This experiment extends the previous one by placing the quads according to the Hilbert curve. The placement procedure uses the algorithm illustrated in Baboo et al.
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November 8, 2019 06:28
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Quaternary numbers (Hilbert)
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| scale = 480 | |
| svg = d3.select 'svg' | |
| vis = svg.append 'g' | |
| .attr | |
| transform: "translate(#{scale/2}, 10)" | |
| width = svg.node().getBoundingClientRect().width | |
| height = svg.node().getBoundingClientRect().height | |
| quad_layout = (mapping, size) -> | |
| return (digits) -> | |
| m = mapping digits | |
| return { | |
| x: m.j/Math.pow(2,m.n)*size, | |
| y: m.i/Math.pow(2,m.n)*size, | |
| dx: 1/Math.pow(2,m.n)*size, | |
| dy: 1/Math.pow(2,m.n)*size, | |
| digits: m.digits | |
| } | |
| hquad = (digits) -> | |
| n = digits.length | |
| l = 1 | |
| i = 0 | |
| j = 0 | |
| for d in digits by -1 | |
| switch d | |
| when '0' | |
| i_temp = i | |
| i = j | |
| j = i_temp | |
| when '1' | |
| i += l | |
| when '2' | |
| i += l | |
| j += l | |
| when '3' | |
| i_temp = i | |
| i = l - j - 1 | |
| j = 2*l - i_temp - 1 | |
| l = 2*l | |
| return { | |
| j: j, | |
| i: i, | |
| n: n, | |
| digits: digits | |
| } | |
| ### Visualization | |
| ### | |
| indices = ["0","10","11","12","13","200","201","202","203","210","211","212","213","220","221","222","223","230","231","232","233","230","231","232","233","3000","3001","3002","301","302","303","31","32"] | |
| quads = indices.map quad_layout(hquad, 480) | |
| rects = vis.selectAll 'rect' | |
| .data quads | |
| rects.enter().append 'g' | |
| rects.append 'rect' | |
| .attr | |
| x: (d) -> d.x | |
| y: (d) -> d.y | |
| width: (d) -> d.dx | |
| height: (d) -> d.dy | |
| .append 'title' | |
| .text (d) -> "x: #{d.x}\ny: #{d.y}\nw/h: #{d.dx}" | |
| rects.append 'text' | |
| .attr | |
| x: (d) -> d.x + (d.dx / 2) | |
| y: (d) -> d.y + (d.dy / 2) | |
| 'text-anchor': 'middle' | |
| dy: '0.35em' | |
| 'font-size': (d) -> d.dx/5 | |
| .text (d) -> d.digits |
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| html, body { | |
| padding: 0; | |
| margin: 0; | |
| height: 100%; | |
| overflow: hidden; | |
| font-family: sans-serif; | |
| } | |
| svg { | |
| width: 100%; | |
| height: 100%; | |
| } | |
| rect { | |
| fill: steelblue; | |
| stroke: #fff; | |
| stroke-width: 0.5px; | |
| } | |
| text { | |
| pointer-events: none; | |
| } |
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| <!doctype html> | |
| <html> | |
| <head> | |
| <meta charset="utf-8"> | |
| <title>Quadtree function</title> | |
| <link type="text/css" rel="stylesheet" href="index.css"/> | |
| <script src="http://d3js.org/d3.v3.min.js"></script> | |
| </head> | |
| <body> | |
| <svg></svg> | |
| <script src="index.js"></script> | |
| </body> | |
| </html> |
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| // Generated by CoffeeScript 1.10.0 | |
| (function() { | |
| var height, hquad, indices, quad_layout, quads, rects, scale, svg, vis, width; | |
| scale = 480; | |
| svg = d3.select('svg'); | |
| vis = svg.append('g').attr({ | |
| transform: "translate(" + (scale / 2) + ", 10)" | |
| }); | |
| width = svg.node().getBoundingClientRect().width; | |
| height = svg.node().getBoundingClientRect().height; | |
| quad_layout = function(mapping, size) { | |
| return function(digits) { | |
| var m; | |
| m = mapping(digits); | |
| return { | |
| x: m.j / Math.pow(2, m.n) * size, | |
| y: m.i / Math.pow(2, m.n) * size, | |
| dx: 1 / Math.pow(2, m.n) * size, | |
| dy: 1 / Math.pow(2, m.n) * size, | |
| digits: m.digits | |
| }; | |
| }; | |
| }; | |
| hquad = function(digits) { | |
| var d, i, i_temp, j, k, l, n; | |
| n = digits.length; | |
| l = 1; | |
| i = 0; | |
| j = 0; | |
| for (k = digits.length - 1; k >= 0; k += -1) { | |
| d = digits[k]; | |
| switch (d) { | |
| case '0': | |
| i_temp = i; | |
| i = j; | |
| j = i_temp; | |
| break; | |
| case '1': | |
| i += l; | |
| break; | |
| case '2': | |
| i += l; | |
| j += l; | |
| break; | |
| case '3': | |
| i_temp = i; | |
| i = l - j - 1; | |
| j = 2 * l - i_temp - 1; | |
| } | |
| l = 2 * l; | |
| } | |
| return { | |
| j: j, | |
| i: i, | |
| n: n, | |
| digits: digits | |
| }; | |
| }; | |
| /* Visualization | |
| */ | |
| indices = ["0", "10", "11", "12", "13", "200", "201", "202", "203", "210", "211", "212", "213", "220", "221", "222", "223", "230", "231", "232", "233", "230", "231", "232", "233", "3000", "3001", "3002", "301", "302", "303", "31", "32"]; | |
| quads = indices.map(quad_layout(hquad, 480)); | |
| rects = vis.selectAll('rect').data(quads); | |
| rects.enter().append('g'); | |
| rects.append('rect').attr({ | |
| x: function(d) { | |
| return d.x; | |
| }, | |
| y: function(d) { | |
| return d.y; | |
| }, | |
| width: function(d) { | |
| return d.dx; | |
| }, | |
| height: function(d) { | |
| return d.dy; | |
| } | |
| }).append('title').text(function(d) { | |
| return "x: " + d.x + "\ny: " + d.y + "\nw/h: " + d.dx; | |
| }); | |
| rects.append('text').attr({ | |
| x: function(d) { | |
| return d.x + (d.dx / 2); | |
| }, | |
| y: function(d) { | |
| return d.y + (d.dy / 2); | |
| }, | |
| 'text-anchor': 'middle', | |
| dy: '0.35em', | |
| 'font-size': function(d) { | |
| return d.dx / 5; | |
| } | |
| }).text(function(d) { | |
| return d.digits; | |
| }); | |
| }).call(this); |
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