31:T8ac,function emulator({rows, cols, fov, dist, alpha, beta, fun, iterCount}) { const cos = x => Math.cos(x * Math.PI / 180), sin = x => Math.sin(x * Math.PI / 180), tan = x => Math.tan(x * Math.PI / 180); const pixelSize = tan(fov / 2) / ((rows - 1) / 2), camX = dist * cos(alpha) * cos(beta), camY = dist * sin(beta), camZ = dist * sin(alpha) * cos(beta), ux = -pixelSize * sin(alpha), uz = +pixelSize * cos(alpha), vx = +pixelSize * cos(alpha) * sin(beta), vy = -pixelSize * cos(beta), vz = +pixelSize * sin(alpha) * sin(beta), x0 = -cos(alpha) * cos(beta), y0 = -sin(beta), z0 = -sin(alpha) * cos(beta), dist0 = fun(camX, camY, camZ); const Xrows = [], Yrows = [], Zrows = [], Xcols = [], Zcols = []; for (let row=0; row `1 - IF(i${iterCount - 1}!${addr} - i${iterCount - 2}!${addr} < 0.00000000000001, 0.09, MAX(0, MIN(1, (i${iterCount}!${addr} - i${iterCount - 1}!${addr}) / (i${iterCount - 1}!${addr} - i${iterCount - 2}!${addr}))))`, }), 'R'); XLSX.utils.book_append_sheet(book, makeSheet({ cols, rows, cellSize, I1: ['pixelSize:', 'TAN(RADIANS(R!AI1 / 2)) / (R!I1 / 2)'], formula: (addr, col, row) => `1 / SQRT(POWER(X!${row} + X!${col}, 2) + POWER(Y!${row}, 2) + POWER(Z!${row} + Z!${col}, 2))` }), 'N'); XLSX.utils.book_append_sheet(book, makeSheet({ cols, rows, cellSize, I1: ['camX:', ' R!AV1 * COS(RADIANS(R!BV1)) * COS(RADIANS(R!BI1))'], V1: ['ux:', '-N!I1 * SIN(RADIANS(R!BI1))'], AI1: ['vx:', ' N!I1 * SIN(RADIANS(R!BV1)) * COS(RADIANS(R!BI1))'], AV1: ['x0:', '-COS(RADIANS(R!BV1)) * COS(RADIANS(R!BI1))'], colsFormula: 'AV1 + V1 * (COLUMN() - 1 - (R!V1 + 1) / 2)', rowsFormula: 'AI1 * (ROW() - 2 - (R!I1 + 1) / 2)', formula: (addr, col, row) => `(${col} + ${row}) * N!${addr}`, }), 'X'); XLSX.utils.book_append_sheet(book, makeSheet({ cols, rows, cellSize, I1: ['camY:', ' R!AV1 * SIN(RADIANS(R!BV1))'], V1: ['vy:', '-N!I1 * COS(RADIANS(R!BV1))'], AI1: ['y0:', '-SIN(RADIANS(R!BV1))'], rowsFormula: 'AI1 + V1 * (ROW() - 2 - (R!I1 + 1) / 2)', formula: (addr, col, row) => `${row} * N!${addr}`, }), 'Y'); XLSX.utils.book_append_sheet(book, makeSheet({ cols, rows, cellSize, I1: ['camZ:', ' R!AV1 * COS(RADIANS(R!BV1)) * SIN(RADIANS(R!BI1))'], V1: ['uz:', ' N!I1 * COS(RADIANS(R!BI1))'], AI1: ['vz:', ' N!I1 * SIN(RADIANS(R!BV1)) * SIN(RADIANS(R!BI1))'], AV1: ['z0:', '-COS(RADIANS(R!BV1)) * SIN(RADIANS(R!BI1))'], colsFormula: 'AV1 + V1 * (COLUMN() - 1 - (R!V1 + 1) / 2)', rowsFormula: 'AI1 * (ROW() - 2 - (R!I1 + 1) / 2)', formula: (addr, col, row) => `(${row} + ${col}) * N!${addr}`, }), 'Z'); const applyFormula = (x, y, z) => formula.replace(/x/g, x).replace(/y/g, y).replace(/z/g, z); for (let i=1; i<=iterCount; i++) { const prevDist = addr => i == 1 ? 'I1' : `i${i - 1}!${addr}` XLSX.utils.book_append_sheet(book, makeSheet({ cols, rows, cellSize, I1: i == 1 ? ['dist0:', applyFormula('X!I1', 'Y!I1', 'Z!I1')] : undefined, formula: addr => `${prevDist(addr)} + ${applyFormula( `X!I1 + X!${addr} * ${prevDist(addr)}`, `Y!I1 + Y!${addr} * ${prevDist(addr)}`, `Z!I1 + Z!${addr} * ${prevDist(addr)}`, )}`, }), 'i' + i); } if (fname) { XLSX.writeFile(book, fname); } } 34:[] 2f:{"title":"Excel 3d engine emulator","cells":[{"id":0,"value":"md`# Excel 3d engine emulator`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1253,"value":"viewof formula = select({\n title: \"Shape formula\",\n description: \"distance function\",\n options: [\"cubeTorus\", \"teapot\", \"customFun\"],\n value: \"cubeTorus\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1207,"value":"viewof alpha = slider({\n min: -180, \n max: 180, \n step: 1, \n value: 47, \n title: \"alpha\",\n description: \"horizontal rotation\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1209,"value":"viewof beta = slider({\n min: -90, \n max: 90, \n step: 1, \n value: 20, \n title: \"beta\",\n description: \"vertical rotation\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1211,"value":"viewof dist = slider({\n min: -1.5, \n max: 1.5, \n step: 0.1, \n value: 0.3, \n title: \"dist\",\n description: \"distance to camera\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":83,"value":"{\n const scale = Math.floor(width / params.cols / 2) / window.devicePixelRatio;\n const ctx = DOM.context2d(params.cols * scale, params.rows * scale);\n ctx.scale(scale, scale);\n params.pixels.forEach((rowItem, row) => rowItem.forEach((colItem, col) => {\n const c = colItem.R * 255;\n ctx.fillStyle = `rgb(${c}, ${c}, ${c})`;\n ctx.fillRect(col, row, 1, 1);\n }));\n return ctx.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1304,"value":"md`

Write your own distance function below (set Shape formula = customFun):`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1234,"value":"// customFun = (x, y, z) => Math.max(Math.abs(x), Math.abs(y), Math.abs(z)) - 0.2\ncustomFun = (x, y, z) => Math.max(Math.abs(x) - 0.3, Math.abs(y) - 0.3, Math.abs(z) - 0.3, - (1 + x * x + y * y + z * z) / 2 + 0.57)","pinned":true,"hidden":false,"mode":"ojs"},{"id":1281,"value":"md`# Download Excel file`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1312,"value":"md`Uncomment fname: 'cube.xlsx' and press Shift + enter`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1318,"value":"md`After download, select all small square cells and set Conditional formatting -> color scale.`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1283,"value":"downloadBook({\n cellSize: 5,\n fov: 39,\n dist: 1.4,\n alpha: 35.0,\n beta: 20,\n rows: 50,\n cols: 77,\n iterCount: 15,\n formula: `MIN(\n MAX(\n ABS(x) - 0.3, ABS(y) - 0.3, ABS(z) - 0.3,\n -SQRT(POWER(x, 2) + POWER(y, 2) + POWER(z, 2)) + 0.375\n ),\n SQRT(POWER(SQRT(POWER(x - 0.25, 2) + POWER(z - 0.25, 2)) - 0.25, 2) + POWER(y, 2)) - 0.05\n )`,\n // fname: 'cube.xlsx', // uncomment this and evaluate for download\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":1294,"value":"downloadBook({\n cellSize: 5,\n fov: 39,\n dist: 1.0,\n alpha: 35.0,\n beta: 20,\n rows: 50,\n cols: 77,\n iterCount: 15,\n formula: `MIN(\n SQRT(POWER(SQRT(POWER(x, 2) + POWER(z, 2)) - 0.3, 2) + POWER(y - 0.18, 2)) - 0.02,\n SQRT(POWER(x, 2) + POWER(y, 2) * 2.5 + POWER(z, 2)) - 0.4,\n MAX(\n x + y - 0.15 - 0.05 - 0.5,\n - (y) + 0.19 - 0.1,\n SQRT(POWER(SQRT(POWER(x - 0.55, 2) + POWER(y - 0.09, 2)) - 0.1, 2) + POWER(z - 0.1, 2)) - 0.04\n ),\n MAX(\n -(- (y) + 0.19 - 0.1),\n SQRT(POWER(SQRT(POWER(x - 0.35, 2) + POWER(y - 0.09, 2)) - 0.1, 2) + POWER(z - 0.1, 2)) - 0.04\n ),\n SQRT(POWER(x, 2) + POWER(y - 0.27, 2) + POWER(z, 2)) - 0.05\n )`,\n // fname: 'teapot.xlsx', // uncomment this and evaluate for download\n})","pinned":true,"hidden":false,"mode":"ojs"},{"id":1276,"value":"md`---\n# Internals\n---`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1221,"value":"cubeTorus = (x, y, z) => Math.min(\n Math.max(\n Math.abs(x) - 0.3,\n Math.abs(y) - 0.3,\n Math.abs(z) - 0.3,\n -Math.sqrt(x ** 2 + y ** 2 + z ** 2) + 0.375\n ),\n Math.sqrt((Math.sqrt((x - 0.25) ** 2 + (z - 0.25) **2) - 0.25) ** 2 + (y - 0.0) ** 2) - 0.05,\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1228,"value":"teapot = (x, y, z) => Math.min(\n Math.sqrt((Math.sqrt(x ** 2 + z**2) - 0.3) ** 2 + (y - 0.18) ** 2) - 0.02,\n Math.sqrt(x ** 2 + y ** 2 * 2.5 + z ** 2) - 0.4,\n Math.max(\n x + y - 0.15 - 0.05 - 0.5,\n - y + 0.19 - 0.1,\n Math.sqrt((Math.sqrt((x - 0.55) ** 2 + (y - 0.09) **2) - 0.1) ** 2 + (z - 0.1) ** 2) - 0.04,\n ),\n Math.max(\n -(- y + 0.19 - 0.1),\n Math.sqrt((Math.sqrt((x - 0.35) ** 2 + (y - 0.09) **2) - 0.1) ** 2 + (z - 0.1) ** 2) - 0.04,\n ),\n Math.sqrt(x ** 2 + (y - 0.27) ** 2 + z ** 2) - 0.05\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":24,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":885,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":534,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":30,"value":"params = emulator({rows: 50, cols: 50 * 1.5, fov: 45, dist: Math.exp(dist), alpha, beta, fun: {cubeTorus, teapot, customFun}[formula], iterCount: 14})\n// params = emulator({rows: 50, cols: 50 * 1.5, fov: 39, dist: 1, alpha: 35.0, beta: 20, fun: funs[1], iterCount: 15})\n// data = emulator({rows: side, cols: side, fov: 39, dist: 1.4, alpha: 35.0, beta: 20, fun: funs[0], iterCount: 15})\n/*\ndata = emulator({\n rows: side, cols: side, fov: 39, dist: 1.5, alpha: 35.0, beta: 25, iterCount: 15,\n fun: (x, y, z) => Math.max(Math.abs(x + 0.4), Math.abs(y), Math.abs(z)) - 0.3,\n // fun: (x, y, z) => Math.sqrt(x ** 2 + y ** 2 + z ** 2) - 0.3,\n // fun: (x, y, z) => Math.sqrt((Math.sqrt(x ** 2 + z**2) - 0.4) ** 2 + y ** 2) - 0.1,\n //fun: (x, y, z) => Math.max(\n // (Math.max(Math.abs(x), Math.abs(y), Math.abs(z)) - 0.32),\n // -(Math.sqrt(x ** 2 + y ** 2 + z ** 2) - 0.4),\n //),\n})\n*/","pinned":false,"hidden":false,"mode":"ojs"},{"id":490,"value":"XLSX = require('https://cdnjs.cloudflare.com/ajax/libs/xlsx/0.12.8/xlsx.full.min.js').then(() => window.XLSX)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1241,"value":"import {slider, select} from \"@jashkenas/inputs\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W34","stdlib":"1","titling":"auto"}