2b:null 2c:["$","title",null,{"children":"Raymarching in Excel | Yaroslav Sergienko | Observable"}] 31:[] 2f:{"id":"106e0b68e52d0934","slug":"raymarching-in-excel","title":"Raymarching in Excel","thumbnail":"54d772ed9fd20d229f0639803d23b02c481f99fb2d298cc9579ebc76093b815f","access_level":"public","create_time":"$D2018-04-04T23:15:38.936Z","update_time":"$D2018-11-29T20:02:48.809Z","view_time":null,"first_public_time":"$D2018-04-08T15:41:15.180Z","fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"ae7dadfe8dcf0cbe","login":"pallada-92","name":"Yaroslav Sergienko","avatar_url":"https://avatars-next.observableusercontent.com/3da8dfae158d0eac994729272d88a21b700faaa2f34a98d6518064aaa722a9c9","tier":"starter_2024"},"version":1427,"publish_version":1427,"role":null,"authored":false,"authors":[{"type":"individual","id":"f19682cf1ab7bdae","login":"pallada-92","name":"Yaroslav Sergienko","avatar_url":"https://avatars-next.observableusercontent.com/3da8dfae158d0eac994729272d88a21b700faaa2f34a98d6518064aaa722a9c9","tier":null}],"members":[{"type":"individual","id":"f19682cf1ab7bdae","login":"pallada-92","name":"Yaroslav Sergienko","avatar_url":"https://avatars-next.observableusercontent.com/3da8dfae158d0eac994729272d88a21b700faaa2f34a98d6518064aaa722a9c9","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":2,"collection":null,"type":"notebook","body":{"title":"Raymarching in Excel","cells":[{"id":0,"value":"md`# Raymarching in Excel`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":957,"value":"{\n const ctx = DOM.context2d(500, 500);\n ctx.translate(250, 250);\n ctx.scale(250, 250);\n for (let u=-1.0; u<1.0; u+=1.0/50.0) {\n for (let v=-1.0; v<1.0; v+=1.0/50.0) {\n const rh = rayHist(u, v);\n \n const val = 1 - Math.pow((rh[i2 + 1] - rh[i2]) / (rh[i1 + 1] - rh[i1]), 1.0 / (i2 - i1));\n ctx.fillStyle = gray(val);\n ctx.fillRect(u, v, 1.0 / 50.0, 1.0/50.0);\n }\n }\n return ctx.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":26,"value":"function sphere(x, y, z) {\n return Math.sqrt(x * x + y * y + z * z) - 0.25 * 1.5;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":178,"value":"function torus(x, y, z) {\n const a = 0.3\n return Math.sqrt(x * x + y * y + z * z - 2 * a * Math.sqrt(x * x + y * y) + a * a) - 0.15;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":279,"value":"function cube(x, y, z) {\n const r = 0.2 * 1.5;\n return Math.max(Math.abs(x) - r, Math.abs(y) - r, Math.abs(z) - r);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1403,"value":"0.2 * 1.5","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1406,"value":"0.25 * 1.5","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":409,"value":"function cylinder(x, y, z) {\n return \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":176,"value":"function map(x, y, z) {\n //return Math.max(Math.abs(y) - 0.23, Math.min(sphere(x, y, z), torus((x + 0.4) * 2, y * 2, z), torus((x - 0.4) * 2, (y + 0.2) * 1.5, z)));\n //return Math.max(cube(x, y, z), -torus(x, y, z - 0.18));\n return Math.max(cube(x, y, z), -sphere(x, y, z));\n //return torus(x, y, z);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":24,"value":"viewof u = DOM.range(-1.0, 1.0, 2.0 / 50.0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":28,"value":"viewof v = DOM.range(-1.0, 1.0, 2.0 / 50.0)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":123,"value":"viewof dist = DOM.range(-1.0, 1.0, 0.01)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":126,"value":"[u, v, dist]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":132,"value":"{\n const ctx = DOM.context2d(200, 200);\n ctx.translate(100, 100);\n ctx.scale(100, 100);\n for (let uu=-1.0; uu<1.0; uu+=2.0/50.0) {\n for (let vv=-1.0; vv<1.0; vv+=2.0/50.0) {\n const [x, y, z] = ray(uu, vv, dist);\n const val = map(x, y, z);\n if (Math.abs(uu - u) < 1.0 / 50.0 && Math.abs(vv - v) < 1.0 / 50.0) {\n ctx.fillStyle = 'red';\n } else if (val <= 0.01) {\n ctx.fillStyle = 'blue';\n } else {\n ctx.fillStyle = gray(val / 2.0);\n }\n ctx.fillRect(uu, vv, 0.1, 0.1);\n }\n }\n return ctx.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":274,"value":"dv = {\n const dv = [0.3, 0.5, -1];\n const s = 1.0 / Math.sqrt(dv[0] * dv[0] + dv[1] * dv[1] + dv[2] * dv[2]); \n return [dv[0] * s, dv[1] * s, dv[2] * s]\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":30,"value":"function ray(u1, v1, d1) {\n return [u1 * 0.7 + d1 * dv[0], v1 * 0.7 + d1 * dv[1], d1 * dv[2]];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":41,"value":"function rayHist(u, v) {\n const res = [0];\n let dist = -1.0;\n for (let iter=0; iter<32; iter++) {\n const [x1, y1, z1] = ray(u, v, dist);\n const rad = map(x1, y1, z1);\n dist += rad;\n res.push(dist);\n }\n return res;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":45,"value":"{\n const ctx = DOM.context2d(500, 200);\n ctx.strokeStyle = 'gray';\n ctx.lineWidth = 3;\n ctx.beginPath();\n ctx.moveTo(0, 0);\n const rh = rayHist(u, v)\n rh.forEach((dist, i) => {\n if (dist < 10000) {\n ctx.lineTo((i + 1) * 50, (rh[i + 1] - dist) * 200);\n }\n });\n ctx.stroke();\n return ctx.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":20,"value":"{\n const ctx = DOM.context2d(500, 200);\n const s = 5;\n ctx.scale(s, s);\n let dist = 0;\n ctx.strokeStyle = 'gray';\n ctx.lineWidth = 1 / s;\n for (let iter=0; iter<32; iter++) {\n ctx.beginPath();\n const rad = ray(u, v, dist);\n ctx.arc(dist, 100 / s, rad, 0, 2 * Math.PI);\n ctx.stroke();\n dist += rad;\n }\n return ctx.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":412,"value":"viewof i1 = DOM.range(1, 11, 1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":414,"value":"viewof i2 = DOM.range(1, 23, 1)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":417,"value":"[i1, i2]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":137,"value":"function gray(val) {\n const int = Math.round(val * 256);\n return 'rgb(' + int + ',' + int + ',' + int + ')';\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":903,"value":"md`## Formulas`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":470,"value":"`Math.max(Math.abs(x) - r, Math.abs(y) - r, Math.abs(z) - r, Math.sqrt(x * x + y * y + z * z) - 0.25 * 1.5);`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":490,"value":"rowsE = 'R.$F$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":491,"value":"colsE = \"R.$N$1\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":494,"value":"fovE = \"R.$V$1\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":496,"value":"rhoE = \"R.$AB$1\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":498,"value":"alphaE = \"R.$AH$1\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":500,"value":"betaE = \"R.$AN$1\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":481,"value":"iE = 'i1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":512,"value":"`camera Y =${rhoE} * COS(RADIANS(${betaE})) * COS(RADIANS(${alphaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":543,"value":"cxE = 'X.$G$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":527,"value":"`camera X =${rhoE} * SIN(RADIANS(${betaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":548,"value":"cyE = 'Y.$G$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":530,"value":"`camera Z =${rhoE} * COS(RADIANS(${betaE})) * SIN(RADIANS(${alphaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":551,"value":"czE = 'Z.$G$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":562,"value":"function sq3(x, y, z, deg=2) {\n return `POWER(${x}, ${deg}) + POWER(${y},${deg}) + POWER(${z}, ${deg})`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":553,"value":"`checkCamDist =${sq3(cxE, cyE, czE, 2)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":581,"value":"`1 cell =TAN(RADIANS(${fovE}) / 2) / ((${rowsE} - 1) / 2)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":577,"value":"oneCellE = `X.$Q$1`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":600,"value":"`View alpha =RADIANS(${alphaE} + 180)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":598,"value":"viewAlphaE = 'X.$Z$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":608,"value":"`View beta =RADIANS(${betaE} + 180)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":613,"value":"viewBetaE = 'X.$AI$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":591,"value":"cellAlphaE = `${viewAlphaE} + ATAN((COLUMN() - (${colsE} + 1) / 2) * ${oneCellE})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":612,"value":"cellBetaE = `${viewBetaE} - ATAN((ROW() - 2 - (${rowsE} + 1) / 2) * ${oneCellE})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":616,"value":"`X =COS(${cellBetaE}) * COS(${cellAlphaE})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":619,"value":"`Y =SIN(${cellBetaE})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":621,"value":"`Z =COS(${cellBetaE}) * SIN(${cellAlphaE})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":729,"value":"`x0 =-COS(RADIANS(${betaE})) * COS(RADIANS(${alphaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":781,"value":"x0E = `X.$AR$1`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":731,"value":"`y0 =-SIN(RADIANS(${betaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":783,"value":"y0E = 'Y.$X$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":733,"value":"`z0 =-COS(RADIANS(${betaE})) * SIN(RADIANS(${alphaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":785,"value":"z0E = 'Z.$AG$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":717,"value":"`ux =-${oneCellE} * SIN(RADIANS(${alphaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":790,"value":"uxE = 'X.$Z$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":763,"value":"uyE = `***`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":765,"value":"`uz =${oneCellE} * COS(RADIANS(${alphaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":795,"value":"uzE = 'Z.$O$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":722,"value":"`vx =${oneCellE} * SIN(RADIANS(${betaE})) * COS(RADIANS(${alphaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":809,"value":"vxE = `X.$AI$1`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":768,"value":"`vy =- ${oneCellE} * COS(RADIANS(${betaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":811,"value":"vyE = 'Y.$O$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":770,"value":"`vz =${oneCellE} * SIN(RADIANS(${betaE})) * SIN(RADIANS(${alphaE}))`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":817,"value":"vzE = 'Z.$X$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":754,"value":"uE = `COLUMN() - 1 - (${colsE} + 1) / 2`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":757,"value":"vE = `ROW() - 3 - (${rowsE} + 1) / 2`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":822,"value":"`uxComp =${x0E} + ${uxE} * (${uE})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":837,"value":"uxCompE = `X.B$3`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":827,"value":"`vxComp =${vxE} * (${vE})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":839,"value":"vxCompE = 'X.$A4'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":844,"value":"`vyComp =${y0E} + ${vyE} * (${vE})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":849,"value":"vyCompE = 'Y.$A4'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":852,"value":"`uzComp =${z0E} + ${uzE} * (${uE})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":858,"value":"uzCompE = `Z.B$3`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":855,"value":"`vzComp =${vzE} * (${vE})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":860,"value":"vzCompE = 'Z.$A4'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":743,"value":"rawXE = `${uxCompE} + ${vxCompE}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":761,"value":"rawYE = vyCompE","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":773,"value":"rawZE = `${uzCompE} + ${vzCompE}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":737,"value":"`N =1 / SQRT(${sq3(rawXE, rawYE, rawZE)})`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":873,"value":"NE = `N.B4`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":735,"value":"`X =(${rawXE}) * ${NE}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":876,"value":"`Y =${rawYE} * ${NE}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":878,"value":"`Z =(${rawZE}) * ${NE}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":645,"value":"i0 = 'i0'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":644,"value":"distE = `${i0}.${cell}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":636,"value":"xE = (distE) => `${cxE} + X.${cell} * ${distE}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":653,"value":"yE = (distE) => `${cyE} + Y.${cell} * ${distE}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":657,"value":"zE = (distE) => `${czE} + Z.${cell} * ${distE}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":634,"value":"mapE = (xE, yE, zE) => `MAX(ABS(${xE}) - 1, ABS(${yE}) - 1, ABS(${zE}) - 1)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":689,"value":"mapEdist = (distE) => mapE(xE(distE), yE(distE), zE(distE))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":693,"value":"`dist0 =${mapE(cxE, cyE, czE)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":698,"value":"dist0E = '$G$1'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1234,"value":"cell = 'B4'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":696,"value":"`i1 =${dist0E} + ${mapEdist(dist0E)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":707,"value":"inE = (n) => `=i${n}.${cell} + ${mapEdist(`i${n}.${cell}`)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":709,"value":"inE(4)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":632,"value":"`i =${distE} + ${mapEdist(1)}`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":905,"value":"md`## Import`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":928,"value":"X = require('https://cdnjs.cloudflare.com/ajax/libs/xlsx/0.12.8/xlsx.full.min.js').then(() => window.XLSX)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":969,"value":"viewof file = DOM.input(\"file\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1007,"value":"buf = Files.buffer(file)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1013,"value":"X.read(new Uint8Array(buf), {type: 'array'})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1037,"value":"md`## Export`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1199,"value":"function a(r, c, sheet, fixRow, fixCol) {\n const letter = (fixCol ? '$' : '') + X.utils.encode_cell({r: 0, c}).slice(0, -1);\n const number = (fixRow ? '$' : '') + (r + 1);\n return (sheet ? sheet + '!' : '') + letter + number;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1263,"value":"function local(addr) {\n const t = addr.split('!');\n if (t.length === 1) {\n return addr;\n } else {\n return t[1];\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1103,"value":"xCellSize = 7","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1105,"value":"xRows = 50","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1109,"value":"xCols = 50","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1183,"value":"xHeaderHeight = 20","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1119,"value":"function cc(val) {\n if (typeof val === 'string' && val[0] === '=') {\n return {t: 'n', f: val.slice(1)};\n } else if (typeof val === 'number') {\n return {t: 'n', v: val};\n } else {\n return {t: 's', v: val};\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1164,"value":"function getSheetSize(sheet) {\n const {r, c} = X.utils.decode_cell(sheet['!ref'].split(':')[1]);\n return [r, c];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1150,"value":"function extendRef(sheet, cellR, cellC) {\n const [r, c] = getSheetSize(sheet);\n sheet['!ref'] = 'A1:' + a(Math.max(r, cellR), Math.max(c, cellC));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1111,"value":"function makeHeader(sheet, fields, sheetName) {\n const refs = {};\n let col = 0;\n for (const {id, text, textW, val, valW} of fields) {\n sheet[a(0, col)] = cc(text);\n sheet['!merges'].push({s: a(0, col), e: a(0, col + textW - 1)});\n col += textW;\n sheet[a(0, col)] = cc(val);\n refs[id] = a(0, col, sheetName, 1, 1);\n sheet['!merges'].push({s: a(0, col), e: a(0, col + valW - 1)});\n col += valW;\n extendRef(sheet, 0, col - 1);\n }\n return refs;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1191,"value":"function makeBodyMatrix(sheet, topR, topC, rows, cols, body, headerRows, headerCols) {\n if (headerRows) {\n for (let r=0; r {\n const p0 = a(r, c, `i${iMax - 0}`);\n const p1 = a(r, c, `i${iMax - 1}`);\n const p2 = a(r, c, `i${iMax - 2}`);\n return `=(${p1} - ${p0}) / (${p2} - ${p1})`;\n }); \n setCellsSizes(sheet, xCellSize);\n return {s: sheet, h: header};\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1278,"value":"function xCamVecXZ(r, c, coord) {\n return `${a(1, c, coord, 1, 0)} + ${a(r, 0, coord, 0, 1)}`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1283,"value":"function xCamVecY (r, c, coord) {\n return `${a(r, 0, coord, 1, 0)}`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1261,"value":"shN = {\n const sheet = {\n '!ref': 'A1:A1',\n '!merges': [],\n };\n const R = shR.h;\n const header = makeHeader(sheet, [\n {id: 'cell', text: '1 cell:', textW: 8, val: `=TAN(RADIANS(${R.fov} / 2)) / ((${R.rows} - 1) / 2)`, valW: 5},\n ], 'N');\n makeBodyMatrix(sheet, 1, 0, xRows, xCols, (r, c) => `= 1 / SQRT(POWER(${xCamVecXZ(r, c, 'X')}, 2) + POWER(${xCamVecY(r, c, 'Y')}, 2) + POWER(${xCamVecXZ(r, c, 'Z')}, 2))`);\n setCellsSizes(sheet, xCellSize);\n return {s: sheet, h: header};\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1303,"value":"shX = {\n const sheet = {\n '!ref': 'A1:A1',\n '!merges': [],\n };\n const [al, bt, c, r] = [shR.h.a, shR.h.b, shN.h.cell, shR.h.rho];\n const header = makeHeader(sheet, [\n {id: 'cx', text: 'Cam X:', textW: 8, val: `=${r} * COS(${bt}) * COS(${al})`, valW: 5},\n {id: 'ux', text: 'ux:', textW: 8, val: `=-${c} * SIN(${al})`, valW: 5},\n {id: 'vx', text: 'vx:', textW: 8, val: `=${c} * SIN(${bt}) * COS(${al})`, valW: 5},\n {id: 'x0', text: 'x0:', textW: 8, val: `=-COS(${bt}) * COS(${al})`, valW: 5},\n ], 'X');\n const [rows, cols] = [shR.h.rows, shR.h.cols];\n const [vx, ux, x0] = [local(header.vx), local(header.ux), local(header.x0)];\n makeBodyMatrix(\n sheet, 1, 0, xRows, xCols, \n (r, c) => `= (${xCamVecXZ(r, c)}) * ${a(r, c, 'N')}`, `=${vx} * (ROW() - 2 - (${rows} + 1) / 2)`, `=${x0} + ${ux} * (COLUMN() - 1 - (${cols} + 1) / 2)`);\n setCellsSizes(sheet, xCellSize);\n return {s: sheet, h: header};\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1343,"value":"shY = {\n const sheet = {\n '!ref': 'A1:A1',\n '!merges': [],\n };\n const [al, bt, c, r] = [shR.h.a, shR.h.b, shN.h.cell, shR.h.rho];\n const header = makeHeader(sheet, [\n {id: 'cy', text: 'Cam Y:', textW: 8, val: `=${r} * SIN(${bt})`, valW: 5},\n {id: 'vy', text: 'vy:', textW: 8, val: `=-${c} * COS(${bt})`, valW: 5},\n {id: 'y0', text: 'y0:', textW: 8, val: `=-SIN(${bt})`, valW: 5},\n ], 'Y');\n const rows = shR.h.rows;\n const [vy, y0] = [local(header.vy), local(header.y0)];\n makeBodyMatrix(\n sheet, 1, 0, xRows, xCols, \n (r, c) => `= ${xCamVecY(r, c)} * ${a(r, c, 'N')}`, `=${y0} + ${vy} * (ROW() - 2 - (${rows} + 1) / 2)`);\n setCellsSizes(sheet, xCellSize);\n return {s: sheet, h: header};\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1345,"value":"shZ = {\n const sheet = {\n '!ref': 'A1:A1',\n '!merges': [],\n };\n const [al, bt, c, r] = [shR.h.a, shR.h.b, shN.h.cell, shR.h.rho];\n const header = makeHeader(sheet, [\n {id: 'cz', text: 'Cam Z:', textW: 8, val: `=${r} * COS(${bt}) * SIN(${al})`, valW: 5},\n {id: 'uz', text: 'uz:', textW: 8, val: `=${c} * COS(${al})`, valW: 5},\n {id: 'vz', text: 'vz:', textW: 8, val: `=${c} * SIN(${bt}) * SIN(${al})`, valW: 5},\n {id: 'z0', text: 'z0:', textW: 8, val: `=-COS(${bt}) * SIN(${al})`, valW: 5},\n ], 'Z');\n const [rows, cols] = [shR.h.rows, shR.h.cols];\n const [vz, uz, z0] = [local(header.vz), local(header.uz), local(header.z0)];\n makeBodyMatrix(\n sheet, 1, 0, xRows, xCols, \n (r, c) => `= (${xCamVecXZ(r, c)}) * ${a(r, c, 'N')}`, `=${vz} * (ROW() - 2 - (${rows} + 1) / 2)`, `=${z0} + ${uz} * (COLUMN() - 1 - (${cols} + 1) / 2)`);\n setCellsSizes(sheet, xCellSize);\n return {s: sheet, h: header};\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1389,"value":"function shI(i, formula) {\n const sheet = {\n '!ref': 'A1:A1',\n '!merges': [],\n };\n const [cx, cy, cz] = [shX.h.cx, shY.h.cy, shZ.h.cz];\n const dist0 = i == 1 ? makeHeader(sheet, [\n {id: 'dist0', text: 'dist0:', textW: 8, val: `=${formula(cx, cy, cz)}`, valW: 5},\n ]).dist0 : null;\n makeBodyMatrix(\n sheet, 1, 0, xRows, xCols, \n (r, c) => {\n const pd = i == 1 ? dist0 : a(r, c, `i${i - 1}`);\n return `=${pd} + ${formula(\n `${cx} + ${a(r, c, 'X')} * ${pd}`,\n `${cy} + ${a(r, c, 'Y')} * ${pd}`,\n `${cz} + ${a(r, c, 'Z')} * ${pd}`,\n )}`;\n }\n );\n setCellsSizes(sheet, xCellSize);\n return {s: sheet};\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1329,"value":"book = {\n const res = X.utils.book_new();\n const formula = (x, y, z) => `MAX(ABS(${x}) - 0.3, ABS(${y}) - 0.3, ABS(${z}) - 0.3, -(SQRT(POWER(${x}, 2) + POWER(${y}, 2) + POWER(${z}, 2)) - 0.375))`;\n X.utils.book_append_sheet(res, shR.s, 'R');\n X.utils.book_append_sheet(res, shN.s, 'N');\n X.utils.book_append_sheet(res, shX.s, 'X');\n X.utils.book_append_sheet(res, shY.s, 'Y');\n X.utils.book_append_sheet(res, shZ.s, 'Z');\n for (let i=1; i<=iMax; i++) {\n X.utils.book_append_sheet(res, shI(i, formula).s, `i${i}`);\n }\n return res;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1048,"value":"//X.writeFile(book, 'test.xlsx')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"