31:T2e6b,model = ({ // Turret platform frame: (angle) => ln.rotate(new ln.Vector(1, 0, 0), (controls.orbit + 60) * toRad) .translate(new ln.Vector(0,4,0)), shape: squaredrectangle(8,8), folds: [{ // Turret flap 1 frame: (controls) => ln.rotate(new ln.Vector(1, 0, 0), (controls.flaps) * toRad) .rotate(new ln.Vector(0, 0, 1), (90) * toRad) .translate(new ln.Vector(8,8,0)), shape: squaredrectangle(8,2) },{ // Turret flap 2 frame: (controls) => ln.rotate(new ln.Vector(1, 0, 0), (controls.flaps) * toRad) .rotate(new ln.Vector(0, 0, 1), (180) * toRad) .translate(new ln.Vector(8,0, 0)), shape: squaredrectangle(8,2) },{ // Turret flap 3 frame: (controls) => ln.rotate(new ln.Vector(1, 0, 0), (controls.flaps) * toRad) .rotate(new ln.Vector(0, 0, 1), (270) * toRad) .translate(new ln.Vector(0,0, 0)), shape: squaredrectangle(8,2) },{ // Turret flap 4 frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (360) * toRad) .rotate(new ln.Vector(1, 0, 0), (controls.turret) * toRad) .translate(new ln.Vector(0, 8, 0)), shape: squaredrectangle(8,3), folds: range(4).map((idx) => ({ frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), 0 * toRad) .rotate(new ln.Vector(1, 0, 0), controls.crenulations * toRad) .translate(new ln.Vector(idx * 2, 3, 0)), shape: squaredrectangle(1,1) })).concat(range(4).map((idx) => ({ frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), 0 * toRad) .rotate(new ln.Vector(0, 0, 1), 0 * toRad) .translate(new ln.Vector(idx * 2 + 1, 3, 0)), shape: squaredrectangle(1,1) })).concat([{ frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (360) * toRad) .rotate(new ln.Vector(1, 0, 0), (-2*controls.turret) * toRad) .translate(new ln.Vector(1, 4, 0)), shape: squaredrectangle(1,1), folds: [{ // Middle (most connected component) frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (360) * toRad) .rotate(new ln.Vector(1, 0, 0), (0) * toRad) .translate(new ln.Vector(-1, 1, 0)), shape: squaredrectangle(8,3), folds: [{ // Wrap around upper wall frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (0) * toRad) .rotate(new ln.Vector(0,-1, 0), (controls.curl) * toRad) .translate(new ln.Vector(8, 0, 0)), shape: squaredrectangle(8,3), folds: range(4).map((idx) => ({ // Crenulations frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), 0 * toRad) .rotate(new ln.Vector(1, 0, 0), (180 + controls.crenulations) * toRad) .translate(new ln.Vector(idx * 2, 0, 0)), shape: squaredrectangle(1,1) })).concat(range(4).map((idx) => ({ frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), 0 * toRad) .rotate(new ln.Vector(0, 0, -1), 0 * toRad) .translate(new ln.Vector(idx * 2 + 1, -1, 0)), shape: squaredrectangle(1,1) })).concat([{ // Wall 1 - Seat frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (0) * toRad) .rotate(new ln.Vector(1, 0, 0), (controls.seat) * toRad) .translate(new ln.Vector(0, 3, 0)), shape: squaredrectangle(8,1), folds: [{ // Wall 1 - Main frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (0) * toRad) .rotate(new ln.Vector(1, 0, 0), (-controls.seat) * toRad) .translate(new ln.Vector(1, 1, 0)), shape: squaredrectangle(6,9), folds: [{ // Wall 1 - flap around frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (270) * toRad) .rotate(new ln.Vector(0, 1, 0), (-controls.flaps) * toRad) .translate(new ln.Vector(0, 1, 0)), shape: squaredrectangle(4,2), }] }] },{ frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (360) * toRad) .rotate(new ln.Vector(0, 1, 0), (-controls.curl) * toRad) .translate(new ln.Vector(8, 0, 0)), shape: squaredrectangle(8,3), folds: range(4).map((idx) => ({ // Crenulations frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), 0 * toRad) .rotate(new ln.Vector(1, 0, 0), (180 + controls.crenulations) * toRad) .translate(new ln.Vector(idx * 2, 0, 0)), shape: squaredrectangle(1,1) })).concat(range(4).map((idx) => ({ frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), 0 * toRad) .rotate(new ln.Vector(0, 0, -1), 0 * toRad) .translate(new ln.Vector(idx * 2 + 1, -1, 0)), shape: squaredrectangle(1,1) })).concat([{ // Wall 2 - Seat frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (0) * toRad) .rotate(new ln.Vector(1, 0, 0), (controls.seat) * toRad) .translate(new ln.Vector(0, 3, 0)), shape: squaredrectangle(8,1), folds: [{ // Wall 2 - Main frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (0) * toRad) .rotate(new ln.Vector(1, 0, 0), (-controls.seat) * toRad) .translate(new ln.Vector(1, 1, 0)), shape: squaredrectangle(6,9), folds: [{ // Wall 2 - flap around frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (270) * toRad) .rotate(new ln.Vector(0, 1, 0), (-controls.flaps) * toRad) .translate(new ln.Vector(0, 1, 0)), shape: squaredrectangle(4,2), }] }] },{ frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (360) * toRad) .rotate(new ln.Vector(0, 1, 0), (-controls.curl) * toRad) .translate(new ln.Vector(8, 0, 0)), shape: squaredrectangle(8,3), folds: range(4).map((idx) => ({ // Crenulations frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), 0 * toRad) .rotate(new ln.Vector(1, 0, 0), (180 + controls.crenulations) * toRad) .translate(new ln.Vector(idx * 2, 0, 0)), shape: squaredrectangle(1,1) })).concat(range(4).map((idx) => ({ frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), 0 * toRad) .rotate(new ln.Vector(0, 0, -1), 0 * toRad) .translate(new ln.Vector(idx * 2 + 1, -1, 0)), shape: squaredrectangle(1,1) })).concat([{ // Wall 3 - Seat frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (0) * toRad) .rotate(new ln.Vector(1, 0, 0), (controls.seat) * toRad) .translate(new ln.Vector(0, 3, 0)), shape: squaredrectangle(8,1), folds: [{ // Wall 3 - Main frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (0) * toRad) .rotate(new ln.Vector(1, 0, 0), (-controls.seat) * toRad) .translate(new ln.Vector(1, 1, 0)), shape: squaredrectangle(6,9), folds: [{ // Wall 3 - flap around frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (270) * toRad) .rotate(new ln.Vector(0, 1, 0), (-controls.flaps) * toRad) .translate(new ln.Vector(0, 1, 0)), shape: squaredrectangle(4,2), }] }] },{ // Wall 3 - loop closing flap frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (0) * toRad) .rotate( new ln.Vector(0, 1, 0), (controls.flaps) * toRad) .translate(new ln.Vector(8, 1, 0)), shape: squaredrectangle(2,2), }])) }])) }])) },{ // Wall 0 - Seat frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (0) * toRad) .rotate(new ln.Vector(1, 0, 0), (controls.seat) * toRad) .translate(new ln.Vector(0, 3, 0)), shape: squaredrectangle(8,1), folds: [{ // Wall 0 - Main frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (0) * toRad) .rotate(new ln.Vector(1, 0, 0), (-controls.seat) * toRad) .translate(new ln.Vector(1, 1, 0)), shape: squaredrectangle(6,9), folds: [{ // Wall 0 - flap around frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (270) * toRad) .rotate(new ln.Vector(0, 1, 0), (-controls.flaps) * toRad) .translate(new ln.Vector(0, 1, 0)), shape: squaredrectangle(4,2), }, { // Wall 0 - flap to bottom frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (270) * toRad) .rotate(new ln.Vector(1, 0, 0), (controls.bPivot) * toRad) .translate(new ln.Vector(6, 9, 0)), shape: squaredrectangle(2,6), folds: [{ // bottom floor frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (270) * toRad) .rotate(new ln.Vector(0, 1, 0), (180-controls.bFloor) * toRad) .translate(new ln.Vector(2, 0, 0)), shape: squaredrectangle(6,6), folds: [{ // bottom floor flap 1 frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), (270) * toRad) .rotate(new ln.Vector(0, 1, 0), (controls.bFlaps) * toRad) .translate(new ln.Vector(0, 0, 0)), shape: squaredrectangle(6,2), },{ // bottom floor flap 2 frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), 0) .rotate(new ln.Vector(-1, 0, 0), -controls.bFlaps * toRad) .translate(new ln.Vector(0, 6, 0)), shape: squaredrectangle(6,2), },{ // bottom floor flap 3 frame: (controls) => ln.rotate(new ln.Vector(0, 0, 1), 0) .rotate(new ln.Vector(0, -1, 0), (controls.bFlaps) * toRad) .translate(new ln.Vector(6, 0, 0)), shape: squaredrectangle(2,6), }] }] }] }] }] }] }])) }] })32:T8ed,md`### Diary I had many endorphins rushes developing the development of this software. There is something neurologically satisfying about closing sensorimotor loops outside the body. This software is not just about folding on a computer. It is also to help me record Kirigami designs. In real life, I use white school glue and thick (100gsm) squared paper. Square paper greatly improves precision and is the only "specialized equipment" required for the hobby. Squared paper helps with many Kirigami jobs. - Squared paper helps with copying the design to and from paper. - When cutting outlines, you can flip the paper to cut from the other side on a 2nd pass, (the grid should be aligned on both sides). - Alignment of fold surfaces over long ranges "magnifies" the accuracy of a crease. - Joining precisely to other pieces of squared paper to fix mistakes. Here are some real-life pictures. Note the next design is different in every picture! The medium is forgiving of mistakes, it's very easy to extend the paper and add missing flaps. You do not need to get it right the first time. I can use the computer to record the "best" design so far. The castle gains strength by having floors to reinforce the plan layout. The nest is large enough to fit a figure. You can paint it with Crayola Supertips. ### Programming Kirigami Programming Kirigami is just another level to Kirigami. With Programming Kirigami the symmetries in the pattern can be folded with subroutines in a program. I was not brave enough to refactor the _model_ cell. Instead, I built up the kinematic structure up slowly and deliberately. Just like when I make the model in real life! ### Enabled with Observable I do not think that such a thing could be programmed without Observable. I needed the trial-and-error instant "in-the-moment" recomputation that the workflow on Observable enables. For example, to probe for polarity issues one joint at a time. You need to be able to "feel around in the dark" when assembling spatial programs, it's how you orientate to the local frame of reference. The fact that Observable allows me to recompile small parts and keep everything else fixed was a huge help. I am thankful to all those who contributed to this notebook directly and indirectly. ` 33:[{"id":"5297d25c9b2c8ea3c5cd3832f9c4701c46a7294382cb4f38ea4a11028ea69954a187c59975755b781bd3f42b6649368babfad984aa44918035b5af62a13e8c3c","href":"https://static.observableusercontent.com/files/5297d25c9b2c8ea3c5cd3832f9c4701c46a7294382cb4f38ea4a11028ea69954a187c59975755b781bd3f42b6649368babfad984aa44918035b5af62a13e8c3c","name":"IMG_20201213_122435.jpg","type":"image/jpeg","lastModified":1607981468155.732,"size":503334},{"id":"2706e34ef0232f897e800ffe345dc91da652a3f372f7d1c017a8dc0f978e38df7059e8773dcd96a930bfaf72f6ddb5b35e7b650d8dbee371e959d7f3664b94cd","href":"https://static.observableusercontent.com/files/2706e34ef0232f897e800ffe345dc91da652a3f372f7d1c017a8dc0f978e38df7059e8773dcd96a930bfaf72f6ddb5b35e7b650d8dbee371e959d7f3664b94cd","name":"IMG_20201213_133504 (1).jpg","type":"image/jpeg","lastModified":1608107096635.328,"size":1046055},{"id":"1334e500923dfe6ea370035254dd28dc31bd0fa2914d7fae221033018e407d5d93513e21823d587d81dc95db93194bef78a096310886ba505ee625dc2be068d9","href":"https://static.observableusercontent.com/files/1334e500923dfe6ea370035254dd28dc31bd0fa2914d7fae221033018e407d5d93513e21823d587d81dc95db93194bef78a096310886ba505ee625dc2be068d9","name":"kirigami.jpg","type":"image/jpeg","lastModified":1608074217002.079,"size":117104},{"id":"d511610fe5cbdd4007919f7647bc9a39c15dc53d577aa65d24ed52c9415cee8bc7f0b26169b4c4488255fac7d22b1d71736585b28e96f0180aa94edd7ab3187a","href":"https://static.observableusercontent.com/files/d511610fe5cbdd4007919f7647bc9a39c15dc53d577aa65d24ed52c9415cee8bc7f0b26169b4c4488255fac7d22b1d71736585b28e96f0180aa94edd7ab3187a","name":"IMG_20201216_093441.jpg","type":"image/jpeg","lastModified":1608107900744.701,"size":933008}] 2f:{"title":"Programming Kirigami: The Castle Turret","cells":[{"id":114,"value":"md`# Programming Kirigami: The Castle Turret\n\nKirigami is paper folding and cutting.\n\n![Kirigami Turret picture](${await FileAttachment(\"kirigami.jpg\").url()})\n\nEnjoy the art of Kirigami...\n\n`\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":296,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":881,"value":"controls","pinned":false,"hidden":false,"mode":"ojs"},{"id":808,"value":"viewof controls = {\n const labels = [\"orbit\", \"flaps\", \"turret\", \"curl\", \"seat\", \"bPivot\", \"bFloor\", \"bFlaps\", \"crenulations\"]\n return form(html`

\n \n \n ${labels.map(label => html``)}\n \n \n \n \n ${labels.map(label => html``)}\n \n

${label}

`)\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":519,"value":"view = {\n return new Promise((resolve) => {\n let eye = new ln.Vector(6,10,40);\n \n let center = new ln.Vector(eye.x, eye.y, 0);\n let up = new ln.Vector(0, 1, 0);\n const height = 500\n let paths = scene.render(eye, center, up, width, height, 35, 0.5, 100, 0.3)\n \n resolve(html`\n ${ln.toSVG(paths, width, height)}\n `)\n });\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":813,"value":"html``","pinned":false,"hidden":false,"mode":"ojs"},{"id":123,"value":"scene = {\n // first thing is to create a scene\n const scene = new ln.Scene()\n \n function loadModel(scene, frame, model) {\n const f = frame.mul(model.frame(controls));\n scene.add(new ln.TransformedShape(model.shape, f));\n (model.folds || []).forEach(fold => {\n loadModel(scene, f, fold);\n })\n }\n \n loadModel(scene, ln.identity(), model);\n\n return scene;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":217,"value":"squaredrectangle = (w, h) => {\n const thickness= 0.01;\n const min = new ln.Vector(0, 0, 0)\n const max = new ln.Vector(w, h, thickness)\n const cube = new ln.Cube(min, max)\n\n cube.insec\n \n // we can specify which paths to render and create new ones:\n cube.paths = function() {\n const paths = []\n const { x: x1, y: y1} = this.min\n const { x: x2, y: y2} = this.max\n for(let i = 0; i <= w; i++) {\n const x = x1 + (x2 - x1) * (i / w);\n paths.push([new ln.Vector(x, 0, thickness), new ln.Vector(x, h, thickness)])\n paths.push([new ln.Vector(x, 0, 0), new ln.Vector(x, h, 0)])\n }\n \n for(let j = 0; j <= h; j++) {\n const y = y1 + (y2 - y1) * (j / h);\n paths.push([new ln.Vector(0, y, thickness), new ln.Vector(w, y, thickness)])\n paths.push([new ln.Vector(0, y, 0), new ln.Vector(w, y, 0)])\n }\n return paths\n }\n return cube;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":647,"value":"range = (n) => [...Array(n).keys()];","pinned":false,"hidden":false,"mode":"ojs"},{"id":378,"value":"toRad = Math.PI / 180","pinned":false,"hidden":false,"mode":"ojs"},{"id":240,"value":"import {slider} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":809,"value":"import {form} from \"@mbostock/form-input\"","pinned":false,"hidden":false,"mode":"ojs"},{"id":147,"value":"ln = import('https://unpkg.com/@lnjs/core@0.5.0/es/index.js?module')","pinned":false,"hidden":false,"mode":"ojs"},{"id":922,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":855,"value":"md`\n\n### Gallery \n![](${await FileAttachment(\"IMG_20201216_093441.jpg\").url()})\n\n![](${await FileAttachment(\"IMG_20201213_133504 (1).jpg\").url()})\n\n![](${await FileAttachment(\"IMG_20201213_122435.jpg\").url()})\n`","pinned":true,"hidden":false,"mode":"ojs"},{"id":990,"value":"import { footer } from \"@tomlarkworthy/footer\"","pinned":true,"hidden":false,"mode":"ojs"},{"id":1008,"value":"footer","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W33","stdlib":"1","titling":"auto"}