3e:null 3f:["$","title",null,{"children":"SQL 3d engine (interactive preview) | Yaroslav Sergienko | Observable"}] 45:T779,preHTML(`WITH RECURSIVE numbers AS ( SELECT 0 AS n UNION ALL SELECT n+1 FROM numbers WHERE n<${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 = ${c.maxCol - 1} THEN X'0A' ELSE '' END , '') FROM res; `)46:T680,{ const sqIt = (e, i) => (i + e / i) / 2; const sqrt = 0 ? x => Math.sqrt(x) : x => sqIt(x, sqIt(x, sqIt(x, 1))); const sqrt1a = (x) => (1 + x) / 2; const sqrt1b = (x) => 0.14 + 1.78 * x; const sqrt1 = (x, init=1) => sqIt(x, init); const sqrt2 = (x, init=1) => sqIt(x, sqIt(x, init)); const fun = 1 ? (x, y, z) => Math.max( Math.abs(x) - 0.3, Math.abs(y) - 0.3, Math.abs(z) - 0.3, -sqrt1b(x * x + y * y + z * z) + 0.42 ) : (x, y, z) => Math.max(Math.abs(x), Math.abs(y), Math.abs(z)) - 0.3; const iterCount = c.iters; let res = '\n'; for (let row=c.minRow; row 0.3 ? '#' : ' '; } res += '\n'; }; return preCanvas(res); }47:T701,preHTML(`WITH RECURSIVE numbers AS ( SELECT 0 AS n UNION ALL SELECT n+1 FROM numbers WHERE n<${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 * ${ascii.length}))), 1) || CASE WHEN no % 1000 = 0 THEN X'0A' ELSE '' END , '') FROM res; `)48:[] 43:{"id":"a4c8d3208b813afc","slug":"sql-3d-engine","title":"SQL 3d engine (interactive 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rotation\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":560,"value":"viewof fov = slider({\n min: 1, \n max: 100, \n step: 1, \n value: 26, \n title: \"fov\",\n description: \"camera field of 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https://beta.observablehq.com/@pallada-92/excel-3d-engine-emulator`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":619,"value":"preHTML(range(80).map(() => '-').join(''))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":515,"value":"viewof sqInit = slider({\n min: 0.1, \n max: 1.0, \n step: 0.01, \n value: 0.28, \n title: \"sqInit\",\n description: \"initial value of square root\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":537,"value":"viewof colorShift = slider({\n min: -1.0, \n max: 1.0, \n step: 0.1, \n value: 0, \n title: \"colorShift\",\n description: \"color shift\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"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","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":602,"value":"formula = (x, y, z) => `MAX(ABS(${x}) - 0.3, ABS(${y}) - 0.3, ABS(${z}) - 0.3, -${sqrt1SQL(`((${x}) * (${x}) + (${y}) * (${y}) + (${z}) * (${z}))`, sqInit.toString())} + 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2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":726,"value":"preCanvas = txt => {\n const ctx = DOM.context2d(width, width);\n const fontSize = Math.round(width / 60);\n ctx.font = `${fontSize}px monospace`;\n ctx.fillStyle = 'black';\n txt.split('\\n').map((line, no) => ctx.fillText(line, 5, 5 + no * fontSize * 1.4));\n return ctx.canvas;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":580,"value":"preHTML = txt => html`

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