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interpolation.html
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interpolation.html
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<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<style>
body{font-family: monospace;font-size:14px;}
div#drop {border: 2px dashed gray; width: 100px; height: 75px;font-size:1.2em;
font-weight:bold;text-align:center;vertical-align:middle;display:table-cell;color:gray;}
input[type="range"]{width:5em;}
input[type="number"]{width:4em;}
div#ui {padding-left:1em;display:table-cell;}
div#top{box-shadow: 5px 5px #a9a; background-color:#fef; border:1px solid #ede; padding: 0.4em;display:inline-block;}
html{overflow:hidden;}
div#download{display:inline-block; vertical-align:top;padding-left:1em;}
</style>
</head>
<body>
<div id="top">
<div id="drop">Drop the input file here</div>
<div id="ui">
<form>
<label>Tension:</label><input type="range" id="tension" min="0" max="10" value="8"><br>
<label>Input Line: </label> <input type="checkbox" id="input_line" checked> <label>Markers:</label><input type="checkbox" id="input_markers" checked><br>
<label>Fit Line: </label> <input type="checkbox" id="fit_line" checked> <label>Markers:</label><input type="checkbox" id="fit_markers" checked><br>
<label>Number of points:</label> <input type="number" id="npoints" value="24">
</form>
</div>
</div>
<div id="download"></div>
<br>
<canvas id="c"></canvas>
<script>
window.onload=function(){init();}
var ctx;
var w,h;
function init()
{
// Setup the dnd listeners.
var dropZone = document.getElementById('drop');
dropZone.addEventListener('dragover', handleDragOver, false);
dropZone.addEventListener('dragleave', handleDragLeave, true);
dropZone.addEventListener('drop', handleFileSelect, false);
document.getElementById("tension").addEventListener('input',(function(){setSplines();draw();}),false);
document.getElementById("input_line").addEventListener('change',(function(){draw();}),false);
document.getElementById("input_markers").addEventListener('change',(function(){draw();}),false);
document.getElementById("fit_line").addEventListener('change',(function(){draw();}),false);
document.getElementById("fit_markers").addEventListener('change',(function(){draw();}),false);
document.getElementById("npoints").addEventListener('change',(function(){recomputePoints();draw();}),false);
window.addEventListener('resize',(function(){resize();}),false);
var c=document.getElementById("c");
ctx=c.getContext("2d");
resize();
}
/*structure to hold data*/
function Data(){
Data.prototype.setHeader = function(header) {this.header=header;}
Data.prototype.append = function(x,y) {
var fx = parseFloat(x);
var fy = parseFloat(y);
if (isNaN(fx)||isNaN(fy)) return;
this.x.push(fx);
this.y.push(fy);
var t = this;
if (fx<t.xlims[0]) t.xlims[0]=fx;
if (fx>t.xlims[1]) t.xlims[1]=fx;
if (fy<t.ylims[0]) t.ylims[0]=fy;
if (fy>t.ylims[1]) t.ylims[1]=fy;
}
/*simple sorting function*/
Data.prototype.sort = function() {
var flipped,tmp;
do{
flipped=false;
for (var i=0;i<this.x.length-1;i++)
{
if (this.x[i]>this.x[i+1])
{
tmp=this.x[i];this.x[i]=this.x[i+1];this.x[i+1]=tmp;
tmp=this.y[i];this.y[i]=this.y[i+1];this.y[i+1]=tmp;
flipped=true;
}
}
} while(flipped);
}
this.x = [];
this.y = [];
this.header = "";
this.xlims =[1e36,-1e36];
this.ylims = [1e36,-1e36];
}
/*file reader*/
var input;
function draw()
{
if (typeof input=="undefined") return;
/*clear*/
ctx.fillStyle="#FFF";
ctx.fillRect(0,0,w,h);
ctx.strokeStyle="#000";
var X = input.x;
var Y = input.y;
var xlims = input.xlims;
var ylims = input.ylims;
/*plot input line and markers*/
plot(X,Y,xlims,ylims,"input");
/*draw fit*/
plotSplines(xlims,ylims);
/*draw markers*/
if (document.getElementById("fit_markers").checked)
{
plotMarkers(fitP,xlims,ylims);
}
}
var fitP=[];
/*recomputes fit points*/
function recomputePoints()
{
/*add up spline lengths*/
var x0=[];
var ns =splines.length; //number of splines
for (var i=0;i<ns;i++)
{
x0[i] = splines[i].P0[0];
}
x0[ns] = splines[ns-1].P3[0];
var np = parseInt(document.getElementById("npoints").value);
if (np<2) np = 2;
if (np>1000) np=1000;
var dx = (x0[ns]-x0[0])/(np-1); //uniform spacing
//add points
fitP=[];
var s = 0; //current spline
for (var p=0;p<np;p++)
{
var x=x0[0]+p*dx;
/*evaluate current position*/
while(x>x0[s+1]) {s++;}
if (s>ns-1) s=ns-1;
var ft = (x-x0[s])/(x0[s+1]-x0[s]);
fitP[p] = [x, splines[s].YatX(x,ft)];
}
var body = input.header;
for (var p=0;p<np;p++)
body+=fitP[p][0].toFixed(4)+" "+fitP[p][1].toFixed(4)+"\n";
var e = document.getElementById("link");
link.setAttribute('href',"data:text/plain;charset=utf-8,"+encodeURIComponent(body));
draw();
}
function resize()
{
var bw = window.innerWidth;
var bh = window.innerHeight;
var c=document.getElementById("c");
c.width = parseInt(bw)-50;
c.height = parseInt(bh)-150;
w=c.width;
h=c.height;
ctx.translate(0,h);
ctx.scale(1,-1);
draw();
}
/*make x-y plot*/
function plot(x,y,xlims,ylims,name)
{
if (!ctx.setLineDash) {
ctx.setLineDash = function () {}
}
if (document.getElementById("input_line").checked)
{
ctx.setLineDash([10,5]);
ctx.beginPath();
ctx.moveTo(XtoS(x[0],xlims),YtoS(y[0],ylims));
for (var i=1;i<x.length;i++)
{
ctx.lineTo(XtoS(x[i],xlims),YtoS(y[i],ylims));
}
ctx.lineWidth=3;
ctx.strokeStyle="black";
ctx.stroke();
ctx.setLineDash([0]);
}
/*make markers*/
if (document.getElementById('input_markers').checked)
{
for (var i=0;i<x.length;i++)
{
var sx = XtoS(x[i],xlims);
var sy = YtoS(y[i],ylims);
ctx.beginPath();
ctx.arc(sx, sy, 4, 0, 2 * Math.PI, false);
ctx.fillStyle = '#aaa';
ctx.fill();
ctx.lineWidth = 1;
ctx.strokeStyle = 'black';
ctx.stroke();
}
}
}
/*plots bezier cubics*/
function plotSplines(xlims,ylims)
{
if (document.getElementById("fit_line").checked)
{
ctx.beginPath();
for (var i=0;i<splines.length;i++)
{
var s = splines[i];
var v1 = s.P0;
var p1 = s.P1;
var p2 = s.P2;
var v2 = s.P3;
if (i==0)
ctx.moveTo(XtoS(v1[0],xlims),YtoS(v1[1],ylims));
ctx.bezierCurveTo(XtoS(p1[0],xlims),YtoS(p1[1],ylims),
XtoS(p2[0],xlims),YtoS(p2[1],ylims),
XtoS(v2[0],xlims),YtoS(v2[1],ylims));
}
ctx.lineWidth=2;
ctx.strokeStyle = "red";
ctx.stroke();
}
/*draw control points*/
/*
for (var i=0;i<x.length-1;i++)
{
var p1 = [px.p1[i],py.p1[i]];
var p2 = [px.p2[i],py.p2[i]];
var sx = XtoS(p1[0],xlims);
var sy = YtoS(p1[1],ylims);
ctx.beginPath();
ctx.arc(sx, sy, 3, 0, 2 * Math.PI, false);
ctx.fillStyle = 'blue';
ctx.fill();
ctx.lineWidth = 1;
ctx.strokeStyle = 'black';
ctx.stroke();
var sx = XtoS(p2[0],xlims);
var sy = YtoS(p2[1],ylims);
ctx.beginPath();
ctx.arc(sx, sy, 3, 0, 2 * Math.PI, false);
ctx.fillStyle = 'green';
ctx.fill();
ctx.lineWidth = 1;
ctx.strokeStyle = 'black';
ctx.stroke();
}
*/
}
/*plots circles for points P*/
function plotMarkers(P,xlims,ylims)
{
/*draw control points*/
for (var i=0;i<P.length;i++)
{
var sx = XtoS(P[i][0],xlims);
var sy = YtoS(P[i][1],ylims);
ctx.beginPath();
ctx.arc(sx, sy, 4, 0, 2 * Math.PI, false);
ctx.fillStyle = '#44f';
ctx.fill();
ctx.lineWidth = 1;
ctx.strokeStyle = 'black';
ctx.stroke();
}
}
function path(x1,y1,px1,py1,px2,py2,x2,y2)
{
return "M "+x1+" "+y1+" C "+px1+" "+py1+" "+px2+" "+py2+" "+x2+" "+y2;
}
/*translates from X coordinates to screen coordinates*/
var PADDING=10,TOP=50;
function XtoS(x,xlims){ return PADDING+(w-2*PADDING)*(x-xlims[0])/(xlims[1]-xlims[0]);}
function YtoS(y,ylims){return PADDING+(h-PADDING-TOP)*(y-ylims[0])/(ylims[1]-ylims[0]);}
/*------- FILE READING ------*/
function handleFileSelect(evt) {
evt.stopPropagation();
evt.preventDefault();
evt.target.style.background="white";
var files = evt.dataTransfer.files; // FileList object.
/*read only first file*/
f=files[0];
/*parse file*/
var reader = new FileReader();
// Closure to capture the file information.
reader.onload = (function(file,target) {
return function(e) {
if (target.id=="drop")
{
parse(e.target.result);
draw();
}
target.innerHTML=file.name;
console.log("Done reading "+file.name);
};
})(f,evt.target);
var data = reader.readAsText(f);
}
function handleDragOver(evt) {
evt.dataTransfer.dropEffect = 'copy';
evt.stopPropagation();
evt.preventDefault();
evt.target.style.background="yellow";
}
function handleDragLeave(evt) {
/*evt.target seems to be the new element over the mouse, currentTarget is the original*/
evt.currentTarget.style.background="white";
}
/*computes slopes*/
function computeSlopes(K)
{
/*get tension*/
var e=document.getElementById('tension');
c = e.value/10;
if (c<0) c= 0;
if (c>1) c= 1;
p1 = [];
p2 = [];
m = [];
var n = K.length;
for (var i=0;i<n;i++)
{
var im = i-1;
var ip = i+1;
if (im<0) im=0;
if (ip>n-1) ip=n-1;
m[i] = (1-c)*(K[ip]-K[im])/(ip-im);
}
/*compute bezier coeffs*/
for (var i=0;i<n-1;i++)
{
p1[i] = K[i]+m[i]/3;
p2[i] = K[i+1]-m[i+1]/3;
}
return {p1:p1, p2:p2};
}
var Spline = function(P0,P1,P2,P3){
/*recursive length finder*/
Spline.prototype.splineSubL = function(t_min,t_max)
{
/*start, end, and midpoint*/
var t_mid = 0.5*(t_min+t_max);
var A = this.pos(t_min);
var B = this.pos(t_mid);
var C = this.pos(t_max);
/*two vectors pointing out of B*/
var v1 = sub(A,B);
var v2 = sub(C,B);
var v1_mag = mag(v1);
var v2_mag = mag(v2);
var cos_theta = dot(v1,v2)/(v1_mag*v2_mag);
if (cos_theta<-0.984) //170 degrees
{
/*accept*/
return v1_mag+v2_mag;
}
else
{
return this.splineSubL(t_min,t_mid)+
this.splineSubL(t_mid,t_max);
}
}
/*evaluates position on a cubic spline*/
Spline.prototype.pos = function(t)
{
var a=(1-t)*(1-t)*(1-t);
var b=3*(1-t)*(1-t)*t;
var c=3*(1-t)*t*t;
var d=t*t*t;
var x=[];
for (var dim=0;dim<2;dim++)
{
x[dim] = a*this.P0[dim]+b*this.P1[dim]+c*this.P2[dim]+d*this.P3[dim];
}
return x;
}
/*uses newton's method to find value Y at postion X, given initial guess*/
Spline.prototype.YatX = function(x,t0)
{
/*first need to compute t that gives us this x*/
/*10 iterations of newton's method*/
var t=t0;
var a,b,c,d;
for (var it=0;it<10;it++)
{
a=(1-t)*(1-t)*(1-t);
b=3*(1-t)*(1-t)*t;
c=3*(1-t)*t*t;
d=t*t*t;
f = a*this.P0[0]+b*this.P1[0]+c*this.P2[0]+d*this.P3[0]-x;
/*derivative*/
p = 3*(1-t)*(1-t);
r = 6*(1-t)*t;
s = 3*t*t;
fprime = p*(this.P1[0]-this.P0[0]) + r*(this.P2[0]-this.P1[0]) +
s*(this.P3[0]-this.P2[0]);
if (fprime==0) break;
t = t-f/fprime;
}
return this.pos(t)[1];
}
this.P0 = P0;
this.P1 = P1;
this.P2 = P2;
this.P3 = P3;
this.length = this.splineSubL(0,1);
};
/*vector helper functions*/
function sub(v1,v2)
{
return [v1[0]-v2[0], v1[1]-v2[1]];
}
function mag(v1)
{
return Math.sqrt(v1[0]*v1[0]+v1[1]*v1[1])
}
function dot(v1,v2)
{
return (v1[0]*v2[0]+v1[1]*v2[1]);
}
var splines = [];
/*parses the primary file*/
function parse(buffer)
{
input = new Data();
/*split into lines*/
var lines = buffer.split("\n");
var header="";
/*the test data starts on line 3*/
for (var l=0;l<lines.length;l++)
{
pieces = lines[l].trim().split(/[\s\,]+/);
/*is this numeric data?*/
if (pieces.length==2 && isNumber(pieces[0]) && isNumber(pieces[1]))
input.append(pieces[0], pieces[1]);
else if (l<5) header=header+lines[l]+"\n";
}
input.setHeader(header);
input.sort();
/*show output link, need to call before setSplines()*/
document.getElementById("download").innerHTML="Download <a id=\"link\" href=\"\" download=\"output.txt\">output.txt</a>";
setSplines();
}
/*per http://stackoverflow.com/questions/18082/validate-decimal-numbers-in-javascript-isnumeric*/
function isNumber(val) {return isFinite(parseFloat(val));}
function setSplines() {
/*now we have data, process the spline*/
var X = input.x;
var Y = input.y;
var px = computeSlopes(X);
var py = computeSlopes(Y);
splines = [];
for (var i=0;i<X.length-1;i++)
{
var K1 = [X[i],Y[i]];
var K2 = [X[i+1],Y[i+1]];
var P1 = [px.p1[i],py.p1[i]];
var P2 = [px.p2[i],py.p2[i]];
splines.push(new Spline(K1,P1,P2,K2));
}
recomputePoints();
}
</script>
</body>
</html>