Created
July 17, 2013 14:18
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Animated Joukowski map
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<!DOCTYPE html> | |
<meta charset="utf-8"> | |
<style> | |
.ani .line { fill: none; stroke: steelblue; stroke-width: 1.5px; } | |
.grd .line { fill: none; stroke: black; stroke-width: 0.5px; } | |
</style> | |
<body> | |
<script src="http://d3js.org/d3.v3.min.js"></script> | |
<script> | |
function Complex(re, im) { this.re = re; this.im = im; }; | |
Complex.prototype.clone = function(){ return new Complex(this.re,this.im); }; | |
Complex.prototype.add = function(z) { this.re += z.re; this.im += z.im; return this; }; | |
Complex.prototype.sub = function(z) { this.re -= z.re; this.im -= z.im; return this; }; | |
Complex.prototype.mul = function(z) | |
{ | |
var tmp = this.re; | |
this.re = this.re*z.re - this.im*z.im; | |
this.im = tmp*z.im + this.im*z.re; | |
return this; | |
}; | |
Complex.prototype.div = function(z) | |
{ | |
var tmp = this.re, | |
n = z.re*z.re + z.im*z.im; | |
this.re = (this.re*z.re + this.im*z.im)/n; | |
this.im = ( -tmp*z.im + this.im*z.re)/n; | |
return this; | |
}; | |
var width = 960, height = 500; | |
var svg = d3.select("body") | |
.append("svg") | |
.attr("width", width) | |
.attr("height", height); | |
var grd = svg.append("g").attr("class","grd"); | |
var ani = svg.append("g").attr("class","ani"); | |
var x = d3.scale.linear() | |
.range( [ 0, width]) | |
.domain([ -5, 5]); | |
var y = d3.scale.linear() | |
.range( [height, 0]) | |
.domain([ -5, 5]); | |
var line = d3.svg.line() | |
.x(function(d) { return x(d.re); }) | |
.y(function(d) { return y(d.im); }); | |
function ProduceData(roff,poff) | |
{ | |
var data = d3.range(0.87+roff,roff,-0.02).map(function(r){ | |
return d3.range(-Math.PI/4+poff,7*Math.PI/4,Math.PI/50).map(function(p){ | |
return new Complex(r*Math.cos(p)-0.2,r*Math.sin(p)+0.2);})}) | |
data.forEach(function(d){d.forEach(function(z) {z.add((new Complex(1,0)).div(z));})}); | |
return data; | |
} | |
var data = ProduceData(0,0.01); | |
var save = data[0]; | |
data = d3.transpose(data); | |
save.push(save[0]); | |
data.unshift(save); | |
var paths = grd.selectAll('path').data(data); | |
paths.enter().append('path').attr('class','line'); | |
paths.attr('d',line) | |
function plot(offset) | |
{ | |
var data = ProduceData(offset,0); | |
var paths = ani.selectAll('path').data(data); | |
paths.enter().append('path').attr('class','line'); | |
paths.attr('d',function(d) { return line(d) + 'Z'; }) | |
.attr('stroke-opacity', function(d,i){ if(i<20) return i/20; else return 1.; }); | |
paths.exit().remove(); | |
} | |
var off = 0; | |
d3.timer(function() { plot(off); off -= 0.001; if(off<0) off=0.019;}); | |
</script> | |
</body> |
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