// C21Padj.fe // Surface Evolver datafile for adjoint of Schoen's C21(P) surface on p. B, bottom. // genus 21 surface complementary to P surface // Programmer: Ken Brakke, brakke@susqu.edu, http://www.susqu.edu /* Commands: gogo - typical evolution showcube - cubic unit cell, as on web page 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. */ view_transform_generators 5 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 1 // a: mirror on long curved edge swap_colors // just for the next one -1 0 0 0 0 0 -1 0 0 -1 0 0 0 0 0 1 // b: C2 rotation on straight edge -1 0 0 -2 0 1 0 0 0 0 1 0 0 0 0 1 // c: mirror plane x = -1 1 0 0 0 0 -1 0 -2 0 0 1 0 0 0 0 1 // d: mirror plane y = -1 1 0 0 0 0 1 0 0 0 0 -1 -2 0 0 0 1 // e: mirror plane z = -1 (bottom edges) parameter alpha = 0.360816714408623 // shape parameter, for period killing constraint 1 // mirror plane in adjoint formula: y = z // Constraints for use after adjoint transformation constraint 3 formula: y = 1 constraint 4 formula: z = -1 constraint 5 formula: y = x constraint 6 formula: x = 0 constraint 7 formula: y+z= 0 constraint 10 formula: 0 // dummy to control edge deletion vertices 1 0 0 0 fixed 2 -1 alpha alpha fixed 3 -1 alpha 0 fixed 4 -1 1 0 fixed edges 1 1 2 constraint 1 2 2 3 fixed constraint 10 3 3 4 fixed constraint 10 4 4 1 fixed constraint 10 faces 1 -4 -3 -2 -1 read hessian_normal // to refine edges on border with narrow triangles border := { refine edge ee where valence == 1 and (ee.facet[1].area < ee.length^2/3); } // good evolution, getting lots of facets near vertex 2 cusp. gg := { refine edge where valence == 1; g 5; r; g 10; u; V; refine vertex[2].edge where on_constraint 1; g5; hessian;hessian; refine vertex[2].edge; g 5; hessian; hessian; r; g 5; u; V; u; g 5; hessian; hessian; refine vertex[2].edge where on_constraint 1; g5; hessian;hessian; r; g 5; u; V; u; g 5; hessian; hessian; refine vertex[2].edge; g 5; V; u; V; hessian; hessian; refine edge where original == 4; r; g 5; u; V; u; g 5; hessian; hessian; border; g 5; V; u; V; hessian; hessian; } // Period to kill calc := { edge2dy := sum(edge ee where original==2, sum(ee.facet ff, ff.x*ee.z/sqrt(ff.x^2+ff.y^2+ff.z^2))); printf "edge2dy: %g \n",edge2dy; } read "adjoint.cmd" // Call this to do adjoint transformation! adj := { unset vertex constraint 1; unset edge constraint 1; unset vertex constraint 10; unset edge constraint 10; adjoint; } // Applying constraints after adjointing frame := { unfix vertices; unfix edges; xoff := vertex[1].x; set vertex x x-xoff; yoff := vertex[1].y; set vertex y y-yoff; zoff := vertex[1].z; set vertex z z-zoff; maxy := max(vertex,y); set vertex x x/maxy; set vertex y y/maxy; minz := min(vertex,z); set vertex z z/(-minz); foreach edge ee where original==1 do { fix ee.vertex; set ee.vertex constraint 6; set ee.vertex constraint 7; set ee constraint 6; set ee constraint 7; }; foreach edge ee where original==2 do { set ee constraint 4; set ee.vertex constraint 4; }; foreach edge ee where original==3 do { set ee constraint 3; set ee.vertex constraint 3; }; foreach edge ee where original==4 do { set ee constraint 5; set ee.vertex constraint 5; }; t .005; } // for displaying full cube showcube := { transform_expr "cdeababab"; show_trans "R";} setcolor := { set facet backcolor yellow; } // To get true parameters after evolving after adjointing true_alpha := { printf "True alpha: %20.15f\n", sum(edge where original == 2,length)*sqrt(2)/ sum(edge where original==4,length); } true:={true_alpha;} // for nice border bands for Postscript output read "band.cmd" bandwidth := 0.005; bandcolor := black; bandflag := 0; banding := { if bandflag then { errprintf "Already did banding. Exiting banding.\n"; return; }; edgenum := 1; while ( edgenum <= 4 ) do { set edge inband original==edgenum ; makeband; edgenum += 1; }; show edge where 0; ps_gridflag off; ps_colorflag on; ps_labelflag off; bandflag := 1; } // Typical evolution. Can be followed by "cube" gogo := { gg; adj; frame; show_trans "R"; hessian; hessian; }