// clasp514p4096.dmp: Dump of structure. // datafilename: clasp/clasp258p1024.dmp // Total energy: 1264.71094017842 STRING LINEAR PARAMETER knot_power = 4096 PARAMETER knot_power_ind = 0 PARAMETER height = 4.52216874986642 PARAMETER hooke2_power = 2 PARAMETER zcolor0 = 15 PARAMETER zcolor1 = 0 PARAMETER zcolors = 2 PARAMETER zebra_quiet = 1 PARAMETER zcomp = 2 PARAMETER zcount = 510 PARAMETER ze_id = 0 PARAMETER zclen = 13.3080484228139 PARAMETER zcnum = 255 PARAMETER z1st_e = 508 PARAMETER zv_id = 259 PARAMETER zcolor = 3 PARAMETER newv_id = 1 PARAMETER newe_id = 0 PARAMETER zclen1 = 13.3077097465197 PARAMETER eq_len = 0.419211119871866 PARAMETER eq_pr = 0 PARAMETER eqcomp = 0 PARAMETER eqincount = 0 PARAMETER eqoutcount = 0 PARAMETER eq_rem = 0 PARAMETER eq_e = 0 PARAMETER eq_cstart = 0 PARAMETER first_e = 508 PARAMETER eq_v = 0 PARAMETER eq_vx = 0 PARAMETER eq_vy = 0 PARAMETER eq_vz = 0 PARAMETER eq_next = 0 PARAMETER eq_ex = 0 PARAMETER eq_ey = 0 PARAMETER eq_ez = 0 PARAMETER eq_nn = 0 PARAMETER hooke_length = 0.0519839026744798 PARAMETER vi = 9 PARAMETER wi = 257 PARAMETER uu = 138 PARAMETER xx = 129 PARAMETER scaleby = 1 PARAMETER e_id = 0 PARAMETER v_id = 1 PARAMETER ii = 0 PARAMETER totlen = 13.3080484228139 VIEW_MATRIX 0.199370654168697 -0.115106700852809 0.024196403534179 0.000000000000000 0.115740740740741 0.200468843468620 0.000000000000000 0.000000000000000 -0.020954700140818 0.012098201767090 0.230213401705619 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 1.000000000000000 TOTAL_TIME 0.0212373 SCALE: 0 SCALE_LIMIT: 0.0001 CONSTRAINT_TOLERANCE: 1e-12 ZOOM_VERTEX 0 define vertex attribute znum integer define vertex attribute old integer define edge attribute hooke_size real define edge attribute zcave real QUANTITY thickp ENERGY method knot_thickness_p global QUANTITY thickp2 ENERGY modulus 0 method knot_thickness_p2 global QUANTITY thickp0 ENERGY method knot_thickness_0 global QUANTITY hooke1 ENERGY modulus 0 method hooke_energy global QUANTITY hooke ENERGY modulus 40960000 method hooke2_energy global QUANTITY len FIXED = 26.6157581693336 lagrange_multiplier -205441.717005991 method edge_length global QUANTITY thick INFO_ONLY method knot_thickness global QUANTITY thick2 INFO_ONLY method knot_thickness2 global QUANTITY thickl INFO_ONLY method knot_local_thickness global QUANTITY twist INFO_ONLY method twist global QUANTITY avex INFO_ONLY method true_average_crossings global QUANTITY writhe INFO_ONLY method true_writhe global CONSTRAINT 1 FUNCTION: X3 + height CONSTRAINT 2 FUNCTION: X3 - height vertices /* coordinates */ 1 -2.00019404809991 -1.04876760648946e-06 -4.52216874986642 constraints 1 original 11 znum 0 old 1 2 -2.00022576787073 -2.25278705188044e-07 -1.19519263174339 original 12 znum 447 old 1 3 -2.3688976002188e-07 -2.82044241478111e-08 1.05556687470272 original 13 znum 383 old 1 4 2.00022587197377 -8.76299419068722e-08 -1.19519233973726 original 14 znum 319 old 1 5 2.00019652900009 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90 density 0 original 24 hooke_size 0.0521870970451754 zcave 0 409 411 91 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 410 412 92 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 411 413 93 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 412 414 94 density 0 original 14 hooke_size 0.0521884251875056 zcave 0.597844181593716 413 415 95 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 414 416 96 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 415 417 97 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 416 418 98 density 0 original 24 hooke_size 0.0521870970451754 zcave 0.597844181593716 417 419 99 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 418 420 100 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 419 421 101 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 420 422 102 density 0 original 14 hooke_size 0.0521884251875056 zcave 0 421 423 103 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 422 424 104 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 423 425 105 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 424 426 106 density 0 original 24 hooke_size 0.0521870970451754 zcave 0 425 427 107 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 426 428 108 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 427 429 109 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 428 430 110 density 0 original 14 hooke_size 0.0521884251875056 zcave 1.26120387496374 429 431 111 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 430 432 112 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 431 433 113 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 432 434 114 density 0 original 24 hooke_size 0.0521870970451754 zcave 1.26120387496374 433 435 115 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 434 436 116 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 435 437 117 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 436 438 118 density 0 original 14 hooke_size 0.0521884251875056 zcave 0 437 439 119 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 438 440 120 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 439 441 121 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 440 442 122 density 0 original 24 hooke_size 0.0521870970451754 zcave 0 441 443 123 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 442 444 124 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 443 445 125 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 444 446 126 density 0 original 14 hooke_size 0.0521884251875056 zcave 0.432874458174231 445 447 127 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 446 448 128 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 447 449 129 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 448 450 130 density 0 original 24 hooke_size 0.0521870970451754 zcave 0.432874685968307 449 451 35 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 450 452 36 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 451 453 37 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 452 454 38 density 0 original 14 hooke_size 0.0521884251875056 zcave 0 453 455 39 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 454 456 40 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 455 457 41 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 456 458 42 density 0 original 24 hooke_size 0.0521870970451754 zcave 0 457 459 43 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 458 460 44 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 459 461 45 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 460 462 46 density 0 original 14 hooke_size 0.0521884251875056 zcave 1.26120387496374 461 463 47 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 462 464 48 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 463 465 49 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 464 466 50 density 0 original 24 hooke_size 0.0521870970451754 zcave 1.26120387496374 465 467 51 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 466 468 52 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 467 469 53 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 468 470 54 density 0 original 14 hooke_size 0.0521884251875056 zcave 0 469 471 55 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 470 472 56 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 471 473 57 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 472 474 58 density 0 original 24 hooke_size 0.0521870970451754 zcave 0 473 475 59 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 474 476 60 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 475 477 61 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 476 478 62 density 0 original 14 hooke_size 0.0521884251875056 zcave 0.597844181593716 477 479 63 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 478 480 64 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 479 481 65 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 480 482 66 density 0 original 24 hooke_size 0.0521870970451754 zcave 0.597844181593716 481 483 19 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 482 484 20 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 483 485 21 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 484 486 22 density 0 original 14 hooke_size 0.0521884251875056 zcave 0 485 487 23 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 486 488 24 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 487 489 25 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 488 490 26 density 0 original 24 hooke_size 0.0521870970451754 zcave 0 489 491 27 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 490 492 28 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 491 493 29 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 492 494 30 density 0 original 14 hooke_size 0.0521884251875056 zcave 1.26120387496374 493 495 31 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 494 496 32 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 495 497 33 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 496 498 34 density 0 original 24 hooke_size 0.0521870970451754 zcave 1.26120387496374 497 499 11 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 498 500 12 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 499 501 13 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 500 502 14 density 0 original 14 hooke_size 0.0521884251875056 zcave 0 501 503 15 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 502 504 16 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 503 505 17 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 504 506 18 density 0 original 24 hooke_size 0.0521870970451754 zcave 0 505 507 2 density 0 original 11 hooke_size 0.0521884251875056 zcave 0 506 508 3 density 0 original 12 hooke_size 0.0521884251875056 zcave 0 507 509 4 density 0 original 13 hooke_size 0.0521884251875056 zcave 0 508 510 5 density 0 original 14 hooke_size 0.0521884251875056 zcave 0.0521884251875056 509 511 7 density 0 original 21 hooke_size 0.0521870970451754 zcave 0 510 512 8 density 0 original 22 hooke_size 0.0521870970451754 zcave 0 511 513 9 density 0 original 23 hooke_size 0.0521870970451754 zcave 0 512 514 10 density 0 original 24 hooke_size 0.0521870970451754 zcave 0.0521870970451754 faces /* edge loop */ bodies /* facets */ read knotname := "clasp" tempname := "clasp514p4096.plt" dumpname := "clasp514p4096.dmp" report := {printf "Rl: %.8g\tTau: %.8g\t" ,total_length/min(vertices ,thick), min(vertices ,thick); if (total thickp > 0.1) then printf "En: %.9g\t" ,total thickp else if (total thickp > 1e-07) then printf "E6: %.9g\t" ,1000000*total thickp else printf "En: %g\t",total thickp; printf "Hk: %g\t" ,total hooke; if (scale > 0) then printf "lS: %g\n" ,-log(scale)/2.30258509299405 else printf "lS: Zero\n"} rep2 := {printf " // R_in = %.9g\n" ,min(edges ee ,len/sum(ee.vertices ,tan(dihedral/2)))} rep3 := {printf "TotCurv = %g\tWrithe = %g\tAve Xing = %g\n" ,sum(vertices ,dihedral), total writhe, total avex} gg := {g ; {if (scale > 0) then g }19; report } loosen := {unset vertices boundary 1; unset edges boundary 1} zebra_hook := {} zebra := { set edges color (zcolor0); zcomp := 0; zcount := 0; if (max(vertices ,valence) > 2) then print "Error: Not a link" else {do {ze_id := 0; foreach edges ee where color == zcolor0 && min(ee.vertices ,valence) == 1 do ze_id := id; if (ze_id == 0) then foreach edges ee where color == zcolor0 do ze_id := id; if (ze_id == 0) then break ; zclen := 0; zcnum := 0; z1st_e := ze_id; zv_id := edge[ze_id].vertex[1].id; foreach edge[ze_id].vertices vv where valence == 1 do zv_id := vv.id; zcolor := zcolor1; do { set vertex[zv_id] znum (zcount); set edge[ze_id] color (zcolor); zclen += edge[ze_id].length; zebra_hook ; foreach edge[ze_id].vertices vv where id != zv_id do { newv_id := vv.id; newe_id := 0; foreach vv.edges ee where id != ze_id do newe_id := ee.id}; if (newe_id == 0) then break ; ze_id := newe_id; zv_id := newv_id; zcolor := (zcolor == zcolor1)?(zcomp + zcolors):(zcolor1); zcount += 1; zcnum += 1} while (ze_id != z1st_e && zcount <= edge_count) ; edge[z1st_e].zcave := (zclen/zcnum); if (zcomp == 0) then zclen1 := zclen; zcomp += 1; if ( not zebra_quiet) then printf "// Cmpt %g: len %g * %g = %g, ratio %g\n" ,zcomp, zcnum, zclen/zcnum, zclen, zclen/zclen1; if (zcomp + zcolors == zcolor0) then {print "Error: too many components"; break }} while (1) }} orderdmp := {list topinfo ; printf "\nVertices\n"; zebra_hook := {printf "%g\t%g\t%g\t%g\n" ,vertex[zv_id].znum + 1, vertex[zv_id].X1, vertex[zv_id].X2, vertex[zv_id].X3}; zebra ; printf "\nEdges\n"; zebra_hook := {printf "%g\t%g\t%g\n" ,zcount + 1, edge[ze_id].vertex[1].znum + 1, edge[ze_id].vertex[2].znum + 1}; zebra ; zebra_hook := {}; list bottominfo } eq_print := {eqoutcount += 1; eq_nn := (eq_next < 0)?(eqoutcount):(eq_next); if (eq_pr == 0) then printf "%g\t%g\t%g\t%g\n" ,eqoutcount, eq_vx, eq_vy, eq_vz else printf "%g\t%g\t%g\n" ,eqoutcount, eqoutcount, eq_nn + 1} eq_sub := { set edges color (15); eqcomp := 0; eqincount := 0; eqoutcount := 0; do {eq_rem := 0; eq_e := 0; foreach edges where color == 15 do eq_e := id; if (eq_e == 0) then break ; eqcomp += 1; eq_cstart := eqoutcount; first_e := eq_e; eq_v := edge[eq_e].vertex[1].id; eq_vx := vertex[eq_v].X1; eq_vy := vertex[eq_v].X2; eq_vz := vertex[eq_v].X3; if (eq_pr == 0) then eq_print ; eq_next := -1; do { set edge[eq_e] color (0); eq_ex := edge[eq_e].X1/edge[eq_e].length; eq_ey := edge[eq_e].X2/edge[eq_e].length; eq_ez := edge[eq_e].X3/edge[eq_e].length; eq_vx := vertex[eq_v].X1 + eq_ex*(eq_len - eq_rem); eq_vy := vertex[eq_v].X2 + eq_ey*(eq_len - eq_rem); eq_vz := vertex[eq_v].X3 + eq_ez*(eq_len - eq_rem); eq_rem += edge[eq_e].length; while (eq_rem >= eq_len) do {eq_print ; eq_rem -= eq_len; eq_vx += eq_ex*eq_len; eq_vy += eq_ey*eq_len; eq_vz += eq_ez*eq_len}; foreach edge[eq_e].vertices vv where id != eq_v do {newv_id := vv.id; foreach vv.edges ee where id != eq_e do newe_id := ee.id}; eq_e := newe_id; eq_v := newv_id; eqincount += 1} while (eq_e != first_e && eqincount <= edge_count) ; if (eq_pr == 1) then {eq_next := eq_cstart; eq_print }} while (1) } equal := {if (min(vertices ,valence) < 2 || max(vertices ,valence) > 2) then print "Error: Not a link" else {printf "#include \qthick.eh\q\n"; printf "\nVertices\n"; eq_pr := 0; eq_sub ; printf "\nEdges\n"; eq_pr := 1; eq_sub ; printf "\n#include \qthick.et\q\n"}} rehooke := {zebra_hook := {if (ze_id == z1st_e) then printf "// was %g " ,edge[ze_id].hooke_size}; zebra_quiet := 0; zebra ; zebra_hook := { set edge[ze_id] hooke_size (edge[z1st_e].zcave)}; zebra_quiet := 1; zebra ; zebra_hook := {}} set_hooke := {hooke_length := len.target/edge_count; rehooke } rr := {r ; set_hooke } unr := {zebra ; delete edges where color != 0; set_hooke } subdiv := { set vertices old (1); rr ; foreach vertices vv where valence == 1 do foreach vv.edge[1].vertices ee do set ee old (1); foreach vertices ee where not old do {vi := ee.edge[1].vertex[2].id; wi := ee.edge[2].vertex[2].id; foreach vertex[vi].edges ve where id != ee.edge[1].id do foreach ve.vertex[2].edges eu where id != ve.id do uu := eu.vertex[2].id; foreach vertex[wi].edges we where id != ee.edge[2].id do foreach we.vertex[2].edges ex where id != we.id do xx := ex.vertex[2].id; ee.X1 += ((vertex[vi].X1 - vertex[uu].X1 + vertex[wi].X1 - vertex[xx].X1)/16); ee.X2 += ((vertex[vi].X2 - vertex[uu].X2 + vertex[wi].X2 - vertex[xx].X2)/16); ee.X3 += ((vertex[vi].X3 - vertex[uu].X3 + vertex[wi].X3 - vertex[xx].X3)/16)}} rescale := {scaleby := min(vertices ,thick); set vertices X1 (X1/scaleby); set vertices X2 (X2/scaleby); set vertices X3 (X3/scaleby); height /= scaleby; set edges hooke_size (hooke_size/scaleby); len.target /= scaleby; hooke_length /= scaleby; U 2; recalc ; printf "*"} plotk := { set edges color (15); printf "%!PS-Adobe-3 EPSF-3\n%%BoundingBox: 0 0 600 400\n"; printf ".005 setlinewidth\n40 400 scale\n/nan 0 def\n"; printf "0 .5 moveto 14 .5 lineto stroke newpath\n"; do {e_id := 0; foreach edges ee where color == 15 && min(ee.vertices ,valence) == 1 do e_id := id; if (e_id == 0) then foreach edges ee where color == 15 do e_id := id; if (e_id == 0) then break ; printf "0 0 moveto\n"; first_e := e_id; totlen := 0; v_id := edge[e_id].vertex[1].id; foreach edge[e_id].vertices vv where valence == 1 do v_id := vv.id; do { set edge[e_id] color (0); totlen += edge[e_id].len; printf "%g %g lineto\n" ,totlen, (vertex[v_id].thickl > 1000000000)?(0):(1/vertex[v_id].thickl); foreach edge[e_id].vertices vv where id != v_id do {newv_id := vv.id; newe_id := 0; foreach vv.edges ee where id != e_id do newe_id := ee.id}; e_id := newe_id; v_id := newv_id; if (e_id == first_e || e_id == 0) then break } while (1) ; printf "stroke newpath\n0 .1 translate\n" } while (1) ; printf "showpage\n"} dumpit := {rescale ; tempname := sprintf "%s%.0fp%.0f.plt" ,knotname, vertex_count, knot_power; plotk >>> tempname; zebra ; dumpname := sprintf "%s%.0fp%.0f.dmp" ,knotname, vertex_count, knot_power; dump dumpname; {printf "//"; report ; rep2 } >> dumpname; if (zcomp > 1) then {zebra_quiet := 0; zebra ; zebra_quiet := 1}>> dumpname; tempname := sprintf "%s.log" ,knotname; printf "%s: ",dumpname>> tempname; system sprintf "date | tr -d '\\012' >> %s" ,tempname; rep2 >> tempname; report >> tempname; rep3 >> tempname; if (zcomp > 1) then {zebra_quiet := 0; zebra ; zebra_quiet := 1} >> tempname; printf "\n">> tempname} perturb := {{j 0.01; {rescale ; report ; g }15}15} restart := {{rehooke ; {report ; rescale ; g 3}4}5; gg } contin := {{gg ; rescale ; gg ; if (scale > 0) then gg 8; rehooke }10; rescale ; gg } more := {gg ; if (scale > 0) then gg (zcomp > 1)?(23):(48); rescale ; rehooke ; gg } moreloop := {ii := 0; while (scale > 0 && ii < 20) do {more (zcomp > 1)?(10):(5); dumpit ; ii += 1}} minim := {restart ; contin ; dumpit ; moreloop } kpow := {knot_power *= 2; hooke.modulus *= 2; U 2; recalc ; minim } unkp := {knot_power /= 2; hooke.modulus /= 2; U 2; recalc ; minim } new := {read "thick.ed"} save1 := {equal >>> sprintf "%se.fe",knotname} save2 := {equal >>> sprintf "%s.fe",knotname} init1 := { set vertices X3 (3*X3); eq_len := 0.2; save1 } init2 := {restart ; eq_len := 0.4; save2 } init3 := {restart ; contin zcomp; eq_len := 0.4; save2 } run := {minim ; kpow 10; subdiv ; minim } conj_grad on quietgo on hessian_normal on metric_conversion off gv_binary off //Rl: 26.615758 Tau: 1 En: 1.05963532 Hk: 871.574 lS: Zero // R_in = 1.00136087 // Cmpt 1: len 255 * 0.0521871 = 13.3077, ratio 1 // Cmpt 2: len 255 * 0.0521884 = 13.308, ratio 1.00003