Plots the first ten Hermite polynomials (physicists' definition), defined using the recursion relation.
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April 4, 2016 17:45
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Hermite Polynomials
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <html> | |
| <head> | |
| <title>Hermite Polynomials</title> | |
| <script src="http://d3js.org/d3.v3.min.js"></script> | |
| <style> | |
| body { | |
| font-family: "Helvetica", sans-serif; | |
| font-size: 10px; | |
| margin: 8px; | |
| } | |
| .axis { | |
| font: 10px sans-serif; | |
| } | |
| .axis path, | |
| .axis line { | |
| fill: none; | |
| stroke: #000; | |
| shape-rendering: crispEdges; | |
| } | |
| .path { | |
| fill: none; | |
| stroke: rgba(189,54,19,1); | |
| stroke-width: 2px; | |
| } | |
| </style> | |
| </head> | |
| <body> | |
| <script> | |
| (function() { | |
| var margin = {top: 20, right: 20, bottom: 40, left: 40}, | |
| width = 944 - margin.left - margin.right, | |
| height = 480 - margin.top - margin.bottom; | |
| var xMin = -5; | |
| var xMax = 5; | |
| var yMin = -200; | |
| var yMax = 200; | |
| var drawDelay = 1000; | |
| var nMax = 6; | |
| var xSteps = 101; | |
| var xRange = d3.range(xMin, xMax, (xMax-xMin)/xSteps); | |
| // recursive definition | |
| function hermite(x, n) { | |
| switch(n) { | |
| case 0: | |
| return 1; | |
| case 1: | |
| return 2*x; | |
| default: | |
| return 2.*x*hermite(x, n-1) - 2.*(n-1)*hermite(x, n-2); | |
| } | |
| } | |
| // X scale | |
| var xScale = d3.scale.linear() | |
| .domain([xMin, xMax]) | |
| .range([0, width]); | |
| // Y scale | |
| var yScale = d3.scale.linear() | |
| .domain([yMin, yMax]) | |
| .range([height, 0]); | |
| // Draw SVG | |
| var svg = d3.select("body").append("svg") | |
| .attr("width", width + margin.left + margin.right) | |
| .attr("height", height + margin.top + margin.bottom) | |
| .append("g") | |
| .attr("transform", "translate(" + margin.left + "," + margin.top + ")"); | |
| // Draw axes | |
| var xAxis = d3.svg.axis() | |
| .scale(xScale) | |
| .ticks(5) | |
| .orient("bottom"); | |
| svg.append("g") | |
| .attr("class", "x axis") | |
| .attr("transform", "translate(0," + height + ")") | |
| .call(xAxis); | |
| var yAxis = d3.svg.axis() | |
| .scale(yScale) | |
| .ticks(3) | |
| .orient("left"); | |
| svg.append("g") | |
| .attr("class", "y axis") | |
| .call(yAxis); | |
| var nText = svg.append("text") | |
| .attr("id", "n-text") | |
| .attr("class", "svg-small-text") | |
| .style("text-anchor", "start") | |
| .attr("x", 20) | |
| .attr("y", 4); | |
| var hermite_path = svg.append("path") | |
| .attr("class", "path"); | |
| var lineFunction = d3.svg.line() | |
| .x(function(d) { return xScale(d[0]); }) | |
| .y(function(d) { return yScale(d[1]); }) | |
| .interpolate("cardinal"); | |
| function drawHermites(n) { | |
| setTimeout(function() { | |
| d3.select('#n-text').text("n: " + (n)); | |
| path_xy = xRange.map(function(i) { return [i, hermite(i, n)]; }); | |
| hermite_path | |
| .datum(path_xy) | |
| .transition() | |
| .attr("class", "path") | |
| .attr("d", lineFunction); | |
| n++; | |
| if (n < nMax) { | |
| drawHermites(n); | |
| } | |
| else { | |
| drawHermites(0); | |
| } | |
| }, drawDelay); | |
| } | |
| drawHermites(0); | |
| })() | |
| </script> | |
| </body> | |
| </html> |
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