// TRadj.fe // Adjoint of Schoen's T'-R' surface // Programmer: Ken Brakke, brakke@susqu.edu, http://www.susqu.edu /* Commands: gogo - typical evolution full - show unit cell seven - seven hexagonal unit cells draw_edges - create edges for outline of hexagonal region setcolor - color back of surface yellow To turn off showing all the edges in the graphics display, hit the "e" key in the graphics window. */ // edge constraints after adjointing parameter rhs1 = 0 parameter rhs2 = 0 parameter rhs3 = 0 parameter rhs4 = 0 parameter rhs5 = 0 constraint 1 formula: x = rhs1 constraint 2 formula: z = rhs2 constraint 3 formula: .5*x - sqrt(3)/2*y = rhs3 constraint 4 formula: y = rhs4 constraint 5 formula: z = rhs5 // Transform generators to show full hexagonal prism view_transform_generators 5 1 0 0 0 // a: for z=0 plane mirror 0 1 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 // b: for y = 0 plane mirror 0 -1 0 0 0 0 1 0 0 0 0 1 .5 sqrt(3)/2 0 0 // c: for slant mirror sqrt(3)/2 -.5 0 0 0 0 1 0 0 0 0 1 1 0 0 0 // d: mirror in z = rhs5 0 1 0 0 0 0 -1 2*rhs5 0 0 0 1 -1 0 0 2*rhs1 // e: mirror in x = rhs1 0 1 0 0 0 0 1 0 0 0 0 1 vertices 1 0 0 0 fixed 2 -.5 0 0 fixed 3 0 -sqrt(3)/2 0 fixed 4 0 0 1 fixed 5 -.5 0 1 fixed 6 0 -sqrt(3)/2 1 fixed edges 1 1 2 fixed 2 2 5 fixed 3 5 6 fixed 4 6 4 fixed 5 4 1 fixed faces 1 1 2 3 4 5 read gg := { l .7; g 5; r; g 20; r; g 12; refine edge where fixed; u; V; u; V; u; V; u; V; g 12; hessian; r; g 5; hessian; V; V; u; V; u; V; u; V; u; V; g 12; hessian; hessian; } read "adjoint.cmd" adj := { adjoint; rhs1 := avg(edge ee where original==1, avg(ee.vertex,x)); rhs2 := avg(edge ee where original==2, avg(ee.vertex,z)); rhs3 := avg(edge ee where original==3, avg(ee.vertex,.5*x-sqrt(3)/2*y)); rhs4 := avg(edge ee where original==4, avg(ee.vertex,y)); rhs5 := avg(edge ee where original==5, avg(ee.vertex,z)); connum := 1; while ( connum <= 6 ) do { foreach edge ee where original == connum do { set ee constraint connum; set ee.vertex constraint connum; unfix ee; unfix ee.vertex; }; connum += 1; }; dz := rhs2; rhs2 := 0; rhs5 -= dz; set vertex z z-dz; dy := rhs4; rhs4 := 0; rhs3 += sqrt(3)/2*dy; set vertex y y-dy; dx := rhs3*2; rhs3 := 0; rhs1 -= dx; set vertex x x-dx; recalc; } full := { transform_expr "abcbcbc"; show_trans "R" } seven := { transform_expr "abcbcbcecbcbc"; show_trans "R" } draw_edges := { va := new_vertex(rhs1,0,rhs5); vb := new_vertex(rhs1,rhs1/sqrt(3),rhs5); vc := new_vertex(rhs1,rhs1/sqrt(3),0); ea := new_edge(va,vb); eb := new_edge(vb,vc); set edge[ea] no_refine; set edge[eb] no_refine; } setcolor := { set facet backcolor yellow } gogo := { gg; adj; setcolor; full; show_trans "R"; } /* Commands: gogo - typical evolution full - show unit cell seven - seven hexagonal unit cells draw_edges - create edges for outline of hexagonal region setcolor - color back of surface yellow To turn off showing all the edges in the graphics display, hit the "e" key in the graphics window. */