet - display 1/8 of cubic unit cell, as on web page showcube - display cubic unit cell showpair - show two fundamental regions, the "bat" showocto - show octahedron, as on web page; if you want the octahedral frame, also run "octa_edge" 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 = 0.45208 // shape parameter, for period killing constraint 1 // mirror plane in adjoint formula: x + z = 1 // Constraints for use after adjoint transformation constraint 3 formula: x = z constraint 4 formula: y = 0.5 constraint 5 formula: y = x constraint 6 formula: x = 0 constraint 7 formula: y+z = 1 view_transform_generators 10 -1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 // a: x mirror 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 // b: x y swap 1 0 0 0 0 0 -1 1 0 -1 0 1 0 0 0 1 // c: y+z=1 swap_colors 0 0 1 0 0 -1 0 1 1 0 0 0 0 0 0 1 // d: C2 rotation -1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 // e: x = 0 mirror 1 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 1 // f: y = 0 mirror 1 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 1 // g: z = 0 mirror -1 0 0 2 0 1 0 0 0 0 1 0 0 0 0 1 // h: x = 1 mirror 1 0 0 0 0 -1 0 2 0 0 1 0 0 0 0 1 // i: y = 1 mirror 1 0 0 0 0 1 0 0 0 0 -1 2 0 0 0 1 // j: z = 1 mirror vertices 1 0 0 0 fixed 2 1 0 0 fixed 3 asize (1-2*asize) (1-asize) fixed 4 asize -asize 0 fixed edges 1 2 1 fixed 2 1 4 fixed 3 4 3 fixed 4 3 2 constraint 1 faces 1 -4 -3 -2 -1 read hessian_normal // good evolution, getting lots of facets near vertex 2 cusp. 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; g 5; u; V; u; g 5; hessian; hessian; refine edge where original == 1 or original == 3; g 5; V; u; V; hessian; hessian; } // Some distances in the adjoint calc := { edge3dx := sum(edge ee where original==3, sum(ee.facet ff, (ff.y*ee.z-ff.z*ee.y)/sqrt(ff.x^2+ff.y^2+ff.z^2))); 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 " edge3dx - edge3dy: %g \n",edge3dx-edge3dy; } read "adjoint.cmd" // Call this to do adjoint transformation! adj := { unset vertex constraint 1; unset edge constraint 1; adjoint; } // Applying constraints after adjointing frame := { unfix vertices; unfix edges; minx := min(vertex,x); set vertex x x-minx; miny := min(vertex,y); set vertex y y-miny; minz := min(vertex,z); set vertex z z-minz; maxyz := max(vertex,y+z); set vertex x x/maxyz; set vertex y y/maxyz; set vertex z z/maxyz; foreach edge ee where original==1 do { set ee.vertex constraint 6; set ee constraint 6; }; 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 7; set ee.vertex constraint 7; }; foreach edge ee where original==4 do { set ee constraint 3; set ee.vertex constraint 3; set ee constraint 4; set ee.vertex constraint 4; fix ee; fix ee.vertex; }; } // To get true asize after evolving after adjointing true_asize := { printf "True asize: %20.15f\n", sum(edge where original == 2,length)/sqrt(2)/sum(edge where original==1,length); } showpair := { transform_expr "d"; show_trans "R"; } showcubelet := { transform_expr "dbcb"; show_trans "R"; } showcube := { transform_expr "efjdbcb"; show_trans "R";} showocto := { transform_expr "igcdada"; show_trans "R"; } octa_edge := { va := new_vertex(.5,.5,.5); vb := new_vertex(0,0,1); ea := new_edge(va,vb); set edge[ea] fixed; set edge[ea] no_refine; vc := new_vertex(0,0,0); eb := new_edge(vb,vc); set edge[eb] fixed; set edge[eb] no_refine; } setcolor := { set facet backcolor yellow } gogo := { gg; adj; frame; show_trans "R"; hessian; hessian; }