32:T635,md`# Hello Tactile.JS! (a library for Escher-esque isohedral tessellations) [tactile-js](https://github.com/isohedral/tactile-js) is a lightweight js library written by [Craig Kaplan](https://twitter.com/cs_kaplan). I recently discovered it & have fallen in love with it 😍. I figure it deserves a bit more attention so I wanted to create a quick demo here on Observable. From the [Github README](https://github.com/isohedral/tactile-js): > _TactileJS is a Javascript library for representing, manipulating, and drawing tilings of the plane. The tilings all belong to a special class called the isohedral tilings. Every isohedral tiling is formed from repeated copies of a single shape, and the pattern of repetition is fairly simple. At the same time, isohedral tilings are very expressive (they form the basis for a lot of the tessellations created by M.C. Escher) and efficient to compute._ >_There are 93 "tiling types", different ways that tiles can relate to each other. Of these, 12 are boring for reasons I won't talk about here; this library lets you manipulate the other 81 types._ If you'd like to see a use-case for this library, checkout [Dithering on non-square Pixels](https://observablehq.com/@mattdzugan/dithering-on-non-square-pixels) where I import this library to do some fun pseudo-gradients. If you'd like to use these funcitons, just: ~~~js import {EdgeShape, numTypes, mul, tilingTypes, tiling_type_data, makePoint, makeMatrix, M_orients, TSPI_U, TSPI_S, IsohedralTiling} from "@mattdzugan/hello-tactile-js-a-library-for-eascher-esque-isohedron-tess" ~~~ `33:T403,{ const height = width/3; const zoom = zoomlevel; const asp = width / height; const h = 6.0 * zoom; const w = asp * h * zoom; const sc = height / (2*h); const M = mul( [1, 0, width/2.0, 0, 1, height/2.0], [sc, 0, 0, 0, -sc, 0] ); const canvas = DOM.canvas(width, height); var context = canvas.getContext("2d"); const COLS = ["#457b9d","#1d3557","#a8dadc"] for( let i of a_tiling.fillRegionBounds( -w-5.0, -h-5.0, w+5.0, h+5.0 ) ) { const TT = i.T; const T = mul( M, TT ); const col = COLS[ a_tiling.getColour( i.t1, i.t2, i.aspect ) + 0 ]; context.fillStyle = col; context.strokeStyle = col; context.beginPath(); var iii = 0; for( let v of tile_shape ) { const P = mul( T, v ); if(iii==0){ context.moveTo( P.x, P.y ); }else{ context.lineTo( P.x, P.y ); } iii++; } var P0 = mul(T,tile_shape[0]); context.lineTo( P0.x, P0.y ); context.fill(); context.stroke(); } return canvas }34:Te494,tiling_type_data = (function() { const es_00 = [ EdgeShape.J, EdgeShape.J, EdgeShape.J ]; const es_01 = [ EdgeShape.S, EdgeShape.J, EdgeShape.S, EdgeShape.S, EdgeShape.S ]; const es_02 = [ EdgeShape.S, EdgeShape.J, EdgeShape.J, EdgeShape.S ]; const es_03 = [ EdgeShape.S, EdgeShape.J, EdgeShape.S, EdgeShape.J ]; const es_04 = [ EdgeShape.S, EdgeShape.S, EdgeShape.S ]; const es_05 = [ EdgeShape.S, EdgeShape.J ]; const es_06 = [ EdgeShape.J ]; const es_07 = [ EdgeShape.S ]; const es_08 = [ EdgeShape.U, EdgeShape.J ]; const es_09 = [ EdgeShape.U, EdgeShape.S, EdgeShape.S ]; const es_10 = [ EdgeShape.J, EdgeShape.I ]; const es_11 = [ EdgeShape.S, EdgeShape.I, EdgeShape.S ]; const es_12 = [ EdgeShape.I, EdgeShape.J ]; const es_13 = [ EdgeShape.I, EdgeShape.S ]; const es_14 = [ EdgeShape.U ]; const es_15 = [ EdgeShape.I ]; const es_16 = [ EdgeShape.S, EdgeShape.J, EdgeShape.J ]; const es_17 = [ EdgeShape.J, EdgeShape.J, EdgeShape.I ]; const es_18 = [ EdgeShape.S, EdgeShape.S, EdgeShape.J, EdgeShape.S ]; const es_19 = [ EdgeShape.S, EdgeShape.S, EdgeShape.J, EdgeShape.I ]; const es_20 = [ EdgeShape.J, EdgeShape.J, EdgeShape.S ]; const es_21 = [ EdgeShape.S, EdgeShape.I, EdgeShape.I ]; const es_22 = [ EdgeShape.J, EdgeShape.I, EdgeShape.I ]; const es_23 = [ EdgeShape.J, EdgeShape.J ]; const es_24 = [ EdgeShape.I, EdgeShape.I ]; const es_25 = [ EdgeShape.J, EdgeShape.S ]; const es_26 = [ EdgeShape.S, EdgeShape.S, EdgeShape.S, EdgeShape.S ]; const es_27 = [ EdgeShape.J, EdgeShape.S, EdgeShape.S ]; const es_28 = [ EdgeShape.I, EdgeShape.S, EdgeShape.I, EdgeShape.S ]; const es_29 = [ EdgeShape.J, EdgeShape.I, EdgeShape.S ]; const es_30 = [ EdgeShape.I, EdgeShape.I, EdgeShape.I, EdgeShape.S ]; const es_31 = [ EdgeShape.S, EdgeShape.S ]; const es_32 = [ EdgeShape.S, EdgeShape.I ]; const es_33 = [ EdgeShape.U, EdgeShape.I ]; const es_34 = [ EdgeShape.U, EdgeShape.S ]; const es_35 = [ EdgeShape.I, EdgeShape.I, EdgeShape.I ]; const es_36 = [ EdgeShape.I, EdgeShape.S, EdgeShape.I ]; const es_37 = [ EdgeShape.I, EdgeShape.S, EdgeShape.S ]; const esi_00 = [ 0, 1, 2, 0, 1, 2 ]; const esi_01 = [ 0, 0, 1, 2, 2, 1 ]; const esi_02 = [ 0, 1, 0, 2, 1, 2 ]; const esi_03 = [ 0, 1, 2, 3, 1, 4 ]; const esi_04 = [ 0, 1, 2, 2, 1, 3 ]; const esi_05 = [ 0, 1, 2, 3, 1, 3 ]; const esi_06 = [ 0, 0, 1, 1, 2, 2 ]; const esi_07 = [ 0, 1, 1, 0, 1, 1 ]; const esi_08 = [ 0, 0, 0, 0, 0, 0 ]; const esi_09 = [ 0, 1, 2, 0, 2, 1 ]; const esi_10 = [ 0, 1, 0, 0, 1, 0 ]; const esi_11 = [ 0, 1, 2, 2, 1, 0 ]; const esi_12 = [ 0, 1, 1, 1, 1, 0 ]; const esi_13 = [ 0, 1, 1, 2, 2 ]; const esi_14 = [ 0, 0, 1, 2, 1 ]; const esi_15 = [ 0, 1, 2, 3, 2 ]; const esi_16 = [ 0, 1, 2, 1, 2 ]; const esi_17 = [ 0, 1, 1, 1, 1 ]; const esi_18 = [ 0, 1, 2, 0 ]; const esi_19 = [ 0, 1, 1, 0 ]; const esi_20 = [ 0, 0, 0, 0 ]; const esi_21 = [ 0, 1, 0 ]; const esi_22 = [ 0, 1, 0, 1 ]; const esi_23 = [ 0, 1, 0, 2 ]; const esi_24 = [ 0, 0, 1, 1 ]; const esi_25 = [ 0, 1, 2, 3 ]; const esi_26 = [ 0, 0, 1, 2 ]; const esi_27 = [ 0, 1, 2 ]; const esi_28 = [ 0, 0, 1 ]; const esi_29 = [ 0, 0, 0 ]; const eo_00 = [ false, false, false, false, false, false, false, true, false, true, false, true ]; const eo_01 = [ false, false, true, true, false, false, false, false, true, true, false, true ]; const eo_02 = [ false, false, false, false, true, true, false, false, false, true, true, true ]; const eo_03 = [ false, false, false, false, false, false, false, false, false, true, false, false ]; const eo_04 = [ false, false, false, false, false, false, true, true, false, true, false, false ]; const eo_05 = [ false, false, false, false, false, false, false, false, true, true, true, true ]; const eo_06 = [ false, false, false, true, false, false, false, true, false, false, false, true ]; const eo_07 = [ false, false, false, false, false, false, false, false, false, false, false, false ]; const eo_08 = [ false, false, false, false, true, true, false, false, false, false, true, true ]; const eo_09 = [ false, false, false, false, true, true, false, true, false, true, true, false ]; const eo_10 = [ false, false, false, false, false, false, false, true, true, false, true, false ]; const eo_11 = [ false, false, false, false, true, true, false, true, true, false, true, false ]; const eo_12 = [ false, false, false, false, false, false, true, false, true, false, true, false ]; const eo_13 = [ false, false, false, false, false, true, true, true, true, false, true, false ]; const eo_14 = [ false, false, false, false, true, false, false, false, false, false, true, false ]; const eo_15 = [ false, false, false, false, false, true, false, false, false, true ]; const eo_16 = [ false, false, true, true, false, false, false, false, false, true ]; const eo_17 = [ false, false, false, false, false, false, false, false, false, true ]; const eo_18 = [ false, false, true, false, false, false, false, false, true, false ]; const eo_19 = [ false, false, false, false, false, false, true, true, true, true ]; const eo_20 = [ false, false, false, false, false, true, true, true, true, false ]; const eo_21 = [ false, false, false, false, false, false, false, true ]; const eo_22 = [ false, false, false, false, false, true, false, true ]; const eo_23 = [ false, false, false, false, true, false, true, false ]; const eo_24 = [ false, false, false, true, false, false, false, true ]; const eo_25 = [ false, false, true, false, true, true, false, true ]; const eo_26 = [ false, false, true, false, false, false, true, false ]; const eo_27 = [ false, false, false, false, false, true ]; const eo_28 = [ false, false, false, false, true, false ]; const eo_29 = [ false, false, false, false, false, true, false, false ]; const eo_30 = [ false, false, false, false, false, true, true, true ]; const eo_31 = [ false, false, true, true, false, false, true, true ]; const eo_32 = [ false, false, false, false, true, true, false, false ]; const eo_33 = [ false, false, false, false, false, false, false, false ]; const eo_34 = [ false, false, false, false, true, true, true, true ]; const eo_35 = [ false, false, true, true, false, false, false, false ]; const eo_36 = [ false, false, false, true, false, false, false, false ]; const eo_37 = [ false, false, false, false, false, true, true, false ]; const eo_38 = [ false, false, false, false, true, false, false, false ]; const eo_39 = [ false, false, true, true, false, true, true, false ]; const eo_40 = [ false, false, false, true, true, true, true, false ]; const eo_41 = [ false, false, false, false, false, false ]; const eo_42 = [ false, false, true, true, false, false ]; const eo_43 = [ false, false, false, true, false, false ]; const eo_44 = [ false, false, true, false, false, false ]; const dp_00 = [ 0.12239750492, 0.5, 0.143395479017, 0.625 ]; const dp_01 = [ 0.12239750492, 0.5, 0.225335752741, 0.225335752741 ]; const dp_02 = [ 0.12239750492, 0.5, 0.225335752741, 0.625 ]; const dp_03 = [ 0.12239750492, 0.5, 0.315470053838, 0.5, 0.315470053838, 0.5 ]; const dp_04 = [ 0.12239750492, 0.5, 0.225335752741, 0.225335752741, 0.5 ]; const dp_05 = [ 0.12239750492, 0.5, 0.225335752741, 0.625, 0.5 ]; const dp_06 = [ 0.6, 0.196416770201 ]; const dp_07 = [ 0.12239750492, 0.5, 0.225335752741 ]; const dp_08 = [ ]; const dp_09 = [ 0.12239750492, 0.225335752741 ]; const dp_10 = [ 0.12239750492, 0.225335752741, 0.5 ]; const dp_11 = [ 0.12239750492, 0.225335752741, 0.225335752741 ]; const dp_12 = [ 0.216506350946 ]; const dp_13 = [ 0.104512294489, 0.65 ]; const dp_14 = [ 0.230769230769, 0.5, 0.225335752741 ]; const dp_15 = [ 0.230769230769, 0.5, 0.225335752741, 0.5 ]; const dp_16 = [ 0.230769230769, 0.225335752741 ]; const dp_17 = [ 0.141304, 0.465108, 0.534891 ]; const dp_18 = [ 0.452827026611, 0.5 ]; const dp_19 = [ 0.366873818946 ]; const dp_20 = [ 0.230769230769 ]; const dp_21 = [ 0.230769230769, 0.5 ]; const dp_22 = [ 0.5, 0.102564102564 ]; const dp_23 = [ 0.230769230769, 0.869565217391 ]; const dp_24 = [ 0.5, 0.230769230769, 0.5, 0.5 ]; const dp_25 = [ 0.230769230769, 0.5, 0.230769230769 ]; const dp_26 = [ 0.5, 0.5, 0.6 ]; const dp_27 = [ 0.5, 0.102564102564, 0.102564102564 ]; const dp_28 = [ 0.230769230769, 0.230769230769 ]; const dp_29 = [ 0.5 ]; const dp_30 = [ 0.105263157895 ]; const dp_31 = [ 0.196416770201 ]; const dp_32 = [ 0.5, 0.196416770201 ]; const tvc_00 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.9, 0, 0, 0, 0.1, 0, 5, 0, 0, -2.5, 3.9, 0, 5.5, 0, -0.4, 0, 5, 0, -4, 0.5, 3.9, 0, 0, 0, 0.1, 0, 5, 0, 0, -1.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -5.5, 0, 0.5, 0, 0, 0, 4, -2 ]; const tvc_01 = [ 3.9, 0, 0, 0, 0.1, 0, 5, 0, 0, -2.5, 3.9, 0, 0, 3.5, -0.4, 0, 5, 0, 0, -2, 3.9, 0, 0, 0, 0.1, 0, 5, 0, 0, -1.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -3.5, 0, 0.5, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]; const tvc_02 = [ 0, 0, -3.5, 0, 0.5, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.9, 0, 0, 0, 0.1, 0, 5, 0, 0, -2.5, 3.9, 0, 3.5, 0, -0.4, 0, 5, 0, 4, -4.5, 3.9, 0, 0, 0, 0.1, 0, 5, 0, 0, -1.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]; const tvc_03 = [ 0, 0, -2.5, 0, 0, 0, 0.5, 0, 0, 0, 3, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.9, 0, 0, 0, 0, 0, 0.1, 0, 5, 0, 0, 0, 0, -2.5, 3.9, 0, 0, 0, 2.5, 0, -0.4, 0, 5, 0, 0, 0, 3, -3.5, 3.9, 0, 0, 0, 0, 0, 0.1, 0, 5, 0, 0, 0, 0, -1.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]; const tvc_04 = [ 3.9, 0, 0, 3.5, 0, -0.4, 0, 5, 0, 0, 5, -4.5, 3.9, 0, 0, 0, 0, 0.1, 0, 5, 0, 0, 0, -1.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -3.5, 0, 0, 0.5, 0, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.9, 0, 0, 0, 0, 0.1, 0, 5, 0, 0, 0, -2.5 ]; const tvc_05 = [ 3.9, 0, 3.5, 0, 0, -0.4, 0, -5, 0, 4, 0, 0.5, 3.9, 0, 0, 0, 5, -2.4, 0, 5, 0, 0, 0, -1.5, 0, 0, 0, 0, 5, -2.5, 0, 0, 0, 0, 0, 1, 0, 0, -3.5, 0, 0, 0.5, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3.9, 0, 0, 0, 0, 0.1, 0, -5, 0, 0, 0, 2.5 ]; const tvc_06 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, -0.288675134595, 0, 0, 1, 0, 0, 0, 2.5, 1.12583302492, -0.721132486541, -1.44337567297, 1.95, 1.06036297108, 5, 0, -2.5, 0, 3.9, 0.1, 2.5, -1.12583302492, -1.27886751346, 1.44337567297, 1.95, -0.671687836487 ]; const tvc_07 = [ 0, 0, 0, 0, 0, 0, 0, 0, 3.9, 0, 0, 0.1, 0, 5, 0, -2.5, 3.9, 0, 3.5, -0.4, 0, 5, 0, -2, 3.9, 0, 0, 0.1, 0, 5, 0, -1.5, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -3.5, 0.5, 0, 0, 0, 0.5 ]; const tvc_08 = [ 1, 0, 0.5, 0.866025403784, -0.5, 0.866025403784, -1, 0, -0.5, -0.866025403784, 0.5, -0.866025403784 ]; const tvc_09 = [ 0, 0, 0, 0, 0, 0, 3.9, 0, 0.1, 0, 0, 0, 3.9, 3.5, -0.4, 0, 0, 0.5, 3.9, 0, 0.1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -3.5, 0.5, 0, 0, 0.5 ]; const tvc_10 = [ 0, 0, 0, 0, 0, 0, 0, 0, 3.9, 0, 0, 0.1, 0, 0, 0, 0, 3.9, 3.5, 0, -0.4, 0, 0, 5, -2, 3.9, 0, 0, 0.1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, -3.5, 0, 0.5, 0, 0, 5, -2 ]; const tvc_11 = [ 3.9, 3.5, -0.4, 0, 0, 0.5, 3.9, 0, 0.1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -3.5, 0.5, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 3.9, 0, 0.1, 0, 0, 0 ]; const tvc_12 = [ 0, -3.5, 0, 0.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 3.9, 0, 0, 0.1, 0, 0, 0, 0, 3.9, 0, 3.5, -0.4, 0, 0, 0, 0.5, 3.9, 0, 0, 0.1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]; const tvc_13 = [ 0, 0.5, 0, -0.288675134595, 0, 1, 0, 0, 1.15470053838, 0.75, 2, 0.144337567297, 0, 0.5, 4, 0, -1.15470053838, 0.25, 2, 0.144337567297, 0, 0, 0, 0 ]; const tvc_14 = [ 0, 0, 1, 0, 0, 0, 0, 5, -2.5, 5.1, 0, -0.1, -1.47224318643, 2.5, -1.22113248654, 2.55, 1.44337567297, -0.771687836487, 0, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, -0.866025403784 ]; const tvc_15 = [ 3.9, 0, 0, 0.1, 0, 5, 0, -2.5, 3.9, 0, 3.5, -0.4, 0, 5, 0, -2, 3.9, 0, 0, 0.1, 0, 5, 0, -1.5, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ]; const tvc_16 = [ 3.9, 0, 0, 0, 0.1, 0, 5, 0, 0, -2.5, 3.9, 0, 3.5, 0, -0.4, 0, 5, 0, 4, -4, 3.9, 0, 0, 0, 0.1, 0, 5, 0, 0, -1.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]; const tvc_17 = [ 3.9, 0, 0.1, 0, 0, 0, 3.9, 3.5, -0.4, 0, 0, 0.5, 3.9, 0, 0.1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 ]; const tvc_18 = [ 0, 0, 5, -2.5, 0, 0, 0, 1, 0, 0, -5, 2.5, 0, 10, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 3.9, 0, 0, 0.1, 0, -5, 0, 2.5, 3.9, 0, 5, -2.4, 0, 5, 0, -1.5 ]; const tvc_19 = [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1.95, 2.5, -0.95, -1.95, 2.5, -1.05, 3.9, 0, 0.1, 0, 5, -2, 1.95, -2.5, 1.55, 1.95, 2.5, -0.45 ]; const tvc_20 = [ 0, -1, 0, 0, 0, 1, 0, 0, 4.95, 0.55, 4.95, 0.55, 0, 0, 9.9, 0.1, -4.95, -0.55, 4.95, 0.55 ]; const tvc_21 = [ 0, 1, 0, 0, 2.925, 0.075, 1.68874953738, 0.0433012701892, 0, 0, 0, 0, -2.925, 1.425, 1.68874953738, -0.822724133595 ]; const tvc_22 = [ 1, 0, 0.75, 0.433012701892, 0, 0, 0.75, -0.433012701892 ]; const tvc_23 = [ 0.5, 0, 0, 0.866025403784, -0.5, 0, 0, -0.866025403784 ]; const tvc_24 = [ 0, 0.57735026919, -1, 0, 1, 0 ]; const tvc_25 = [ 0, 0, 0, 0, 0, 0, 3.9, 0, 0.1, 0, 5, -2.5, 3.9, 0, 0.1, 0, 5, -1.5, 0, 0, 0, 0, 0, 1 ]; const tvc_26 = [ 5, 0, -2, 0, -3.9, -0.1, 0, 0, 1, 0, 0, 0, 5, 0, -2, 0, 3.9, 0.1, 0, 0, 0, 0, 0, 0 ]; const tvc_27 = [ 0, 0, 1, 0, 0, 0, 0, -3.45, 4, 3.9, 0, 0.1, 0, 3.45, -3, 3.9, 0, 0.1, 0, 0, 0, 0, 0, 0 ]; const tvc_28 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, -1.5, 0, 3.9, 0, 0, 0.1, 0, 0, 5, 0, -2.5, 0, 0, 0, 5, -1.5 ]; const tvc_29 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -5, 3.9, 2.6, 3.9, 0, 0, 0.1, 0, -5, 0, 2.5, 3.9, 0, 0, 0.1 ]; const tvc_30 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -10, 0, 0, 5, 0, 10, 0, -4, 10, 0, 10, -10, 0, 10, 0, -5, 0, 0, 10, -5 ]; const tvc_31 = [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 3.9, 0.1, 0, 0, 3.9, 0.1 ]; const tvc_32 = [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 3.9, 0.1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, -2, 0, -3.9, 0, -0.1 ]; const tvc_33 = [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3.9, 0, 0.1, 0, 0, 0, 3.9, 0, 0.1, 0, 3.9, 0.1 ]; const tvc_34 = [ 1, 0, 1, 1, 0, 1, 0, 0 ]; const tvc_35 = [ 1.8, 0.1, 0, 0, 0, 1, 0, 1, 0, 0, -1.8, 1.9, 0, 0, 0, 0 ]; const tvc_36 = [ 3.8, 0.1, 0, 0, 0, 0, -3.8, 0.9, -3.8, -0.1, 0, 0, 0, 0, 3.8, -0.9 ]; const tvc_37 = [ 0, 0, 0.57735026919, 0, 0, 1 ]; const tvc_38 = [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 3.9, 0.1 ]; const tvc_39 = [ 0.5, 0.5, 0, 0, 1, 0 ]; const tvc_40 = [ 0, 1, 0, 0, 0, 0.5, 3.9, 0.1, 0, 0, 0, 0 ]; const tvc_41 = [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 5, 0, -2, 0, 3.9, 0.1 ]; const tvc_42 = [ 1, 0, -0.5, 0.866025403784, -0.5, -0.866025403784 ]; const tc_00 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 3.9, 0, 5.5, 0, -0.4, 0, 5, 0, -4, -0.5 ]; const tc_01 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 7.8, 0, 3.5, 3.5, -0.8, 0, 0, 0, 0, 0 ]; const tc_02 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -7.8, 0, -7, 0, 0.8, 0, 0, 0, 0, -1 ]; const tc_03 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -7.8, 0, -2.5, 0, -2.5, 0, 0.8, 0, -10, 0, 3, 0, -3, 4 ]; const tc_04 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -15.6, 0, -7, -7, 0, 1.6, 0, 0, 0, 0, 0, -2 ]; const tc_05 = [ 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -3, 7.8, 0, 7, 0, 0, -0.8, 0, 0, 0, 0, 0, 0 ]; const tc_06 = [ -2.5, -3.37749907476, 0.663397459622, 4.33012701892, -1.95, -3.08108891325, -2.5, 3.37749907476, 2.33660254038, -4.33012701892, -1.95, 2.11506350946 ]; const tc_07 = [ 0, 0, 0, 0, 0, 0, 0, -1, 7.8, 0, 7, -0.8, 0, 0, 0, 0 ]; const tc_08 = [ 1.5, 0.866025403784, 1.5, -0.866025403784 ]; const tc_09 = [ 1.5, 0.866025403784, 0, 1.73205080757 ]; const tc_10 = [ 0, 0, 0, 0, 0, -1, 3.9, 3.5, -0.4, 0, 0, -0.5 ]; const tc_11 = [ 0, 0, 0, 0, 0, 0, 0, -1, 7.8, 7, 0, -0.8, 0, 0, 0, 0 ]; const tc_12 = [ 3.9, 3.5, -0.4, 0, 0, 0.5, 3.9, 3.5, -0.4, 0, 0, -0.5 ]; const tc_13 = [ 0, 0, 0, 0, 0, 0, 0, -1, -7.8, -3.5, -3.5, 0.8, 0, 0, 0, 0 ]; const tc_14 = [ 0, 0, -4, -0.866025403784, 3.46410161514, 0.75, -2, -0.433012701892 ]; const tc_15 = [ 4.4167295593, -2.5, 2.66339745962, -2.55, -4.33012701892, 1.34903810568, 0, -5, 2.5, -5.1, 0, -1.63205080757 ]; const tc_16 = [ -7.8, 0, -3.5, 0.3, 0, 0, 0, -0.5, -7.8, 0, -3.5, 0.3, 0, 0, 0, 0.5 ]; const tc_17 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 7.8, 0, 3.5, 0, -0.3, 0, 10, 0, 4, -7.5 ]; const tc_18 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 15.6, 0, 7, 0, -0.6, 0, 0, 0, 0, 0 ]; const tc_19 = [ 0, 0, 0, 0, 0, 0, 0, 1, -15.6, 0, -7, 0.6, 0, 0, 0, 0 ]; const tc_20 = [ 0, 0, 0, 0, 0, 1, -7.8, -3.5, 0.3, 0, 0, 0.5 ]; const tc_21 = [ 0, 0, 0, 0, 0, 10, 0, -3, -7.8, 0, -10, 4.8, 0, 0, 0, 0 ]; const tc_22 = [ -3.9, 5, -3.1, -3.9, -5, 1.9, -3.9, -5, 1.9, 3.9, -5, 3.1 ]; const tc_23 = [ 9.9, 1.1, -9.9, -1.1, -9.9, -1.1, -9.9, -1.1 ]; const tc_24 = [ 0, 0, 0, 1.73205080757, 0, 1.5, 0, -0.866025403784 ]; const tc_25 = [ -1.5, 0.866025403784, -1.5, -0.866025403784 ]; const tc_26 = [ 0, 1.73205080757, 1.5, -0.866025403784 ]; const tc_27 = [ -1, 1.73205080757, 1, 1.73205080757 ]; const tc_28 = [ 1, 1.73205080757, -1, 1.73205080757 ]; const tc_29 = [ 1, 1.73205080757, 2, 0 ]; const tc_30 = [ 0, 0, 0, 0, 0, -1, 3.9, 0, 0.1, 0, 5, -2.5 ]; const tc_31 = [ 0, 0, 0, 0, 0, -1, 7.8, 0, 0.2, 0, 0, 0 ]; const tc_32 = [ 0, 0, 0, 0, -7.8, -0.2, 0, 0, 1, 0, 0, 0 ]; const tc_33 = [ 0, -6.9, 8, 0, 0, 0, 0, -3.45, 4, -3.9, 0, -0.1 ]; const tc_34 = [ -5, 0, -5, 0, 5, 0, -3.9, 0, -5, 1.4, -5, 0, 0, 0, 1.5, 0, -3.9, 0, 0, -0.1 ]; const tc_35 = [ 0, 0, 0, 0, 0, -1, 7.8, 0, 0.2, 0, 10, -5 ]; const tc_36 = [ 0, 0, 0, 0, -7.8, 0, 0, -0.2, 0, 0, 3.9, 1.1, 0, 0, 0, 0 ]; const tc_37 = [ -15.6, 0, -0.4, 0, 0, 0, 0, 0, 0, 0, 0, -1 ]; const tc_38 = [ 0, 0, 0, 0, -20, 0, -20, 20, 0, 0, 0, -2, 0, 0, 0, 0 ]; const tc_39 = [ 0, 2, 0, 0, 0, 0, -7.8, -0.2 ]; const tc_40 = [ 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7.8, -7.8, -0.4 ]; const tc_41 = [ -7.8, 0, -0.2, 0, 0, 0, -3.9, 0, -0.1, 0, 3.9, 1.1 ]; const tc_42 = [ 0, 2, 2, 0 ]; const tc_43 = [ 0, 0, 0, 4, 0, -2, 0, 2 ]; const tc_44 = [ 0, 0, -7.6, 1.8, 7.6, 0.2, -7.6, 1.8 ]; const tc_45 = [ 1, 1, 1, -1 ]; const tc_46 = [ 1, 0, 0, 1 ]; const tc_47 = [ 0, 0, -3.9, -0.1, 0, 1, 0, 0 ]; const tc_48 = [ 0, 0, -3.9, -0.1, 0, 2, 0, 0 ]; const tc_49 = [ 0, -3.45, 4, -3.9, 0, -0.1, 0, -3.45, 4, 3.9, 0, 0.1 ]; const tc_50 = [ 3.8, 0.1, -3.8, 0.9, -3.8, -0.1, -3.8, 0.9 ]; const tc_51 = [ 0, 2, -1.73205080757, 1 ]; const tc_52 = [ 0, 2, 0, 0, 0, 1, 3.9, 0.1 ]; const tc_53 = [ 0, 1, -1, 0 ]; const tc_54 = [ -1, 1, -2, 0 ]; const tc_55 = [ 0, 1, 1, 0 ]; const tc_56 = [ 0, 0.5, -3.9, -0.1, 0, -0.5, -3.9, -0.1 ]; const tc_57 = [ -5, 0, 2, 0, -3.9, -0.1, -5, 0, 3, 0, -3.9, -0.1 ]; const tc_58 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 7.8, 0.2 ]; const tc_59 = [ 0, 1, 0, 0, 0, 0, 7.8, 0.2 ]; const tc_60 = [ -1.5, 2.59807621135, -3, 0 ]; const tc_61 = [ 0, -0.5, -3.9, -0.1, 0, 0.5, -3.9, -0.1 ]; const ac_00 = [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ]; const ac_01 = [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 7.8, 0, 0, 3.5, -0.3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -0.5 ]; const ac_02 = [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3.9, 0, -3.5, 0, 0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 5, 0, 4, -4.5 ]; const ac_03 = [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2.5, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3, 0, 0, -1 ]; const ac_04 = [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 7.8, 0, 0, 3.5, 0, -0.3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 10, 0, 0, 5, -6, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -3.5, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -0.5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -7.8, 0, -3.5, -3.5, 0, 0.8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 10, 0, 0, 5, -7.5 ]; const ac_05 = [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 7.8, 0, 3.5, 0, 5, -2.8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 4, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 3.9, 0, 0, 0, 5, -2.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, 0, 0, -1.5, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3.9, 0, 3.5, 0, 0, -0.4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -5, 0, 4, 0, 0.5 ]; const ac_06 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -0.5, 0, 0, -0.866025403784, 0, 0, 0.5, 0, 0, 0.866025403784, 0, 0, -0.5, 0, 0, -0.866025403784, 0, 0, -0.5, 0, 0, 0.866025403784, 0, 0, 1, 0, 0, -0.866025403784, 0, 0, -0.5, 0, 0, 0 ]; const ac_07 = [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 7.8, 0, 3.5, -0.3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -0.5 ]; const ac_08 = [ 1, 0, 0, 0, 1, 0 ]; const ac_09 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]; const ac_10 = [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 7.8, 3.5, 0, -0.3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 5, -2 ]; const ac_11 = [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -3.5, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0.5 ]; const ac_12 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0.5, 0, 0.866025403784, 0, 0.5, 0, 0.866025403784, 0, -0.5, 0, -0.866025403784, 0, -0.5, 0, -0.866025403784, 0, 0.5, 0, 0.866025403784, 0, -0.5, 0, -0.866025403784 ]; const ac_13 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0.5, 0, 0, 0.866025403784, 0, 0, 1, 0, 0, -0.866025403784, 0, 0, 0.5, 0, 0, 0, 0, 0, -0.5, 0, 0, 0.866025403784, 0, 0, 1.5, 0, 0, -0.866025403784, 0, 0, -0.5, 0, 0, -0.866025403784, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1.73205080757, 0, 0, -0.5, 0, 0, -0.866025403784, 0, 0, 0, 0, 0, 0.866025403784, 0, 0, -0.5, 0, 0, -1.73205080757, 0, 0, 0.5, 0, 0, -0.866025403784, 0, 0, -0.5, 0, 0, 0.866025403784, 0, 0, 0.5, 0, 0, -0.866025403784 ]; const ac_14 = [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]; const ac_15 = [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 7.8, 0, 3.5, 0, -0.3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 10, 0, 4, -6.5 ]; const ac_16 = [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 7.8, 0, 3.5, 0, -0.3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 10, 0, 4, -6.5, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 15.6, 0, 7, 0, -0.6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 7.8, 0, 3.5, 0, -0.3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 10, 0, 4, -6.5 ]; const ac_17 = [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, -7.8, 0, -3.5, 0.3, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -0.5, 0, 0, 0, 1, 0, 0, 0, 0, -7.8, 0, -3.5, 0.3, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0.5 ]; const ac_18 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1 ]; const ac_19 = [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 10, 0, -3, 0, 0, 0, 1, 0, 0, 0, 0, -3.9, 0, -5, 2.4, 0, 0, 0, 0, 0, 0, 0, -1, 0, 5, 0, -1.5, 0, 0, 0, -1, 0, 0, 0, 0, 3.9, 0, 5, -2.4, 0, 0, 0, 0, 0, 0, 0, 1, 0, 5, 0, -1.5 ]; const ac_20 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, -3.9, 0, -0.1, 0, 0, 1, 0, 0, 0, 0, -5, 3, 0, 0, 0, 0, 0, 1, -3.9, 0, -1.1, 0, 0, -1, 0, 0, 0, 0, -5, 3 ]; const ac_21 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 9.9, 1.1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, -9.9, -1.1, 0, 1, 0, 0, 0, 0 ]; const ac_22 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -0.5, 0, 0.866025403784, 0, 1.5, 0, -0.866025403784, 0, -0.5, 0, 0.866025403784, 0, -0.5, 0, -0.866025403784, 0, 1.5, 0, 0.866025403784, 0, -0.5, 0, -0.866025403784, 0, 0.5, 0, 0.866025403784, 0, 0, 0, 0.866025403784, 0, -0.5, 0, 0, 0, -1, 0, 0, 0, 1.5, 0, 0, 0, 1, 0, 0.866025403784, 0, 0.5, 0, -0.866025403784, 0, 0, 0, -0.866025403784, 0, -0.5, 0, 1.73205080757 ]; const ac_23 = [ 1, 0, 0, 0, 1, 0, 0.5, -0.866025403784, 0, 0.866025403784, 0.5, 0, -0.5, -0.866025403784, 0, 0.866025403784, -0.5, 0, -1, 0, 0, 0, -1, 0, -0.5, 0.866025403784, 0, -0.866025403784, -0.5, 0, 0.5, 0.866025403784, 0, -0.866025403784, 0.5, 0 ]; const ac_24 = [ 1, 0, 0, 0, 1, 0, -0.5, -0.866025403784, 1.5, 0.866025403784, -0.5, -0.866025403784, -0.5, 0.866025403784, 1.5, -0.866025403784, -0.5, 0.866025403784, 0.5, 0.866025403784, 0, 0.866025403784, -0.5, 0, 0.5, -0.866025403784, 0, -0.866025403784, -0.5, 1.73205080757, -1, 0, 1.5, 0, 1, 0.866025403784 ]; const ac_25 = [ 1, 0, 0, 0, 1, 0, -0.5, 0.866025403784, 0.75, -0.866025403784, -0.5, 0.433012701892, -0.5, -0.866025403784, 0.75, 0.866025403784, -0.5, -0.433012701892 ]; const ac_26 = [ 1, 0, 0, 0, 1, 0, 0.5, -0.866025403784, 0.75, 0.866025403784, 0.5, 0.433012701892, -0.5, -0.866025403784, 0.75, 0.866025403784, -0.5, 1.29903810568 ]; const ac_27 = [ 1, 0, 0, 0, 1, 0, 0.5, 0.866025403784, 0.75, 0.866025403784, -0.5, 0.433012701892, -0.5, -0.866025403784, 0.75, 0.866025403784, -0.5, -0.433012701892 ]; const ac_28 = [ 1, 0, 0, 0, 1, 0, -0.5, -0.866025403784, 0.75, -0.866025403784, 0.5, 0.433012701892, -0.5, 0.866025403784, 0.75, 0.866025403784, 0.5, -0.433012701892 ]; const ac_29 = [ 1, 0, 0, 0, 1, 0, -0.5, 0.866025403784, -0.5, -0.866025403784, -0.5, 0.866025403784, -0.5, -0.866025403784, 0.5, 0.866025403784, -0.5, 0.866025403784, -0.5, 0.866025403784, -1.5, 0.866025403784, 0.5, 0.866025403784, -0.5, -0.866025403784, -0.5, -0.866025403784, 0.5, 0.866025403784, 1, 0, -1, 0, -1, 1.73205080757 ]; const ac_30 = [ 1, 0, 0, 0, 1, 0, -0.5, 0.866025403784, -0.5, -0.866025403784, -0.5, 0.866025403784, -0.5, -0.866025403784, 0.5, 0.866025403784, -0.5, 0.866025403784, 0.5, -0.866025403784, -0.5, 0.866025403784, 0.5, 0.866025403784, 0.5, 0.866025403784, -1.5, -0.866025403784, 0.5, 0.866025403784, -1, 0, -1, 0, -1, 1.73205080757 ]; const ac_31 = [ 1, 0, 0, 0, 1, 0, -0.5, -0.866025403784, 0.5, 0.866025403784, -0.5, 0.866025403784, -0.5, 0.866025403784, -0.5, -0.866025403784, -0.5, 0.866025403784, 0.5, 0.866025403784, 0.5, -0.866025403784, 0.5, 0.866025403784, 0.5, -0.866025403784, 1.5, 0.866025403784, 0.5, 0.866025403784, -1, 0, 1, 0, -1, 1.73205080757 ]; const ac_32 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 7.8, 0, 0.2, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]; const ac_33 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3.9, 0, 0.1, 0, 0, 0, 0, 0, -1, 0, 5, -1.5 ]; const ac_34 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 5, 0, -1, 0, 0, 0, 0, 0, 1, 0, -3.9, -0.1 ]; const ac_35 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -3.45, 4, 0, 0, 0, 0, 0, -1, 3.9, 0, 0.1 ]; const ac_36 = [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0 ]; const ac_37 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 7.8, 0, 0.2, 0, 0, 0, 0, 0, -1, 0, 10, -4 ]; const ac_38 = [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -5, 3.9, 3.6, 0, 0, 0, 0, 0, 0, 0, -1, 3.9, 0, 0, 0.1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -5, 3.9, 3.6, 0, 0, 0, 0, 0, 0, 0, 1, 3.9, 0, 0, 0.1 ]; const ac_39 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, -1, 0, 0, 0, 7.8, 0, 0.2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -7.8, 0, -0.2, 0, 0, 0, 0, 0, -1, 0, 0, 1 ]; const ac_40 = [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 10, 0, -5, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 10, -5, 0, 0, 0, -1, 0, 0, 0, 0, 0, 10, 0, -4, 0, 0, 0, 0, 0, 0, 0, 1, -10, 0, -10, 10, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -1, -10, 0, 0, 5 ]; const ac_41 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, -3.9, -0.1, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 3.9, 0.1 ]; const ac_42 = [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 5, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -1, 0, -3.9, 0, -0.1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0.5, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 3.9, 0.1, 0, 0, 0, -1, 0, 0, 0, 0, 5, 0, 0, -2.5, 0, 0, 0, 0, 0, 0, 0, 1, 0, -3.9, -3.9, -0.2 ]; const ac_43 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 3.9, 0, 0.1, 0, 0, 0, 0, 0, -1, 0, 3.9, 1.1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -3.9, 0, -0.1, 0, 0, 0, 0, 0, -1, 0, 3.9, 1.1 ]; const ac_44 = [ 1, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 2, -1, 0, 2, 0, -1, 2, 0, -1, 2, 1, 0, 0 ]; const ac_45 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 2, 0, 0, 0, -1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, -1, 0, 2, 0, -1, 0, 0, 0, 4 ]; const ac_46 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 3.8, 0.1, 0, 0, 0, -1, -3.8, 0.9 ]; const ac_47 = [ 1, 0, 0, 0, 1, 0, 0, -1, 2, 1, 0, 0 ]; const ac_48 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]; const ac_49 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -1, 3.9, 0.1 ]; const ac_50 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -3.45, 5, 0, 0, 0, 0, 0, -1, 3.9, 0, 0.1 ]; const ac_51 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 5, 0, -1, 0, 0, 0, 0, 0, -1, 0, -3.9, -0.1 ]; const ac_52 = [ 1, 0, 0, 0, 1, 0, 0, -1, 2, 1, 0, 0, -1, 0, 2, 0, -1, 2, 0, 1, 0, -1, 0, 2 ]; const ac_53 = [ 1, 0, 0, 0, 1, 0, 0.5, 0.866025403784, -0.866025403784, -0.866025403784, 0.5, 0.5, -0.5, 0.866025403784, -0.866025403784, -0.866025403784, -0.5, 1.5, -1, 0, 0, 0, -1, 2, -0.5, -0.866025403784, 0.866025403784, 0.866025403784, -0.5, 1.5, 0.5, -0.866025403784, 0.866025403784, 0.866025403784, 0.5, 0.5, -1, 0, 0, 0, 1, 0, -0.5, 0.866025403784, -0.866025403784, 0.866025403784, 0.5, 0.5, 0.5, 0.866025403784, -0.866025403784, 0.866025403784, -0.5, 1.5, 1, 0, 0, 0, -1, 2, 0.5, -0.866025403784, 0.866025403784, -0.866025403784, -0.5, 1.5, -0.5, -0.866025403784, 0.866025403784, -0.866025403784, 0.5, 0.5 ]; const ac_54 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 3.9, 0.1, 0, -1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, -1, 3.9, 0.1 ]; const ac_55 = [ 1, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, -1, 0, 1, 0, -1, 1, 0, -1, 1, 1, 0, 0 ]; const ac_56 = [ 1, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, -1, 0, 1, 0, -1, 1, 0, -1, 1, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, -1, 0, -1, 0, 1, 1, 0, -1, 0, -1, 1, 0, 1, -1, 1, 0, 0 ]; const ac_57 = [ 1, 0, 0, 0, 1, 0, 0, -1, 1, 1, 0, 0, -1, 0, 1, 0, -1, 1, 0, 1, 0, -1, 0, 1 ]; const ac_58 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0 ]; const ac_59 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0 ]; const ac_60 = [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 5, 0, -1, 0, 0, 0, 0, 0, -1, 0, 3.9, 0.1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 7.8, 0.2, 0, 0, -1, 0, 0, 0, 5, 0, -1, 0, 0, 0, 0, 0, 1, 0, 3.9, 0.1 ]; const ac_61 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 7.8, 0.2, 0, 1, 0, 0, 0, 0.5, 0, 0, 0, -1, 3.9, 0.1, 0, -1, 0, 0, 0, 1.5, 0, 0, 0, 1, 3.9, 0.1 ]; const ac_62 = [ 1, 0, 0, 0, 1, 0, 0.5, -0.866025403784, 0.5, 0.866025403784, 0.5, 0.866025403784, -0.5, -0.866025403784, 0, 0.866025403784, -0.5, 1.73205080757, -1, 0, -1, 0, -1, 1.73205080757, -0.5, 0.866025403784, -1.5, -0.866025403784, -0.5, 0.866025403784, 0.5, 0.866025403784, -1, -0.866025403784, 0.5, 0 ]; const ac_63 = [ 1, 0, 0, 0, 1, 0, -1, 0, 0.5, 0, -1, 0.866025403784 ]; const ac_64 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0 ]; const c_00 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 3 ]; const c_01 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 2, 3 ]; const c_02 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 1, 3 ]; const c_03 = [ 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 1, 3 ]; const c_04 = [ 0, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 2, 3 ]; const c_05 = [ 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 3 ]; const c_06 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 2, 3 ]; const c_07 = [ 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 3 ]; const c_08 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 3 ]; const c_09 = [ 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 2, 0, 3 ]; const c_10 = [ 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 1, 2, 3 ]; const c_11 = [ 0, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 3 ]; const c_12 = [ 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 2, 3 ]; const c_13 = [ 0, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 3 ]; const c_14 = [ 0, 1, 2, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 3 ]; const c_15 = [ 0, 2, 1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 3 ]; const c_16 = [ 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 2, 0, 3 ]; const c_17 = [ 1, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 1, 3 ]; const c_18 = [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 2 ]; const c_19 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 2 ]; const c_20 = [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 2 ]; const c_21 = [ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 2 ]; const c_22 = [ 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 2, 2 ]; const c_23 = [ 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 2 ]; const c_24 = [ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 2 ]; const c_25 = [ 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 2 ]; const c_26 = [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 2 ]; const c_27 = [ 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 2, 2 ]; const c_28 = [ 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 2 ]; return [ // IH00 is undefined null, // IH01 { num_params: 4, num_aspects: 1, num_vertices: 6, num_edge_shapes: 3, edge_shapes: es_00, edge_orientations: eo_00, edge_shape_ids: esi_00, default_params: dp_00, vertex_coeffs: tvc_00, translation_coeffs: tc_00, aspect_coeffs: ac_00, colouring: c_00 }, // IH02 { num_params: 4, num_aspects: 2, num_vertices: 6, num_edge_shapes: 3, edge_shapes: es_00, edge_orientations: eo_01, edge_shape_ids: esi_01, default_params: dp_01, vertex_coeffs: tvc_01, translation_coeffs: tc_01, aspect_coeffs: ac_01, colouring: c_01 }, // IH03 { num_params: 4, num_aspects: 2, num_vertices: 6, num_edge_shapes: 3, edge_shapes: es_00, edge_orientations: eo_02, edge_shape_ids: esi_02, default_params: dp_02, vertex_coeffs: tvc_02, translation_coeffs: tc_02, aspect_coeffs: ac_02, colouring: c_02 }, // IH04 { num_params: 6, num_aspects: 2, num_vertices: 6, num_edge_shapes: 5, edge_shapes: es_01, edge_orientations: eo_03, edge_shape_ids: esi_03, default_params: dp_03, vertex_coeffs: tvc_03, translation_coeffs: tc_03, aspect_coeffs: ac_03, colouring: c_02 }, // IH05 { num_params: 5, num_aspects: 4, num_vertices: 6, num_edge_shapes: 4, edge_shapes: es_02, edge_orientations: eo_04, edge_shape_ids: esi_04, default_params: dp_04, vertex_coeffs: tvc_04, translation_coeffs: tc_04, aspect_coeffs: ac_04, colouring: c_03 }, // IH06 { num_params: 5, num_aspects: 4, num_vertices: 6, num_edge_shapes: 4, edge_shapes: es_03, edge_orientations: eo_05, edge_shape_ids: esi_05, default_params: dp_05, vertex_coeffs: tvc_05, translation_coeffs: tc_05, aspect_coeffs: ac_05, colouring: c_04 }, // IH07 { num_params: 2, num_aspects: 3, num_vertices: 6, num_edge_shapes: 3, edge_shapes: es_00, edge_orientations: eo_06, edge_shape_ids: esi_06, default_params: dp_06, vertex_coeffs: tvc_06, translation_coeffs: tc_06, aspect_coeffs: ac_06, colouring: c_05 }, // IH08 { num_params: 4, num_aspects: 1, num_vertices: 6, num_edge_shapes: 3, edge_shapes: es_04, edge_orientations: eo_07, edge_shape_ids: esi_00, default_params: dp_00, vertex_coeffs: tvc_00, translation_coeffs: tc_00, aspect_coeffs: ac_00, colouring: c_00 }, // IH09 { num_params: 3, num_aspects: 2, num_vertices: 6, num_edge_shapes: 2, edge_shapes: es_05, edge_orientations: eo_08, edge_shape_ids: esi_07, default_params: dp_07, vertex_coeffs: tvc_07, translation_coeffs: tc_07, aspect_coeffs: ac_07, colouring: c_06 }, // IH10 { num_params: 0, num_aspects: 1, num_vertices: 6, num_edge_shapes: 1, edge_shapes: es_06, edge_orientations: eo_06, edge_shape_ids: esi_08, default_params: dp_08, vertex_coeffs: tvc_08, translation_coeffs: tc_08, aspect_coeffs: ac_08, colouring: c_00 }, // IH11 { num_params: 0, num_aspects: 1, num_vertices: 6, num_edge_shapes: 1, edge_shapes: es_07, edge_orientations: eo_07, edge_shape_ids: esi_08, default_params: dp_08, vertex_coeffs: tvc_08, translation_coeffs: tc_09, aspect_coeffs: ac_08, colouring: c_00 }, // IH12 { num_params: 2, num_aspects: 1, num_vertices: 6, num_edge_shapes: 2, edge_shapes: es_08, edge_orientations: eo_09, edge_shape_ids: esi_07, default_params: dp_09, vertex_coeffs: tvc_09, translation_coeffs: tc_10, aspect_coeffs: ac_09, colouring: c_00 }, // IH13 { num_params: 3, num_aspects: 2, num_vertices: 6, num_edge_shapes: 3, edge_shapes: es_09, edge_orientations: eo_10, edge_shape_ids: esi_09, default_params: dp_10, vertex_coeffs: tvc_10, translation_coeffs: tc_11, aspect_coeffs: ac_10, colouring: c_06 }, // IH14 { num_params: 2, num_aspects: 1, num_vertices: 6, num_edge_shapes: 2, edge_shapes: es_10, edge_orientations: eo_11, edge_shape_ids: esi_10, default_params: dp_09, vertex_coeffs: tvc_11, translation_coeffs: tc_12, aspect_coeffs: ac_09, colouring: c_00 }, // IH15 { num_params: 3, num_aspects: 2, num_vertices: 6, num_edge_shapes: 3, edge_shapes: es_11, edge_orientations: eo_12, edge_shape_ids: esi_11, default_params: dp_11, vertex_coeffs: tvc_12, translation_coeffs: tc_13, aspect_coeffs: ac_11, colouring: c_06 }, // IH16 { num_params: 1, num_aspects: 3, num_vertices: 6, num_edge_shapes: 2, edge_shapes: es_12, edge_orientations: eo_13, edge_shape_ids: esi_12, default_params: dp_12, vertex_coeffs: tvc_13, translation_coeffs: tc_14, aspect_coeffs: ac_12, colouring: c_05 }, // IH17 { num_params: 2, num_aspects: 1, num_vertices: 6, num_edge_shapes: 2, edge_shapes: es_13, edge_orientations: eo_14, edge_shape_ids: esi_07, default_params: dp_09, vertex_coeffs: tvc_09, translation_coeffs: tc_10, aspect_coeffs: ac_09, colouring: c_00 }, // IH18 { num_params: 0, num_aspects: 1, num_vertices: 6, num_edge_shapes: 1, edge_shapes: es_14, edge_orientations: eo_06, edge_shape_ids: esi_08, default_params: dp_08, vertex_coeffs: tvc_08, translation_coeffs: tc_09, aspect_coeffs: ac_08, colouring: c_00 }, // IH19 is undefined null, // IH20 { num_params: 0, num_aspects: 1, num_vertices: 6, num_edge_shapes: 1, edge_shapes: es_15, edge_orientations: eo_07, edge_shape_ids: esi_08, default_params: dp_08, vertex_coeffs: tvc_08, translation_coeffs: tc_09, aspect_coeffs: ac_08, colouring: c_00 }, // IH21 { num_params: 2, num_aspects: 6, num_vertices: 5, num_edge_shapes: 3, edge_shapes: es_16, edge_orientations: eo_15, edge_shape_ids: esi_13, default_params: dp_13, vertex_coeffs: tvc_14, translation_coeffs: tc_15, aspect_coeffs: ac_13, colouring: c_07 }, // IH22 { num_params: 3, num_aspects: 2, num_vertices: 5, num_edge_shapes: 3, edge_shapes: es_17, edge_orientations: eo_16, edge_shape_ids: esi_14, default_params: dp_14, vertex_coeffs: tvc_15, translation_coeffs: tc_16, aspect_coeffs: ac_14, colouring: c_06 }, // IH23 { num_params: 4, num_aspects: 2, num_vertices: 5, num_edge_shapes: 4, edge_shapes: es_18, edge_orientations: eo_17, edge_shape_ids: esi_15, default_params: dp_15, vertex_coeffs: tvc_16, translation_coeffs: tc_17, aspect_coeffs: ac_15, colouring: c_08 }, // IH24 { num_params: 4, num_aspects: 4, num_vertices: 5, num_edge_shapes: 4, edge_shapes: es_19, edge_orientations: eo_17, edge_shape_ids: esi_15, default_params: dp_15, vertex_coeffs: tvc_16, translation_coeffs: tc_18, aspect_coeffs: ac_16, colouring: c_09 }, // IH25 { num_params: 3, num_aspects: 4, num_vertices: 5, num_edge_shapes: 3, edge_shapes: es_20, edge_orientations: eo_16, edge_shape_ids: esi_14, default_params: dp_14, vertex_coeffs: tvc_15, translation_coeffs: tc_19, aspect_coeffs: ac_17, colouring: c_10 }, // IH26 { num_params: 2, num_aspects: 2, num_vertices: 5, num_edge_shapes: 3, edge_shapes: es_21, edge_orientations: eo_18, edge_shape_ids: esi_14, default_params: dp_16, vertex_coeffs: tvc_17, translation_coeffs: tc_20, aspect_coeffs: ac_18, colouring: c_01 }, // IH27 { num_params: 3, num_aspects: 4, num_vertices: 5, num_edge_shapes: 3, edge_shapes: es_16, edge_orientations: eo_19, edge_shape_ids: esi_16, default_params: dp_17, vertex_coeffs: tvc_18, translation_coeffs: tc_21, aspect_coeffs: ac_19, colouring: c_11 }, // IH28 { num_params: 2, num_aspects: 4, num_vertices: 5, num_edge_shapes: 3, edge_shapes: es_16, edge_orientations: eo_15, edge_shape_ids: esi_13, default_params: dp_18, vertex_coeffs: tvc_19, translation_coeffs: tc_22, aspect_coeffs: ac_20, colouring: c_12 }, // IH29 { num_params: 1, num_aspects: 4, num_vertices: 5, num_edge_shapes: 2, edge_shapes: es_12, edge_orientations: eo_20, edge_shape_ids: esi_17, default_params: dp_19, vertex_coeffs: tvc_20, translation_coeffs: tc_23, aspect_coeffs: ac_21, colouring: c_04 }, // IH30 { num_params: 1, num_aspects: 6, num_vertices: 4, num_edge_shapes: 3, edge_shapes: es_22, edge_orientations: eo_21, edge_shape_ids: esi_18, default_params: dp_20, vertex_coeffs: tvc_21, translation_coeffs: tc_24, aspect_coeffs: ac_22, colouring: c_13 }, // IH31 { num_params: 0, num_aspects: 6, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_23, edge_orientations: eo_22, edge_shape_ids: esi_19, default_params: dp_08, vertex_coeffs: tvc_22, translation_coeffs: tc_25, aspect_coeffs: ac_23, colouring: c_14 }, // IH32 { num_params: 0, num_aspects: 6, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_24, edge_orientations: eo_23, edge_shape_ids: esi_19, default_params: dp_08, vertex_coeffs: tvc_22, translation_coeffs: tc_26, aspect_coeffs: ac_24, colouring: c_15 }, // IH33 { num_params: 0, num_aspects: 3, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_23, edge_orientations: eo_22, edge_shape_ids: esi_19, default_params: dp_08, vertex_coeffs: tvc_23, translation_coeffs: tc_08, aspect_coeffs: ac_25, colouring: c_05 }, // IH34 { num_params: 0, num_aspects: 3, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_06, edge_orientations: eo_24, edge_shape_ids: esi_20, default_params: dp_08, vertex_coeffs: tvc_23, translation_coeffs: tc_09, aspect_coeffs: ac_26, colouring: c_05 }, // IH35 is undefined null, // IH36 { num_params: 0, num_aspects: 3, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_06, edge_orientations: eo_25, edge_shape_ids: esi_20, default_params: dp_08, vertex_coeffs: tvc_23, translation_coeffs: tc_08, aspect_coeffs: ac_27, colouring: c_05 }, // IH37 { num_params: 0, num_aspects: 3, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_15, edge_orientations: eo_26, edge_shape_ids: esi_20, default_params: dp_08, vertex_coeffs: tvc_23, translation_coeffs: tc_08, aspect_coeffs: ac_28, colouring: c_05 }, // IH38 { num_params: 0, num_aspects: 6, num_vertices: 3, num_edge_shapes: 2, edge_shapes: es_10, edge_orientations: eo_27, edge_shape_ids: esi_21, default_params: dp_08, vertex_coeffs: tvc_24, translation_coeffs: tc_27, aspect_coeffs: ac_29, colouring: c_15 }, // IH39 { num_params: 0, num_aspects: 6, num_vertices: 3, num_edge_shapes: 2, edge_shapes: es_25, edge_orientations: eo_27, edge_shape_ids: esi_21, default_params: dp_08, vertex_coeffs: tvc_24, translation_coeffs: tc_28, aspect_coeffs: ac_30, colouring: c_16 }, // IH40 { num_params: 0, num_aspects: 6, num_vertices: 3, num_edge_shapes: 2, edge_shapes: es_24, edge_orientations: eo_28, edge_shape_ids: esi_21, default_params: dp_08, vertex_coeffs: tvc_24, translation_coeffs: tc_29, aspect_coeffs: ac_31, colouring: c_17 }, // IH41 { num_params: 2, num_aspects: 1, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_23, edge_orientations: eo_22, edge_shape_ids: esi_22, default_params: dp_21, vertex_coeffs: tvc_25, translation_coeffs: tc_30, aspect_coeffs: ac_09, colouring: c_18 }, // IH42 { num_params: 2, num_aspects: 2, num_vertices: 4, num_edge_shapes: 3, edge_shapes: es_22, edge_orientations: eo_29, edge_shape_ids: esi_23, default_params: dp_21, vertex_coeffs: tvc_25, translation_coeffs: tc_31, aspect_coeffs: ac_32, colouring: c_19 }, // IH43 { num_params: 2, num_aspects: 2, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_23, edge_orientations: eo_30, edge_shape_ids: esi_22, default_params: dp_21, vertex_coeffs: tvc_25, translation_coeffs: tc_31, aspect_coeffs: ac_33, colouring: c_19 }, // IH44 { num_params: 2, num_aspects: 2, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_23, edge_orientations: eo_31, edge_shape_ids: esi_24, default_params: dp_22, vertex_coeffs: tvc_26, translation_coeffs: tc_32, aspect_coeffs: ac_34, colouring: c_20 }, // IH45 { num_params: 2, num_aspects: 2, num_vertices: 4, num_edge_shapes: 3, edge_shapes: es_22, edge_orientations: eo_32, edge_shape_ids: esi_23, default_params: dp_23, vertex_coeffs: tvc_27, translation_coeffs: tc_33, aspect_coeffs: ac_35, colouring: c_20 }, // IH46 { num_params: 4, num_aspects: 2, num_vertices: 4, num_edge_shapes: 4, edge_shapes: es_26, edge_orientations: eo_33, edge_shape_ids: esi_25, default_params: dp_24, vertex_coeffs: tvc_28, translation_coeffs: tc_34, aspect_coeffs: ac_36, colouring: c_20 }, // IH47 { num_params: 2, num_aspects: 2, num_vertices: 4, num_edge_shapes: 3, edge_shapes: es_27, edge_orientations: eo_29, edge_shape_ids: esi_23, default_params: dp_21, vertex_coeffs: tvc_25, translation_coeffs: tc_35, aspect_coeffs: ac_37, colouring: c_19 }, // IH48 is undefined null, // IH49 { num_params: 3, num_aspects: 4, num_vertices: 4, num_edge_shapes: 4, edge_shapes: es_28, edge_orientations: eo_33, edge_shape_ids: esi_25, default_params: dp_25, vertex_coeffs: tvc_29, translation_coeffs: tc_36, aspect_coeffs: ac_38, colouring: c_21 }, // IH50 { num_params: 2, num_aspects: 4, num_vertices: 4, num_edge_shapes: 3, edge_shapes: es_29, edge_orientations: eo_29, edge_shape_ids: esi_23, default_params: dp_21, vertex_coeffs: tvc_25, translation_coeffs: tc_37, aspect_coeffs: ac_39, colouring: c_22 }, // IH51 { num_params: 3, num_aspects: 4, num_vertices: 4, num_edge_shapes: 3, edge_shapes: es_27, edge_orientations: eo_32, edge_shape_ids: esi_23, default_params: dp_26, vertex_coeffs: tvc_30, translation_coeffs: tc_38, aspect_coeffs: ac_40, colouring: c_21 }, // IH52 { num_params: 1, num_aspects: 4, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_23, edge_orientations: eo_34, edge_shape_ids: esi_22, default_params: dp_20, vertex_coeffs: tvc_31, translation_coeffs: tc_39, aspect_coeffs: ac_41, colouring: c_23 }, // IH53 { num_params: 3, num_aspects: 4, num_vertices: 4, num_edge_shapes: 3, edge_shapes: es_27, edge_orientations: eo_35, edge_shape_ids: esi_26, default_params: dp_27, vertex_coeffs: tvc_32, translation_coeffs: tc_40, aspect_coeffs: ac_42, colouring: c_21 }, // IH54 { num_params: 2, num_aspects: 4, num_vertices: 4, num_edge_shapes: 4, edge_shapes: es_30, edge_orientations: eo_33, edge_shape_ids: esi_25, default_params: dp_28, vertex_coeffs: tvc_33, translation_coeffs: tc_41, aspect_coeffs: ac_43, colouring: c_22 }, // IH55 { num_params: 0, num_aspects: 4, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_23, edge_orientations: eo_24, edge_shape_ids: esi_24, default_params: dp_08, vertex_coeffs: tvc_34, translation_coeffs: tc_42, aspect_coeffs: ac_44, colouring: c_24 }, // IH56 { num_params: 1, num_aspects: 8, num_vertices: 4, num_edge_shapes: 3, edge_shapes: es_22, edge_orientations: eo_36, edge_shape_ids: esi_26, default_params: dp_29, vertex_coeffs: tvc_35, translation_coeffs: tc_43, aspect_coeffs: ac_45, colouring: c_25 }, // IH57 { num_params: 2, num_aspects: 1, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_31, edge_orientations: eo_33, edge_shape_ids: esi_22, default_params: dp_21, vertex_coeffs: tvc_25, translation_coeffs: tc_30, aspect_coeffs: ac_09, colouring: c_18 }, // IH58 { num_params: 2, num_aspects: 2, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_32, edge_orientations: eo_33, edge_shape_ids: esi_22, default_params: dp_21, vertex_coeffs: tvc_25, translation_coeffs: tc_31, aspect_coeffs: ac_32, colouring: c_19 }, // IH59 { num_params: 1, num_aspects: 2, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_06, edge_orientations: eo_31, edge_shape_ids: esi_20, default_params: dp_30, vertex_coeffs: tvc_36, translation_coeffs: tc_44, aspect_coeffs: ac_46, colouring: c_20 }, // IH60 is undefined null, // IH61 { num_params: 0, num_aspects: 2, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_06, edge_orientations: eo_24, edge_shape_ids: esi_20, default_params: dp_08, vertex_coeffs: tvc_34, translation_coeffs: tc_45, aspect_coeffs: ac_47, colouring: c_20 }, // IH62 { num_params: 0, num_aspects: 1, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_07, edge_orientations: eo_33, edge_shape_ids: esi_20, default_params: dp_08, vertex_coeffs: tvc_34, translation_coeffs: tc_46, aspect_coeffs: ac_08, colouring: c_18 }, // IH63 is undefined null, // IH64 { num_params: 1, num_aspects: 1, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_33, edge_orientations: eo_37, edge_shape_ids: esi_22, default_params: dp_20, vertex_coeffs: tvc_31, translation_coeffs: tc_47, aspect_coeffs: ac_48, colouring: c_18 }, // IH65 is undefined null, // IH66 { num_params: 1, num_aspects: 2, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_34, edge_orientations: eo_37, edge_shape_ids: esi_22, default_params: dp_20, vertex_coeffs: tvc_31, translation_coeffs: tc_48, aspect_coeffs: ac_49, colouring: c_19 }, // IH67 { num_params: 2, num_aspects: 2, num_vertices: 4, num_edge_shapes: 3, edge_shapes: es_21, edge_orientations: eo_38, edge_shape_ids: esi_23, default_params: dp_23, vertex_coeffs: tvc_27, translation_coeffs: tc_49, aspect_coeffs: ac_50, colouring: c_20 }, // IH68 { num_params: 1, num_aspects: 1, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_06, edge_orientations: eo_39, edge_shape_ids: esi_20, default_params: dp_30, vertex_coeffs: tvc_36, translation_coeffs: tc_50, aspect_coeffs: ac_48, colouring: c_18 }, // IH69 { num_params: 2, num_aspects: 2, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_31, edge_orientations: eo_26, edge_shape_ids: esi_24, default_params: dp_22, vertex_coeffs: tvc_26, translation_coeffs: tc_32, aspect_coeffs: ac_51, colouring: c_20 }, // IH70 is undefined null, // IH71 { num_params: 0, num_aspects: 4, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_06, edge_orientations: eo_40, edge_shape_ids: esi_20, default_params: dp_08, vertex_coeffs: tvc_34, translation_coeffs: tc_42, aspect_coeffs: ac_52, colouring: c_24 }, // IH72 { num_params: 1, num_aspects: 1, num_vertices: 4, num_edge_shapes: 2, edge_shapes: es_24, edge_orientations: eo_33, edge_shape_ids: esi_22, default_params: dp_20, vertex_coeffs: tvc_31, translation_coeffs: tc_47, aspect_coeffs: ac_48, colouring: c_18 }, // IH73 { num_params: 0, num_aspects: 2, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_14, edge_orientations: eo_24, edge_shape_ids: esi_20, default_params: dp_08, vertex_coeffs: tvc_34, translation_coeffs: tc_45, aspect_coeffs: ac_47, colouring: c_20 }, // IH74 { num_params: 1, num_aspects: 1, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_07, edge_orientations: eo_26, edge_shape_ids: esi_20, default_params: dp_30, vertex_coeffs: tvc_36, translation_coeffs: tc_50, aspect_coeffs: ac_48, colouring: c_18 }, // IH75 is undefined null, // IH76 { num_params: 0, num_aspects: 1, num_vertices: 4, num_edge_shapes: 1, edge_shapes: es_15, edge_orientations: eo_33, edge_shape_ids: esi_20, default_params: dp_08, vertex_coeffs: tvc_34, translation_coeffs: tc_46, aspect_coeffs: ac_08, colouring: c_18 }, // IH77 { num_params: 0, num_aspects: 12, num_vertices: 3, num_edge_shapes: 3, edge_shapes: es_35, edge_orientations: eo_41, edge_shape_ids: esi_27, default_params: dp_08, vertex_coeffs: tvc_37, translation_coeffs: tc_51, aspect_coeffs: ac_53, colouring: c_26 }, // IH78 { num_params: 1, num_aspects: 4, num_vertices: 3, num_edge_shapes: 3, edge_shapes: es_36, edge_orientations: eo_41, edge_shape_ids: esi_27, default_params: dp_20, vertex_coeffs: tvc_38, translation_coeffs: tc_52, aspect_coeffs: ac_54, colouring: c_22 }, // IH79 { num_params: 0, num_aspects: 4, num_vertices: 3, num_edge_shapes: 2, edge_shapes: es_25, edge_orientations: eo_27, edge_shape_ids: esi_21, default_params: dp_08, vertex_coeffs: tvc_39, translation_coeffs: tc_53, aspect_coeffs: ac_55, colouring: c_27 }, // IH80 is undefined null, // IH81 { num_params: 0, num_aspects: 8, num_vertices: 3, num_edge_shapes: 2, edge_shapes: es_10, edge_orientations: eo_27, edge_shape_ids: esi_21, default_params: dp_08, vertex_coeffs: tvc_39, translation_coeffs: tc_54, aspect_coeffs: ac_56, colouring: c_25 }, // IH82 { num_params: 0, num_aspects: 4, num_vertices: 3, num_edge_shapes: 2, edge_shapes: es_24, edge_orientations: eo_28, edge_shape_ids: esi_21, default_params: dp_08, vertex_coeffs: tvc_39, translation_coeffs: tc_55, aspect_coeffs: ac_57, colouring: c_27 }, // IH83 { num_params: 1, num_aspects: 2, num_vertices: 3, num_edge_shapes: 2, edge_shapes: es_10, edge_orientations: eo_42, edge_shape_ids: esi_28, default_params: dp_31, vertex_coeffs: tvc_40, translation_coeffs: tc_56, aspect_coeffs: ac_58, colouring: c_20 }, // IH84 { num_params: 2, num_aspects: 2, num_vertices: 3, num_edge_shapes: 3, edge_shapes: es_04, edge_orientations: eo_41, edge_shape_ids: esi_27, default_params: dp_32, vertex_coeffs: tvc_41, translation_coeffs: tc_57, aspect_coeffs: ac_59, colouring: c_20 }, // IH85 { num_params: 2, num_aspects: 4, num_vertices: 3, num_edge_shapes: 3, edge_shapes: es_37, edge_orientations: eo_41, edge_shape_ids: esi_27, default_params: dp_32, vertex_coeffs: tvc_41, translation_coeffs: tc_58, aspect_coeffs: ac_60, colouring: c_21 }, // IH86 { num_params: 1, num_aspects: 4, num_vertices: 3, num_edge_shapes: 2, edge_shapes: es_25, edge_orientations: eo_42, edge_shape_ids: esi_28, default_params: dp_31, vertex_coeffs: tvc_40, translation_coeffs: tc_59, aspect_coeffs: ac_61, colouring: c_21 }, // IH87 is undefined null, // IH88 { num_params: 0, num_aspects: 6, num_vertices: 3, num_edge_shapes: 2, edge_shapes: es_25, edge_orientations: eo_43, edge_shape_ids: esi_28, default_params: dp_08, vertex_coeffs: tvc_42, translation_coeffs: tc_60, aspect_coeffs: ac_62, colouring: c_28 }, // IH89 is undefined null, // IH90 { num_params: 0, num_aspects: 2, num_vertices: 3, num_edge_shapes: 1, edge_shapes: es_07, edge_orientations: eo_41, edge_shape_ids: esi_29, default_params: dp_08, vertex_coeffs: tvc_42, translation_coeffs: tc_09, aspect_coeffs: ac_63, colouring: c_20 }, // IH91 { num_params: 1, num_aspects: 2, num_vertices: 3, num_edge_shapes: 2, edge_shapes: es_32, edge_orientations: eo_44, edge_shape_ids: esi_28, default_params: dp_31, vertex_coeffs: tvc_40, translation_coeffs: tc_61, aspect_coeffs: ac_64, colouring: c_20 }, // IH92 is undefined null, // IH93 { num_params: 0, num_aspects: 2, num_vertices: 3, num_edge_shapes: 1, edge_shapes: es_15, edge_orientations: eo_41, edge_shape_ids: esi_29, default_params: dp_08, vertex_coeffs: tvc_42, translation_coeffs: tc_09, aspect_coeffs: ac_63, colouring: c_20 } ];})();35:T1a71,class IsohedralTiling { constructor( tp ) { this.reset( tp ); } reset( tp ) { this.tiling_type = tp; this.ttd = tiling_type_data[ tp ]; this.parameters = this.ttd.default_params.slice( 0 ); this.parameters.push( 1.0 ); this.recompute(); } recompute() { const ntv = this.numVertices(); const np = this.numParameters(); const na = this.numAspects(); // Recompute tiling vertex locations. this.verts = []; for( let idx = 0; idx < ntv; ++idx ) { this.verts.push( makePoint( this.ttd.vertex_coeffs, idx * (2 * (np + 1)), this.parameters ) ); } // Recompute edge transforms and reversals from orientation information. this.reversals = []; this.edges = [] for( let idx = 0; idx < ntv; ++idx ) { const fl = this.ttd.edge_orientations[2*idx]; const ro = this.ttd.edge_orientations[2*idx+1]; this.reversals.push( fl != ro ); this.edges.push( mul( matchSeg( this.verts[idx], this.verts[(idx+1)%ntv] ), M_orients[2*fl+ro] ) ); } // Recompute aspect xforms. this.aspects = [] for( let idx = 0; idx < na; ++idx ) { this.aspects.push( makeMatrix( this.ttd.aspect_coeffs, 6*(np+1)*idx, this.parameters ) ); } // Recompute translation vectors. this.t1 = makePoint( this.ttd.translation_coeffs, 0, this.parameters ); this.t2 = makePoint( this.ttd.translation_coeffs, 2*(np+1), this.parameters ); } getTilingType() { return this.tiling_type; } numParameters() { return this.ttd.num_params; } setParameters( arr ) { if( arr.length == (this.parameters.length-1) ) { this.parameters = arr.slice( 0 ); this.parameters.push( 1.0 ); this.recompute(); } } getParameters() { return this.parameters.slice( 0, -1 ); } numEdgeShapes() { return this.ttd.num_edge_shapes; } getEdgeShape( idx ) { return this.ttd.edge_shapes[ idx ]; } * shape() { for( let idx = 0; idx < this.numVertices(); ++idx ) { const an_id = this.ttd.edge_shape_ids[idx]; yield { T : this.edges[idx], id : an_id, shape : this.ttd.edge_shapes[ an_id ], rev : this.reversals[ idx ] }; } } * parts() { for( let idx = 0; idx < this.numVertices(); ++idx ) { const an_id = this.ttd.edge_shape_ids[idx]; const shp = this.ttd.edge_shapes[an_id]; if( (shp == EdgeShape.J) || (shp == EdgeShape.I) ) { yield { T : this.edges[idx], id : an_id, shape : shp, rev : this.reversals[ idx ], second : false }; } else { const indices = this.reversals[idx] ? [1,0] : [0,1]; const Ms = (shp == EdgeShape.U) ? TSPI_U : TSPI_S; yield { T : mul( this.edges[idx], Ms[indices[0]] ), id : an_id, shape : shp, rev : false, second : false }; yield { T : mul( this.edges[idx], Ms[indices[1]] ), id : an_id, shape : shp, rev : true, second : true }; } } } numVertices() { return this.ttd.num_vertices; } getVertex( idx ) { return { ...this.verts[ idx ] }; } vertices() { return this.verts.map( v => ({ ...v }) ); } numAspects() { return this.ttd.num_aspects; } getAspectTransform( idx ) { return [ ...this.aspects[ idx ] ]; } getT1() { return { ...this.t1 }; } getT2() { return { ...this.t2 }; } * fillRegionBounds( xmin, ymin, xmax, ymax ) { yield* this.fillRegionQuad( { x : xmin, y : ymin }, { x : xmax, y : ymin }, { x : xmax, y : ymax }, { x : xmin, y : ymax } ); } * fillRegionQuad( A, B, C, D ) { const t1 = this.getT1(); const t2 = this.getT2(); const ttd = this.ttd; const aspects = this.aspects; function bc( M, p ) { return { x : M[0]*p.x + M[1]*p.y, y : M[2]*p.x + M[3]*p.y }; }; function sampleAtHeight( P, Q, y ) { const t = (y-P.y)/(Q.y-P.y); return { x : (1.0-t)*P.x + t*Q.x, y : y }; } function* doFill( A, B, C, D, do_top ) { let x1 = A.x; const dx1 = (D.x-A.x)/(D.y-A.y); let x2 = B.x; const dx2 = (C.x-B.x)/(C.y-B.y); const ymin = A.y; let ymax = C.y; if( do_top ) { ymax = ymax + 1.0; } let y = Math.floor( ymin ); while( y < ymax ) { const yi = Math.trunc( y ); let x = Math.floor( x1 ); while( x < (x2 + 1e-7) ) { const xi = Math.trunc( x ); for( let asp = 0; asp < ttd.num_aspects; ++asp ) { let M = aspects[ asp ].slice( 0 ); M[2] += xi*t1.x + yi*t2.x; M[5] += xi*t1.y + yi*t2.y; yield { T : M, t1 : xi, t2 : yi, aspect : asp }; } x += 1.0; } x1 += dx1; x2 += dx2; y += 1.0; } } function* fillFixX( A, B, C, D, do_top ) { if( A.x > B.x ) { yield* doFill( B, A, D, C, do_top ); } else { yield* doFill( A, B, C, D, do_top ); } } function* fillFixY( A, B, C, D, do_top ) { if( A.y > C.y ) { yield* doFill( C, D, A, B, do_top ); } else { yield* doFill( A, B, C, D, do_top ); } } const det = 1.0 / (t1.x*t2.y-t2.x*t1.y); const Mbc = [ t2.y * det, -t2.x * det, -t1.y * det, t1.x * det ]; let pts = [ bc( Mbc, A ), bc( Mbc, B ), bc( Mbc, C ), bc( Mbc, D ) ]; if( det < 0.0 ) { let tmp = pts[1]; pts[1] = pts[3]; pts[3] = tmp; } if( Math.abs( pts[0].y - pts[1].y ) < 1e-7 ) { yield* fillFixY( pts[0], pts[1], pts[2], pts[3], true ); } else if( Math.abs( pts[1].y - pts[2].y ) < 1e-7 ) { yield* fillFixY( pts[1], pts[2], pts[3], pts[0], true ); } else { let lowest = 0; for( let idx = 1; idx < 4; ++idx ) { if( pts[idx].y < pts[lowest].y ) { lowest = idx; } } let bottom = pts[lowest]; let left = pts[(lowest+1)%4]; let top = pts[(lowest+2)%4]; let right = pts[(lowest+3)%4]; if( left.x > right.x ) { let tmp = left; left = right; right = tmp; } if( left.y < right.y ) { const r1 = sampleAtHeight( bottom, right, left.y ); const l2 = sampleAtHeight( left, top, right.y ); yield* fillFixX( bottom, bottom, r1, left, false ); yield* fillFixX( left, r1, right, l2, false ); yield* fillFixX( l2, right, top, top, true ); } else { const l1 = sampleAtHeight( bottom, left, right.y ); const r2 = sampleAtHeight( right, top, left.y ); yield* fillFixX( bottom, bottom, right, l1, false ); yield* fillFixX( l1, right, r2, left, false ); yield* fillFixX( left, r2, top, top, true ); } } } getColour( a, b, asp ) { const clrg = this.ttd.colouring; const nc = clrg[18]; let mt1 = a % nc; if( mt1 < 0 ) { mt1 += nc; } let mt2 = b % nc; if( mt2 < 0 ) { mt2 += nc; } let col = clrg[asp]; for( let idx = 0; idx < mt1; ++idx ) { col = clrg[12+col]; } for( let idx = 0; idx < mt2; ++idx ) { col = clrg[15+col]; } return col; } };36:[] 30:{"title":"Hello Tactile.JS! (a library for Escher-esque isohedral tessellations)","cells":[{"id":0,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":70,"value":"md`## tactile.js`","pinned":false,"hidden":false,"mode":"ojs"},{"id":126,"value":"md`### demo`","pinned":false,"hidden":false,"mode":"ojs"},{"id":209,"value":"viewof tilingID = slider({\n min: 0, \n max: numTypes-1, \n step: 1, \n value: 15, \n title: \"Pick any of the 81 Tiling Types\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":133,"value":"tiling = new IsohedralTiling( tilingTypes[ tilingID ] );","pinned":false,"hidden":false,"mode":"ojs"},{"id":259,"value":"tt_params = tiling.getParameters();","pinned":false,"hidden":false,"mode":"ojs"},{"id":375,"value":"viewof params_in = {\n if(!tt_params.length) return Object.assign(html``, {value: []});\n const form = verticalSliders({\n names: tt_params.map((_,i) => `p${i}`),\n labels: tt_params.map((_,i) => html`Param ${i+1}`),\n values: tt_params,\n mins: tt_params.map((_,i) => 0),\n maxs: tt_params.map((_,i) => 1),\n steps: tt_params.map((_,i) => .001),\n });\n form.querySelector('table').style.width = 'auto';\n return form;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":430,"value":"md`Try playing with the parameters above 👆, and observe how they change the rendered tiling below 👇. I really like the combination of **Tiling #15** (on horizontal slider above) and setting **Param 1** to 0.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":136,"value":"a_tiling = {\n let params = tiling.getParameters();\n if (tiling.numParameters()>0) params[ 0 ] = params_in.p0;\n if (tiling.numParameters()>1) params[ 1 ] = params_in.p1;\n if (tiling.numParameters()>2) params[ 2 ] = params_in.p2;\n if (tiling.numParameters()>3) params[ 3 ] = params_in.p3;\n if (tiling.numParameters()>4) params[ 4 ] = params_in.p4;\n if (tiling.numParameters()>5) params[ 5 ] = params_in.p5;\n tiling.setParameters( params );\n return(tiling)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":139,"value":"M_vec = {\n var M = [];\n for( let i of a_tiling.fillRegionBounds( 0.0, 0.0, 8.0, 5.0 ) ) {\n const T = i.T;\n const col = a_tiling.getColour( i.t1, i.t2, i.aspect );\n M.push(i) \n }\n return(M)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":436,"value":"md` Each edge is initially assumed to be a straight line. \\`tactile.js\\` gives us the ability to modify these lines such that they are no longer straight. Think of the canonical puzzle-piece shape where each side has a \"bite\" taken out, 🧩. We could make such edits to these edges here, but we'll save that complexity for another future notebook.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":354,"value":"edges = {\n // set edges\n const edges = [];\n\tfor( let idx = 0; idx < a_tiling.numEdgeShapes(); ++idx ) {\n\t\tvar ej = [{ x: 0, y: 0 }, { x: 1, y: 0 }];\n\t\tedges.push( ej );\n\t}\n return(edges)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":426,"value":"md` The variable \\`tile_shape\\` below is a polygon that defines the proto-tile that gets rotated and translated across the plane`","pinned":false,"hidden":false,"mode":"ojs"},{"id":358,"value":"tile_shape = {\n // set tile_shape\n const tile_shape = [];\n\tfor( let i of a_tiling.parts() ) {\n\t\tconst ej = edges[i.id];\n\t\tlet cur = i.rev ? (ej.length-2) : 1;\n\t\tconst inc = i.rev ? -1 : 1;\n\n\t\tfor( let idx = 0; idx < ej.length - 1; ++idx ) {\n\t\t\ttile_shape.push( mul( i.T, ej[cur] ) );\n\t\t\tcur += inc;\n\t\t}\n\t}\n return tile_shape\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":295,"value":"viewof zoomlevel = slider({\n min: 0.25, \n max: 3, \n step: 0.25, \n value: 1, \n title: \"Zoom Level\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":144,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":130,"value":"md`### Importing Tactile-JS\nI've pasted the lib directly into observable as it doesn't seem to be available via CDN.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":341,"value":"md`\n\\`\\`\\`\n/*\n * Tactile-JS\n * Copyright 2018 Craig S. Kaplan, csk@uwaterloo.ca\n *\n * Distributed under the terms of the 3-clause BSD license. See the\n * file \"LICENSE\" for more information.\n */\n\\`\\`\\`\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":73,"value":"EdgeShape = {return {\n\tJ : 10001,\n\tU : 10002,\n\tS : 10003,\n\tI : 10004,\n};}","pinned":false,"hidden":false,"mode":"ojs"},{"id":83,"value":"numTypes = 81;","pinned":false,"hidden":false,"mode":"ojs"},{"id":86,"value":"function mul( A, B ) \n{\n\tif( B.hasOwnProperty( 'x' ) ) {\n\t\t// Matrix * Point\n\t\treturn { \n\t\t\tx : A[0]*B.x + A[1]*B.y + A[2],\n\t\t\ty : A[3]*B.x + A[4]*B.y + A[5] };\n\t} else {\n\t\t// Matrix * Matrix\n\t\treturn [A[0]*B[0] + A[1]*B[3], \n\t\t\tA[0]*B[1] + A[1]*B[4],\n\t\t\tA[0]*B[2] + A[1]*B[5] + A[2],\n\n\t\t\tA[3]*B[0] + A[4]*B[3], \n\t\t\tA[3]*B[1] + A[4]*B[4],\n\t\t\tA[3]*B[2] + A[4]*B[5] + A[5]];\n\t}\n};","pinned":false,"hidden":false,"mode":"ojs"},{"id":89,"value":"function matchSeg( p, q )\n{\n\treturn [q.x-p.x, p.y-q.y, p.x, q.y-p.y, q.x-p.x, p.y];\n};","pinned":false,"hidden":false,"mode":"ojs"},{"id":92,"value":"tilingTypes = [\n\t1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 88, 90, 91, 93\n];\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":96,"value":"$34","pinned":false,"hidden":false,"mode":"ojs"},{"id":99,"value":"function makePoint( coeffs, offs, params )\n{\n\tlet ret = { x : 0.0, y : 0.0 }\n\n\tfor( let i = 0; i < params.length; ++i ) {\n\t\tret.x += coeffs[offs+i] * params[i];\n\t\tret.y += coeffs[offs+params.length+i] * params[i];\n\t}\n\n\treturn ret;\n};","pinned":false,"hidden":false,"mode":"ojs"},{"id":102,"value":"\nfunction makeMatrix( coeffs, offs, params )\n{\n\tlet ret = []\n\n\tfor( let row = 0; row < 2; ++row ) {\n\t\tfor( let col = 0; col < 3; ++col ) {\n\t\t\tlet val = 0.0;\n\t\t\tfor( let idx = 0; idx < params.length; ++idx ) {\n\t\t\t\tval += coeffs[offs+idx] * params[idx];\n\t\t\t}\n\t\t\tret.push( val );\n\t\t\toffs += params.length;\n\t\t}\n\t}\n\n\treturn ret;\n};","pinned":false,"hidden":false,"mode":"ojs"},{"id":105,"value":"M_orients = [\n\t[1.0, 0.0, 0.0, 0.0, 1.0, 0.0], // IDENTITY\n\t[-1.0, 0.0, 1.0, 0.0, -1.0, 0.0], // ROT\n\t[-1.0, 0.0, 1.0, 0.0, 1.0, 0.0], // FLIP\n\t[1.0, 0.0, 0.0, 0.0, -1.0, 0.0] // ROFL\n];","pinned":false,"hidden":false,"mode":"ojs"},{"id":108,"value":"TSPI_U = [\n\t[0.5, 0.0, 0.0, 0.0, 0.5, 0.0],\n\t[-0.5, 0.0, 1.0, 0.0, 0.5, 0.0]\n];","pinned":false,"hidden":false,"mode":"ojs"},{"id":111,"value":"TSPI_S = [\n\t[0.5, 0.0, 0.0, 0.0, 0.5, 0.0],\n\t[-0.5, 0.0, 1.0, 0.0, -0.5, 0.0]\n];","pinned":false,"hidden":false,"mode":"ojs"},{"id":114,"value":"$35","pinned":false,"hidden":false,"mode":"ojs"},{"id":203,"value":"md`## Other imports for sake of the demo`","pinned":false,"hidden":false,"mode":"ojs"},{"id":206,"value":"import {slider} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":370,"value":"import {verticalSliders} from '@tomlarkworthy/vertical-sliders'","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W36","stdlib":"1","titling":"auto"}