2b:null 2c:["$","title",null,{"children":"Two Dimensional Eigenmodes (with Mathematica) | Mark McClure | Observable"}] 31:T5c6,membrane = { //let width = width; let height = 0.6 * width; let container = d3 .create('div') .style('width', width.toString() + 'px') .style('height', height.toString() + 'px'); let scene = container .append('x3d') .attr('width', width.toString() + 'px') .attr('height', height.toString() + 'px') .append('scene'); scene .append('viewpoint') .attr('position', eigen_data.viewpoint.position) .attr('orientation', eigen_data.viewpoint.orientation) .attr('centerOfRotation', eigen_data.viewpoint.centerOfRotation); let transform = scene.append('transform'); let edc = eigen_data.coords; let edv = eigen_data.fValues[mode - 1]; let coord_string = d3 .range(edc.length) .map(i => `${edc[i][0]} ${edc[i][1]} ${edv[i].toFixed(5)}`) .toString(); let face_string = eigen_data.triangles; let faces = transform.append('shape'); faces .append('appearance') .append('material') .attr('diffuseColor', '0.19 0.79 0.84'); let indexedFaceSet = faces .append('indexedFaceSet') .attr('solid', false) .attr('creaseAngle', 3.141) .attr('coordIndex', face_string); indexedFaceSet.append('coordinate').attr('point', coord_string); let edges = transform.append('shape'); let indexedLineSet = edges .append('indexedLineSet') .attr('coordIndex', face_string); indexedLineSet.append('coordinate').attr('point', coord_string); yield container.node(); x3dom.reload(); }32:[] 2f:{"id":"6039661965abff13","slug":null,"title":"Two Dimensional Eigenmodes (with Mathematica)","thumbnail":"f1632100cf4013287e9acb041193abfc4ea5fc7674988b87a4cc4d0bc0459738","access_level":"unlisted","create_time":"$D2020-12-04T22:05:20.377Z","update_time":"$D2020-12-19T17:35:00.827Z","view_time":null,"first_public_time":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"d771c8ae812d5130","login":"mcmcclur","name":"Mark McClure","avatar_url":"https://avatars-next.observableusercontent.com/e615e819ce83d43faef607e48c53c5ff63943aa0ba9f5848499bd02fef7396f4","tier":"starter_2024"},"version":311,"publish_version":311,"role":null,"authored":false,"authors":[{"type":"individual","id":"c3301e515dd08a41","login":"mcmcclur","name":"Mark McClure","avatar_url":"https://avatars-next.observableusercontent.com/e615e819ce83d43faef607e48c53c5ff63943aa0ba9f5848499bd02fef7396f4","tier":null}],"members":[{"type":"individual","id":"c3301e515dd08a41","login":"mcmcclur","name":"Mark McClure","avatar_url":"https://avatars-next.observableusercontent.com/e615e819ce83d43faef607e48c53c5ff63943aa0ba9f5848499bd02fef7396f4","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Two Dimensional Eigenmodes (with Mathematica)","cells":[{"id":0,"value":"md`# Two Dimensional Eigenmodes (with Mathematica)\n\nEnter the description of a 2D region in the ${tex`xy`}-plane as a Boolean expression in ${tex`x`} and ${tex`y`} and then hit the \"Beat it!\" button. After a brief consultation with the Wolfram Cloud, an illustration of the first sixteen vibrational modes of the region should appear. Technically, these are eigenfunctions of the Laplacian on that region subject to a zero-valued Dirichlet condition.\n\nThe **Example** menu provides a few examples of reasonable input and you can choose between various modes to visualize.\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":205,"value":"viewof region = textarea({\n title: \"Description of your drum\",\n value: example,\n spellcheck: false,\n width: \"80%\",\n rows: 2,\n submit: \"Beat it!\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":234,"value":"viewof example = select({\n title: \"Example\",\n options: [\n { label: \"unit disk\", value: 'x^2 + y^2 < 1' },\n { label: \"unit square\", value: '0 1 or y > -1 or y < -3 )'\n },\n {\n label: \"square drum with round hold and appendage\",\n value: '-31 or -11 or -1 a.map(x => x.toFixed(5)));\n response.triangles = response.triangles[0]\n .map(a =>\n a\n .map(x => x - 1)\n .toString()\n .replace(/,/g, ' ')\n )\n .toString()\n .replace(/,/g, ' -1 ');\n return response;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":279,"value":"freqs = eigen_data.eValues.map(lambda =>\n Math.sqrt(lambda / eigen_data.eValues[0])\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":252,"value":"// Run the animation\nd3\n .select(membrane)\n .select('transform')\n .attr('scale', `1 1 ${Math.sin((now * freqs[mode - 1]) / 500)}`)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":259,"value":"md`## Imports`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"d3 = require('d3-selection@2', 'd3-array@2')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":2,"value":"x3dom = require('x3dom').catch(() => window['x3dom'])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":120,"value":"import { select, textarea } from \"@jashkenas/inputs\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":262,"value":"md`## Style`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":87,"value":"html``","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W32","stdlib":"1","titling":"auto"}} 30:"$2f:body"