2d:null 2e:["$","title",null,{"children":"Euler angle relative to shell. | lametskas | Observable"}] 33:T5cc,angleBetweenRubAndShellPub = { const realData = vl.markBar() .data(angleAgainstFacet) .encode( vl.x({ axis:{ grid: false, labelFontSize: 15, titleFontSize: 15, tickCount: 4, } }).fieldQ('angle') .bin({maxbins: 20, anchor: 10}) .title(['Angle between the RuBisCo orientation and', 'the average normal vector of neighboring facets', 'from convex hull (deg)']), vl.y({ axis:{ grid: false, labelFontSize: 15, titleFontSize: 15 } }).count().title('Counts'), vl.color() .fieldQ('concentration') .title([`RuBisCO concentration (µM)`]) .scale({scheme: 'viridis', domain: [300, 900]}) .sort('descending') .legend({ orient: 'bottom', titleLimit: 300, width: 400, titleFontSize: 15, labelFontSize: 15, tickCount: 5, padding: 10 }) ) const randomData = vl.markPoint({filled: true, size: 50, opacity: 0.5}) .data(randomAngles) .encode( vl.x({axis:{grid: false}}) .fieldQ('angle') .bin({maxbins: 20, anchor: 10}), vl.y({axis:{grid: false}}) .count(), vl.color({value: 'darkred'}) ) return vl.layer(realData, randomData) .width(350) .height(200) .config({view: {stroke: "transparent"}}) .render({renderer: 'svg'}) }34:T5b6,angleBetweenRubAndShell = { const realData = vl.markBar() .data(angleAgainstFacet) .encode( vl.x({ axis:{ grid: false, labelFontSize: 15, titleFontSize: 15, tickCount: 4, } }).fieldQ('angle') .bin({maxbins: 20, anchor: 10}) .title(['Angle between RuBisCo and the average normal vector of', 'neighboring facets from convex hull (deg)']), vl.y({ axis:{ grid: false, labelFontSize: 15, titleFontSize: 15 } }).count().title('Counts'), vl.color() .fieldQ('concentration') .title([`RuBisCO concentration (µM)`]) .scale({scheme: 'viridis', domain: [300, 900]}) .sort('descending') .legend({ orient: 'bottom', titleLimit: 300, width: 400, titleFontSize: 15, labelFontSize: 15, tickCount: 5, padding: 10 }) ) const randomData = vl.markPoint({filled: true, size: 50, opacity: 0.5}) .data(randomAngles) .encode( vl.x({axis:{grid: false}}) .fieldQ('angle') .bin({maxbins: 20, anchor: 10}), vl.y({axis:{grid: false}}) .count(), vl.color({value: 'darkred'}) ) return vl.layer(realData, randomData) .width(700) .height(500) .config({view: {stroke: "transparent"}}) .render({renderer: 'svg'}) }35:T52a,data = { const results = [] const rubsPerCarb = carbVolumes //.filter(c => [7, 39, 139].includes(c.carbIndex)) .map(c => allDataWithVectors.filter(d => d.reg === c.carbIndex)) for (const rubs of rubsPerCarb) { let index = 0 for (const rub of rubs) { const normals = normalData .filter(d => d.carbIndex === rub.reg) .filter(d => d.rubs.includes(index)) const carb = carbVolumes.find(d => d.carbIndex === rub.reg) if (carb.tagsInside.includes(rub.tag)) { index++ continue } let p = math.matrix([0,0,0]) const friends = new Set() for (const n of normals) { n.rubs.filter(r => r !== rub).forEach(r => friends.add(r)) p = math.add(p, n.normalNormed) } const pNorm = math.norm(p) p = math.divide(p, pNorm) const theta = [] for (const n of normals) { theta.push(180 * math.acos(math.dot(p, n.normalNormed)) / Math.PI) } if (theta.length > 0) { const mean = math.mean(theta) const variance = math.variance(theta, 'uncorrected') const tagFriends = Array.from(friends).map(d => rubs[d].tag) results.push({rub, friends, tagFriends, variance, normals, p, theta, mean, variance, ...carb}) } index++ } } return results }36:T478,normalData = { const result = [] for (const carb of carbVolumes) { const hull = carb.convexHull for (const facet of hull) { const numRidges = facet.ridges.length const dim = 3 const p = new Float32Array(dim) const length = 1 let c = 0 for (let r = 0; r < numRidges; r++) { const ridge = facet.ridges[r] const numVerts = ridge.verts.length for (let v = 0; v < numVerts; v++) { const vert = allDataWithVectors[ridge.verts[v]] p[0] += vert.x p[1] += vert.y p[2] += vert.z c++ } } for (let i = 0; i < dim; ++i) { p[i] /= c; } const start = math.matrix([p[0], p[1], p[2]]) for (let i = 0; i < dim; ++i) { p[i] += facet.plane[i] * length; } const end = math.matrix([p[0], p[1], p[2]]) const normal = math.subtract(end, start) const normalNormed = math.divide(normal, math.norm(normal)) result.push({ carbIndex: carb.carbIndex, normalNormed, rubs: facet.verts }) } } return result }37:T6e7,carbVolumes = { const results = [] for (const carbIndex of Array.from(carbIndexes)) { const data = allDataWithVectors.filter(rub => rub.reg === carbIndex) if (data.length > 0) { const numRub = data.length const convexHull = ty.quickHull(data.map(i => [i.x, i.y, i.z])) const allVertices = new Set() for (const facet of convexHull) { facet.verts.forEach(vert => allVertices.add(vert)) } const pointsInside = data.filter((i, j) => !allVertices.has(j)) const tagsInside = pointsInside.map(p => p.tag) const reference = [ pointsInside[0].x, pointsInside[0].y, pointsInside[0].z ] let vol = 0 const vertList = [] for (const facet of convexHull) { const verts = facet.verts .map(i => data[i]) .map(i => [i.x, i.y, i.z]) .map(vert => math.subtract(vert, reference)) .map(vert => { if (vert[0] < 0) { vert[0] -= rubiscoDiameter/2 } else { vert[0] += rubiscoDiameter/2 } if (vert[1] < 0) { vert[1] -= rubiscoDiameter/2 } else { vert[1] += rubiscoDiameter/2 } if (vert[2] < 0) { vert[2] -= rubiscoDiameter/2 } else { vert[2] += rubiscoDiameter/2 } return vert }) const v = math.dot(verts[0], math.cross(verts[1], verts[2])) vertList.push({verts, v: v/6}) vol += v } const volume = (vol / 6) * (Math.pow(pixelSize, 3)) const innerConcentration = 1000*(tagsInside.length/volume)/avogradoNumber const concentration = 1000*(numRub/volume)/avogradoNumber results.push({ carbIndex, convexHull, numRub, tagsInside, numRubInner: tagsInside.length, volume, verts: vertList, innerConcentration, concentration }) } } return results }38:T500,vl.markPoint({filled: true, size: 50, opacity: 0.5}) .data(randomAngles) .transform( vl.density('angle') .counts(true) .extent([0, 90]) .steps(18), //vl.bin({maxbins: 20, anchor: 10}).field('angle').as('binnedAngles'), //vl.aggregate({op: 'count', as: 'angCount'}).groupby(['binnedAngles', 'binnedAngles_end']), //vl.joinaggregate({op: 'sum', field: 'angCount', as: 'binnedCounts'}), //.field('angle').as('binned'), //vl.calculate(`datum.density*50000/${angleAgainstFacet.length}`).as('binNorm') ) .encode( vl.x({axis:{grid: false}}).fieldQ('value'), vl.y({axis:{grid: false}}).fieldQ('density').title('Count'), //vl.x2().fieldQ('binnedAngles_end'), vl.color({value: 'darkgreen'})//.fieldQ('mean').title([`Mean angle of facets against average (deg)`]).scale({scheme: 'plasma'}).sort('descending').legend({orient: 'bottom', titleLimit: 300, width: 400}), //vl.size().fieldQ('volMicro').title('Carboxysome Volume (µm³)').legend({orient: 'bottom', titleLimit: 300, width: 400}), //vl.tooltip(['rub.tag', 'variance', 'mean', 'angle'])//.fieldN('carbIndex') ) .width(300) .height(200) .config({view: {stroke: "transparent"}}) .render({renderer: 'svg'})39:[{"id":"150a31343c49803a365738ed56680bc27affaa68735425d40066705427f3d66897d0290ab3b8bf42511df53b6d7e2d5ff23e8957e13a2e12bf063ef11a67a73a","href":"https://static.observableusercontent.com/files/150a31343c49803a365738ed56680bc27affaa68735425d40066705427f3d66897d0290ab3b8bf42511df53b6d7e2d5ff23e8957e13a2e12bf063ef11a67a73a","name":"allDataWithVectors@1.json","type":"application/json","lastModified":1625097360663.418,"size":20500057},{"id":"3c91a5f837f5d965cd9a4ed42c7159cd576b1854b0eadf8a205fc6e8c2c6ac13130708e8cf12ee41d13fd343827d4e8c2f2cf49b1693c24f47b09f1b06244aa4","href":"https://static.observableusercontent.com/files/3c91a5f837f5d965cd9a4ed42c7159cd576b1854b0eadf8a205fc6e8c2c6ac13130708e8cf12ee41d13fd343827d4e8c2f2cf49b1693c24f47b09f1b06244aa4","name":"image.png","type":"image/png","lastModified":1625097360663.418,"size":2763810}] 31:{"id":"3a6de849ba31e6c9","slug":"euler-angle-relative-to-shell","title":"Euler angle relative to shell.","thumbnail":"9c0fca82392374fe6e7195993789960947dd38ebcaf9b9248feeb524f2eb0a30","access_level":"public","create_time":"$D2021-06-30T23:56:00.663Z","update_time":"$D2021-06-30T23:56:00.663Z","view_time":null,"first_public_time":"$D2021-12-22T23:15:49.055Z","has_unpublished_edits":null,"fork":true,"stars":0,"starred":false,"owner":{"type":"team","id":"23c25df75ad9e2b8","login":"lametskas","name":"","avatar_url":"https://avatars-next.observableusercontent.com/a20b09ebec8b2b068cfb2e793b5fc4f72ff178a8750f68663dff951311ccef71","tier":"starter_2024"},"version":653,"publish_version":653,"role":null,"authored":false,"authors":[{"type":"individual","id":"041c7ee26ed50f05","login":"lametskas","name":"","avatar_url":"https://avatars-next.observableusercontent.com/a20b09ebec8b2b068cfb2e793b5fc4f72ff178a8750f68663dff951311ccef71","tier":null}],"members":[{"type":"individual","id":"041c7ee26ed50f05","login":"lametskas","name":"","avatar_url":"https://avatars-next.observableusercontent.com/a20b09ebec8b2b068cfb2e793b5fc4f72ff178a8750f68663dff951311ccef71","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"f13eec1c3f58880a","slug":"cbpaper","title":"2021MetskasRubiscoInCarboxysome","owner":{"id":"23c25df75ad9e2b8","login":"lametskas","name":""}},"type":"notebook","body":{"title":"Euler angle relative to shell.","cells":[{"id":0,"value":"# Euler angle relative to shell.\n\nRandom vectors computed based on: https://projecteuclid.org/journals/annals-of-mathematical-statistics/volume-43/issue-2/Choosing-a-Point-from-the-Surface-of-a-Sphere/10.1214/aoms/1177692644.full\n\n> Updated with latest table 06/24/2021 from DatasetSummary","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":222,"value":"FileAttachment(\"image.png\").image()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":617,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":623,"value":"dataForEulerAnglesAgainstShell = angleAgainstFacet.map(d => {\n return {\n angle: d.angle,\n concentration: d.concentration\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":627,"value":"dataForEulerAnglesAgainstShellRandom = randomAngles.map(d => {\n return {\n angle: d.angle\n\n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":134,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":127,"value":"angleAgainstFacet = faceRubs.map(r => {\n const vec = math.matrix(r.rub.vec.data)\n const angle = 180 * math.acos(math.abs(math.dot(vec, r.p))) / Math.PI\n return {\n angle,\n ...r \n }\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"faceRubsTags = faceRubs.map(d => d.rub.tag).join(',')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":211,"value":"faceRubs.map(d => d.rub.tag).includes(1706)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":115,"value":"faceRubs = data//.filter(d => d.variance < 1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":52,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":4,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":23,"value":"rubiscoDiameter = 45.3","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":25,"value":"pixelSize = 0.2208 * Math.pow(10, -9)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":99,"value":"allDataWithVectors = FileAttachment(\"allDataWithVectors@1.json\").json()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":226,"value":"carbIndexes = new Set(allDataWithVectors.map(d => d.reg))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":424,"value":"computeRandomVectors = (N = 100) => {\n const results = []\n for (let i = 0; i < N; i++) {\n const vec = math.matrix([\n Math.random() - 0.5,\n Math.random() - 0.5,\n Math.random() - 0.5\n ])\n const normed = math.dotDivide(vec, math.norm(vec))\n results.push(normed)\n }\n return results\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":438,"value":"$38","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":487,"value":"vl.markTick()\n .data(randomAngles)\n .encode(\n vl.x({axis:{grid: false}}).fieldQ('angle'),\n )\n .width(900)\n .config({view: {stroke: \"transparent\"}})\n .render({renderer: 'svg'})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":427,"value":"calcDeltaAngle = (vec1, vec2) => {\n return 180 * math.acos(math.abs(math.dot(vec1, vec2)/(math.norm(vec1) * math.norm(vec2)))) / Math.PI\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":583,"value":"N = angleAgainstFacet.length","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":524,"value":"vectors = computeRandomVectorsMarsaglia72(N)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":231,"value":"randomAngles = {\n const results = []\n const samples = 1\n //const N = 3000 //Math.ceil(angleAgainstFacet.length)\n\n const vecWall = math.matrix([1,0,0])\n const normWall = math.dotDivide(vecWall, math.norm(vecWall))\n\n for (let j = 0; j < samples; j++) {\n for (let i = 0; i < N; i++) {\n const obj = {\n reg: 'random',\n angle: calcDeltaAngle(vectors[i], normWall),\n normWall,\n wallN: math.norm(normWall),\n vec: vectors[i],\n vecN: math.norm(vectors[i])\n }\n results.push(obj)\n }\n }\n return results\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":557,"value":"computeRandomVectorsMarsaglia72 = (N = 100) => {\n const results = []\n for (let i = 0; i < N; i++) {\n let init = 2\n let v1, v2\n while (init >= 1) {\n v1 = 2*(Math.random() - 0.5)\n v2 = 2*(Math.random() - 0.5)\n init = v1*v1 + v2*v2\n }\n const vec = math.matrix([\n 2*v1*Math.sqrt(1 - init),\n 2*v2*Math.sqrt(1 - init),\n 1 - 2*init\n ])\n const normed = math.dotDivide(vec, math.norm(vec))\n results.push(normed)\n }\n return results\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":603,"value":"avogradoNumber = 6.02214076 * 1E23","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":8,"value":"## Imports","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"ty = await import(\"https://unpkg.com/@derschmale/tympanum@1/build/tympanum.module.js\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":13,"value":"math = require(\"mathjs@9\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W39","stdlib":"1","titling":"auto"}} 32:"$31:body"