30:T779,preHTML(`WITH RECURSIVE numbers AS ( SELECT 0 AS n UNION ALL SELECT n+1 FROM numbers WHERE n<${Math.max(c.maxCol, c.maxRow)} ), pixels AS ( SELECT rows.n as row, cols.n as col FROM numbers as rows CROSS JOIN numbers as cols WHERE rows.n > ${c.minRow - 1} AND rows.n < ${c.maxRow} AND cols.n > ${c.minCol - 1} AND cols.n < ${c.maxCol} ), rawRays AS ( SELECT row, col, ${(c.x0 - c.cols / 2 * c.scaleX * c.ux - c.rows / 2 * c.scaleY * c.vx).toFixed(4)} + col * ${(c.scaleX * c.ux).toFixed(4)} + row * ${(c.scaleY * c.vx).toFixed(4)} as x, ${(c.y0 - c.rows / 2 * c.scaleY * c.vy).toFixed(4)} + row * ${(c.scaleY * c.vy).toFixed(4)} as y, ${(c.z0 - c.cols / 2 * c.scaleX * c.uz - c.rows / 2 * c.scaleY * c.vz).toFixed(4)} + col * ${(c.scaleX * c.uz).toFixed(4)} + row * ${(c.scaleY * c.vz).toFixed(4)} as z FROM pixels ), normsSq AS ( SELECT row, col, x, y, z, x * x + y * y + z * z AS n2 FROM rawRays ), norms AS ( SELECT row, col, x, y, z, ${sqrt1SQL('n2', '1')} as n FROM normsSq ), rays AS ( SELECT row, col, x / n AS x, y / n AS y, z / n AS z FROM norms ), iters AS ( SELECT row, col, 0 as it, 0 as v FROM rays UNION ALL SELECT rays.row, rays.col, it + 1 AS it, v + ${formula(r.x, r.y, r.z)} AS v FROM iters JOIN rays ON rays.row = iters.row AND rays.col = iters.col WHERE it < ${c.iters} ), lastIters AS ( SELECT it0.row, it0.col, it0.v AS v0, it1.v AS v1, it2.v AS v2 FROM iters as it0 JOIN iters AS it1 ON it0.row = it1.row AND it0.col = it1.col JOIN iters AS it2 ON it0.row = it2.row AND it0.col = it2.col WHERE it0.it = ${c.iters} AND it1.it = ${c.iters - 1} AND it2.it = ${c.iters - 2} ), res AS ( SELECT col, (v0 - v1) / (v1 - v2) as v FROM lastIters ) SELECT group_concat( substr('${ascii}', round(1 + max(0, min(${ascii.length - 1}, v * ${ascii.length}))), 1) || CASE WHEN col = ${c.maxCol - 1} THEN X'0A' ELSE '' END , '') FROM res; `)31:T680,{ const sqIt = (e, i) => (i + e / i) / 2; const sqrt = 0 ? x => Math.sqrt(x) : x => sqIt(x, sqIt(x, sqIt(x, 1))); const sqrt1a = (x) => (1 + x) / 2; const sqrt1b = (x) => 0.14 + 1.78 * x; const sqrt1 = (x, init=1) => sqIt(x, init); const sqrt2 = (x, init=1) => sqIt(x, sqIt(x, init)); const fun = 1 ? (x, y, z) => Math.max( Math.abs(x) - 0.3, Math.abs(y) - 0.3, Math.abs(z) - 0.3, -sqrt1b(x * x + y * y + z * z) + 0.42 ) : (x, y, z) => Math.max(Math.abs(x), Math.abs(y), Math.abs(z)) - 0.3; const iterCount = c.iters; let res = '\n'; for (let row=c.minRow; row 0.3 ? '#' : ' '; } res += '\n'; }; return preCanvas(res); }32:T701,preHTML(`WITH RECURSIVE numbers AS ( SELECT 0 AS n UNION ALL SELECT n+1 FROM numbers WHERE n<${Math.max(c.maxCol, c.maxRow)} ), pixels AS ( SELECT rows.n as row, cols.n as col FROM numbers as rows CROSS JOIN numbers as cols WHERE rows.n > ${c.minRow - 1} AND rows.n < ${c.maxRow} AND cols.n > ${c.minCol - 1} AND cols.n < ${c.maxCol} ), rawRays AS ( SELECT row * 100 + col AS no, ${(c.x0 - c.cols / 2 * c.scaleX * c.ux - c.rows / 2 * c.scaleY * c.vx).toFixed(4)} + col * ${(c.scaleX * c.ux).toFixed(4)} + row * ${(c.scaleY * c.vx).toFixed(4)} as x, ${(c.y0 - c.rows / 2 * c.scaleY * c.vy).toFixed(4)} + row * ${(c.scaleY * c.vy).toFixed(4)} as y, ${(c.z0 - c.cols / 2 * c.scaleX * c.uz - c.rows / 2 * c.scaleY * c.vz).toFixed(4)} + col * ${(c.scaleX * c.uz).toFixed(4)} + row * ${(c.scaleY * c.vz).toFixed(4)} as z FROM pixels ), normsSq AS ( SELECT no, x, y, z, x * x + y * y + z * z AS n2 FROM rawRays ), norms AS ( SELECT no, x, y, z, ${sqrt1SQL('n2', '1')} as n FROM normsSq ), rays AS ( SELECT no, x / n AS x, y / n AS y, z / n AS z FROM norms ), iters AS ( SELECT no, 0 as it, 0 as v FROM rays UNION ALL SELECT rays.no, it + 1 AS it, v + ${formula(r.x, r.y, r.z)} AS v FROM iters JOIN rays ON rays.no = iters.no WHERE it < ${c.iters} ), lastIters AS ( SELECT it0.no, it0.v AS v0, it1.v AS v1, it2.v AS v2 FROM iters as it0 JOIN iters AS it1 ON it0.no = it1.no JOIN iters AS it2 ON it0.no = it2.no WHERE it0.it = ${c.iters} AND it1.it = ${c.iters - 1} AND it2.it = ${c.iters - 2} ), res AS ( SELECT no, (v0 - v1) / (v1 - v2) as v FROM lastIters ) SELECT group_concat( substr('${ascii}', round(1 + max(0, min(${ascii.length - 1}, v * ${ascii.length}))), 1) || CASE WHEN no % 1000 = 0 THEN X'0A' ELSE '' END , '') FROM res; `)33:[] 2e:{"title":"SQL 3d engine (interactive preview)","cells":[{"id":0,"value":"md`# SQL 3d engine (interactive preview)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":747,"value":"md`SQLite query:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":721,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":498,"value":"viewof alpha = slider({\n min: -180, \n max: 180, \n step: 1, \n value: -55, \n title: \"alpha\",\n description: \"horizontal rotation\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":502,"value":"viewof beta = slider({\n min: -90, \n max: 90, \n step: 1, \n value: 30, \n title: \"beta\",\n description: \"vertical rotation\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":504,"value":"viewof dist = slider({\n min: 0.5, \n max: 2.5, \n step: 0.1, \n value: 1.5, \n title: \"dist\",\n description: \"distance to camera\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":560,"value":"viewof fov = slider({\n min: 1, \n max: 100, \n step: 1, \n value: 26, \n title: \"fov\",\n description: \"camera field of view\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":507,"value":"$31","pinned":false,"hidden":false,"mode":"ojs"},{"id":760,"value":"md`Explanation article (russian): https://habr.com/post/435390/`","pinned":false,"hidden":false,"mode":"ojs"},{"id":758,"value":"md`You may also want to check out the same thing for Excel: https://beta.observablehq.com/@pallada-92/excel-3d-engine-emulator`","pinned":false,"hidden":false,"mode":"ojs"},{"id":619,"value":"preHTML(range(80).map(() => '-').join(''))","pinned":false,"hidden":false,"mode":"ojs"},{"id":515,"value":"viewof sqInit = slider({\n min: 0.1, \n max: 1.0, \n step: 0.01, \n value: 0.28, \n title: \"sqInit\",\n description: \"initial value of square root\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":535,"value":"viewof gamma = slider({\n min: 0.0, \n max: 2.0, \n step: 0.1, \n value: 1.0, \n title: \"gamma\",\n description: \"gamma correction\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":537,"value":"viewof colorShift = slider({\n min: -1.0, \n max: 1.0, \n step: 0.1, \n value: 0, \n title: \"colorShift\",\n description: \"color shift\"\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":6,"value":"c = ({\n iters: 15,\n minRow: 3,\n maxRow: 40,\n minCol: 0,\n maxCol: 80 + 9,\n rows: 36 + 7,\n cols: 80 + 10,\n scaleX: 0.6,\n scaleY: 1.5,\n camX: +(dist * cos(alpha) * cos(beta)).toFixed(camPrecision),\n camY: +(dist * sin(beta)).toFixed(camPrecision),\n camZ: +(dist * sin(alpha) * cos(beta)).toFixed(camPrecision),\n ux: -pixelSize * sin(alpha),\n uz: +pixelSize * cos(alpha),\n vx: +pixelSize * cos(alpha) * sin(beta),\n vy: -pixelSize * cos(beta),\n vz: +pixelSize * sin(alpha) * sin(beta),\n x0: -cos(alpha) * cos(beta),\n y0: -sin(beta),\n z0: -sin(alpha) * cos(beta),\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":602,"value":"formula = (x, y, z) => `MAX(ABS(${x}) - 0.3, ABS(${y}) - 0.3, ABS(${z}) - 0.3, -${sqrt1SQL(`((${x}) * (${x}) + (${y}) * (${y}) + (${z}) * (${z}))`, sqInit.toString())} + 0.42)`","pinned":false,"hidden":false,"mode":"ojs"},{"id":755,"value":"","pinned":false,"hidden":false,"mode":"ojs"},{"id":594,"value":"md`\n\n---------\n\n---------\n\n---------\n\n# Internals\n\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":678,"value":"camPrecision = 2","pinned":false,"hidden":false,"mode":"ojs"},{"id":726,"value":"preCanvas = txt => {\n const ctx = DOM.context2d(width, width);\n const fontSize = Math.round(width / 60);\n ctx.font = `${fontSize}px monospace`;\n ctx.fillStyle = 'black';\n txt.split('\\n').map((line, no) => ctx.fillText(line, 5, 5 + no * fontSize * 1.4));\n return ctx.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":580,"value":"preHTML = txt => html`

${txt.replace(/&/g, '&').replace(//g, '>')}

`;","pinned":false,"hidden":false,"mode":"ojs"},{"id":480,"value":"cos = x => Math.cos(x * Math.PI / 180)","pinned":false,"hidden":false,"mode":"ojs"},{"id":471,"value":"sin = x => Math.sin(x * Math.PI / 180)\n","pinned":false,"hidden":false,"mode":"ojs"},{"id":482,"value":"tan = x => Math.tan(x * Math.PI / 180)","pinned":false,"hidden":false,"mode":"ojs"},{"id":486,"value":"rows = 36","pinned":false,"hidden":false,"mode":"ojs"},{"id":483,"value":"pixelSize = tan(fov / 2) / ((rows - 1) / 2)","pinned":false,"hidden":false,"mode":"ojs"},{"id":237,"value":"ascii = `$@B%8&WM#*oahkbdpqwmZO0QLCJUYXzcvunxrjft/\\|()1{}[]?-_+~<>i!lI;:,\"^. `","pinned":false,"hidden":false,"mode":"ojs"},{"id":13,"value":"rangeSQL = (name, size) => `${name} AS (SELECT 0 AS v UNION ALL SELECT v+1 FROM ${name} WHERE v<${size})`","pinned":false,"hidden":false,"mode":"ojs"},{"id":24,"value":"sqrt1SQL = (expr, init) => init == 1 ? `(${init} + ${expr}) / 2.0` : `(${init} + ${expr} / ${init}) / 2.0`","pinned":false,"hidden":false,"mode":"ojs"},{"id":45,"value":"sqrt2SQL = (expr, init) => sqrt1SQL(expr, '(' + sqrt1SQL(expr, init) + ')')","pinned":false,"hidden":false,"mode":"ojs"},{"id":62,"value":"sqrt3SQL = (expr, init) => sqrt1SQL(expr, '(' + sqrt1SQL(expr, '(' + sqrt1SQL(expr, init) + ')') + ')')","pinned":false,"hidden":false,"mode":"ojs"},{"id":104,"value":"r = ({\n x: `${c.camX}+v*x`,\n y: `${c.camY}+v*y`,\n z: `${c.camZ}+v*z`,\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":271,"value":"range = n => {\n const res = [];\n for (let i=0; i