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interp.html
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interp.html
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<!-- Always force latest IE rendering engine (even in intranet) & Chrome Frame
Remove this if you use the .htaccess -->
<meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1" />
<title>Interpolations</title>
<meta name="description" content="" />
<meta name="generator" content="Studio 3 http://aptana.com/" />
<meta name="author" content="Alex Cheng" />
<meta name="viewport" content="width=device-width; initial-scale=1.0" />
<!-- Replace favicon.ico & apple-touch-icon.png in the root of your domain and delete these references -->
<link rel="shortcut icon" href="/favicon.ico" />
<link rel="apple-touch-icon" href="/apple-touch-icon.png" />
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.7.1/jquery.min.js" type="text/javascript"></script>
<style>
nav * { display: inline }
canvas { cursor: none; }
</style>
<script type="text/javascript">
(function () {
var zuigan = function (a, b, c, f) {
var n = a.length;
var alf = new Array(n), bta = new Array(n);
alf[0] = b[0];
bta[0] = c[0]/alf[0];
f[0] = f[0]/alf[0];
for(var i = 1; i < n - 1; i ++) {
alf[i] = b[i] - a[i] * bta[i-1];
bta[i] = c[i] / alf[i];
f[i] = (f[i] - a[i] * f[i-1])/alf[i];
}
alf[n-1] = b[n-1] - a[n-1] * bta[n-2];
f[n-1] = (f[n-1] - a[n-1]*f[n-2])/alf[n-1];
for(var i=n-2; i>=0; i--) {
f[i]=f[i]-bta[i]*f[i+1];
}
return f;
};
var test = function() {
var aa = new Array(4), bb = new Array(4), cc = new Array(4), ff = new Array(4);
aa[0] = 0; aa[1] = 2; aa[2] = 2; aa[3] = 1;
bb[0] = 3; bb[1] = 3; bb[2] = 3; bb[3] = 3;
cc[0] = 1; cc[1] = 1; cc[2] = 1; cc[3] = 0;
ff[0] = 1; ff[1] = 0; ff[2] = 1; ff[3] = 0;
var result = zuigan(aa,bb,cc,ff);
};
var CartesianCoord = function (originX, originY) {
if (originX == undefined) {
originX = 0;
}
if (originY == undefined) {
originY = 0;
}
this.originX = originX;
this.originY = originY;
this.padding = 20;
this.arrowSize = 8;
this.draw = function (context) {
if (context == undefined) {
alert("Argument context is required.");
return;
}
var canvasWidth = context.canvas.width;
var canvasHeight = context.canvas.height;
// Draw origin point
context.beginPath();
context.arc(originX, originY, 3, 0, Math.PI * 2, true);
context.fillStyle = "gray";
context.lineWidth = 1;
context.fill();
// Draw X axis
context.beginPath();
context.strokeStyle = "red";
context.moveTo(this.padding, this.originY);
context.lineTo(canvasWidth - this.padding, this.originY);
context.stroke();
// Draw Y axis
context.beginPath();
context.strokeStyle = "green";
context.moveTo(this.originX, this.padding);
context.lineTo(this.originX, canvasHeight - this.padding);
context.stroke();
// Draw arrows
context.beginPath();
context.moveTo(this.originX, this.padding);
context.lineTo(this.originX - this.arrowSize, this.padding + this.arrowSize);
context.moveTo(this.originX, this.padding);
context.lineTo(this.originX + this.arrowSize, this.padding + this.arrowSize);
context.moveTo(canvasWidth - this.padding, originY);
context.lineTo(canvasWidth - this.padding - this.arrowSize, originY - this.arrowSize);
context.moveTo(canvasWidth - this.padding, originY);
context.lineTo(canvasWidth - this.padding - this.arrowSize, originY + this.arrowSize);
context.strokeStyle = "lightgray";
context.stroke();
// Draw X, Y text
context.fillStyle = "white";
context.font = "bold 16px Arial";
context.fillText("Y", this.originX - 10, this.padding);
context.fillText("X", canvasWidth - this.padding + 2, this.originY + 4);
};
this.convertX2XonCanvas = function (x) {
return x + this.originX;
};
this.convertY2YonCanvas = function (y) {
return this.originY - y;
};
};
var Cursor = function (x, y, coords) {
this.positionX = x;
this.positionY = y;
this.coords = coords;
this.valueX = function () {
return this.positionX - this.coords.originX;
};
this.valueY = function () {
return this.coords.originY - this.positionY;
}
this.draw = function (context) {
var cursorSize = 30;
context.beginPath();
context.moveTo(this.positionX - cursorSize / 2, this.positionY);
context.lineTo(this.positionX + cursorSize / 2, this.positionY);
context.moveTo(this.positionX, this.positionY - cursorSize / 2);
context.lineTo(this.positionX, this.positionY + cursorSize / 2);
context.strokeStyle = "white";
context.stroke();
context.fillStyle = "white";
context.font ="normal 11px Arial";
var posText = "(" + this.valueX() + "," + this.valueY() + ")";
context.fillText(posText, this.positionX + cursorSize / 2 + 2, this.positionY - 4);
};
};
var Point = function (x, y, coords) {
this.x = x;
this.y = y;
this.coords = coords;
if(this.x == undefined) {
this.x = 0;
}
if(this.y == undefined) {
this.y = 0;
}
this.draw = function (context) {
// Draw the point
context.beginPath();
context.fillStyle ="pink";
var x = context.coordSys.convertX2XonCanvas(this.x), y = context.coordSys.convertY2YonCanvas(this.y);
context.arc(x, y, 2, 0, Math.PI * 2, true);
context.fill();
// Draw the text (x, y)
var valueText = "(" + this.x + "," + this.y + ")";
context.font = "normal 10px Arial";
context.fillText(valueText, x + 4, y - 2);
};
}
var LinearInterpolation = function (points) {
this.points = points;
this.draw = function (context) {
context.strokeStyle = "BurlyWood";
context.lineWidth = 1;
context.beginPath();
var count = 0;
for(var k in this.points) {
var p = this.points[k];
if( count == 0) {
context.moveTo(context.coordSys.convertX2XonCanvas(p.x), context.coordSys.convertY2YonCanvas(p.y));
}
else {
context.lineTo(context.coordSys.convertX2XonCanvas(p.x), context.coordSys.convertY2YonCanvas(p.y));
}
count ++;
}
context.stroke();
};
};
// End of LinearInterpolation
var LagrangeInterpolation = function (points) {
this.points = points;
this.draw = function (context) {
// w2 is w'(x_k) = (x_k - x0)(x_k - x1)...(x_k - x_k-1)(x_k - x_k+1)...(x_k - x_n)
var w2 = new Array();
for(var k = 0; k < this.points.length; k++) {
var x_k = this.points[k].x;
var w_k = 1.0;
for(var i = 0; i < this.points.length; i++) {
if( i != k ) {
w_k = w_k * (x_k - this.points[i].x); // (x_k - x_i) i = 0,1,...,n-1
}
}
w2[k] = w_k;
}
//$("h1").text(w2.join());
context.strokeStyle = "Chartreuse";
context.lineWidth = 1;
context.beginPath();
var minX = 10000000;
var maxX = -10000000;
for(var i = 0; i < this.points.length; i++) {
var x = this.points[i].x;
if(maxX < x) {
maxX = x;
}
if(minX > x) {
minX = x;
}
}
context.beginPath();
var first = true;
for(var x = minX; x <= maxX; x++) {
var l = 0;
for(var k = 0; k < this.points.length; k++) {
var y_k = this.points[k].y;
var w = 1; // w = (x - x0)(x - x1)...(x - x_k-1)(x - x_k+1)...(x - x_n)
for(var j = 0; j < this.points.length; j++) {
if(k != j) {
w *= (x - this.points[j].x);
}
}
l += (y_k * (w / w2[k]));
}
if(first) {
context.moveTo(context.coordSys.convertX2XonCanvas(x), context.coordSys.convertY2YonCanvas(l));
first = false;
}
else {
context.lineTo(context.coordSys.convertX2XonCanvas(x), context.coordSys.convertY2YonCanvas(l));
}
}
context.stroke();
};
};
// End of LagrangeInterpolation
// H(x) = sigma(f_j x a_j(x) + m_j x b_j(x)), j=0,1,...,n m_j = f'(x_j) = 0
var HermiteInterpolation = function (points) {
this.points = points;
this.X = function (j) {
return this.points[j].x;
};
this.Y = function (j) {
return this.points[j].y;
};
this.alpha = function(j, x) {
var n = this.points.length - 1;
if(j != 0 && this.X(j-1) <= x && x <= this.X(j)) {
return Math.pow((x - this.X(j-1)) / (this.X(j) - this.X(j-1)), 2) * (1 + 2 * ( (x - this.X(j)) / (this.X(j-1) - this.X(j)) ) );
}
if(j != n && this.X(j+1) >= x && x >= this.X(j)) {
return Math.pow((x-this.X(j+1))/(this.X(j)-this.X(j+1)),2) * (1 + 2 * ((x - this.X(j)) / (this.X(j+1) - this.X(j)) ) );
}
return 0;
}
this.draw = function (context) {
context.strokeStyle = "Red";
context.lineWidth = 1;
context.beginPath();
var minX = 10000000;
var maxX = -10000000;
for(var i = 0; i < this.points.length; i++) {
var x = this.X(i);
if(maxX < x) {
maxX = x;
}
if(minX > x) {
minX = x;
}
}
context.beginPath();
var n = this.points.length - 1;
var thePoints = this.points;
var first = true;
for(var x = minX; x <= maxX; x++) {
var h = 0;
for(var j = 0; j <= n; j++) {
h += this.Y(j) * this.alpha(j,x);
}
if(first) {
context.moveTo(context.coordSys.convertX2XonCanvas(x), context.coordSys.convertY2YonCanvas(h));
first = false;
}
else {
context.lineTo(context.coordSys.convertX2XonCanvas(x), context.coordSys.convertY2YonCanvas(h));
}
}
context.stroke();
};
};
// End of HermiteInterpolation
var Spline3Interpolation = function (points) {
this.points = points;
this.X = function (j) {
return this.points[j].x;
};
this.Y = function (j) {
return this.points[j].y;
};
this.H = function (j) {
return this.X(j+1) - this.X(j);
};
this.F = function (j, k) {
return (this.Y(k) - this.Y(j)) / (this.X(k) - this.X(j));
};
this.M = new Array();
this.initM = function () {
var n = this.points.length - 1; // 0,1,...,n
if(n <= 1) {
this.M = new Array();
return;
}
var gamma = new Array(); // gamma1, gamma2,...,gamma_n-1
var mu = new Array(); // mu1, mu2,...,mu_n-1
var g = new Array(); // g0, g1,...,g_n
g[0] = 3 * this.F(0, 1);
g[n] = 3 * this.F(n-1, n);
for(var j = 1; j <= n-1; j ++) {
gamma[j] = this.H(j) / (this.H(j-1) + this.H(j));
mu[j] = this.H(j-1)/(this.H(j-1) + this.H(j));
g[j] = 3 * (gamma[j] * this.F(j-1, j) + mu[j] * this.F(j, j+1));
}
// Resolve formula Ax = f
var bb = new Array();
for(var i = 0; i <= n; i++) {
bb[i] = 2;
}
gamma[0] = 0; gamma[n] = 1;
mu[0] = 1; mu[n] = 0;
this.M = zuigan(gamma, bb, mu, g);
};
this.alpha = function(j, x) {
var n = this.points.length - 1;
if(j != 0 && this.X(j-1) <= x && x <= this.X(j)) {
return Math.pow((x - this.X(j-1)) / (this.X(j) - this.X(j-1)), 2) * (1 + 2 * ( (x - this.X(j)) / (this.X(j-1) - this.X(j)) ) );
}
if(j != n && this.X(j+1) >= x && x >= this.X(j)) {
return Math.pow((x-this.X(j+1))/(this.X(j)-this.X(j+1)),2) * (1 + 2 * ((x - this.X(j)) / (this.X(j+1) - this.X(j)) ) );
}
return 0;
}
this.beta = function(j, x) {
var n = this.points.length - 1;
if(j != 0 && this.X(j-1) <= x && x <= this.X(j)) {
return Math.pow((x-this.X(j-1))/(this.X(j)-this.X(j-1)), 2) * (x - this.X(j));
}
if(j != n && this.X(j+1) >= x && x >= this.X(j)) {
return Math.pow((x-this.X(j+1))/(this.X(j)-this.X(j+1)), 2) * (x - this.X(j));
}
return 0;
}
this.draw = function (context) {
if(this.points.length < 3) {
return;
}
context.strokeStyle = "Gold";
context.lineWidth = 1;
context.beginPath();
var minX = 10000000;
var maxX = -10000000;
for(var i = 0; i < this.points.length; i++) {
var x = this.X(i);
if(maxX < x) {
maxX = x;
}
if(minX > x) {
minX = x;
}
}
context.beginPath();
var n = this.points.length - 1;
var thePoints = this.points;
this.initM();
var first = true;
for(var x = minX; x <= maxX; x++) {
var h = 0;
for(var j = 0; j <= n; j++) {
h += this.Y(j) * this.alpha(j,x) + this.M[j] * this.beta(j, x);
}
if(first) {
context.moveTo(context.coordSys.convertX2XonCanvas(x), context.coordSys.convertY2YonCanvas(h));
first = false;
}
else {
context.lineTo(context.coordSys.convertX2XonCanvas(x), context.coordSys.convertY2YonCanvas(h));
}
}
context.stroke();
};
};
// End of Spline3Interpolation
$(window).load(function () {
// test();
// return;
var canvas = $("#canvas").get(0);
var ctx = canvas.getContext('2d');
canvas.width = 1000;
canvas.height = 600;
canvas.clean = function () {
ctx.fillStyle = '#000';
ctx.fillRect(0, 0, canvas.width, canvas.height);
};
canvas.clean();
var coordSys = new CartesianCoord(canvas.width / 4, canvas.height / 2);
ctx.coordSys = coordSys;
var cursor = new Cursor(100, 100, ctx.coordSys);
var points = new Array();
var linearInter = new LinearInterpolation(points);
var lagrangeInter = new LagrangeInterpolation(points);
var hermiteInter = new HermiteInterpolation(points);
var splineInter = new Spline3Interpolation(points);
canvas.redraw = function () {
canvas.clean();
coordSys.draw(ctx);
cursor.draw(ctx);
for (var i in points) {
points[i].draw(ctx);
};
$("input[type=checkbox]").each(function(index, ele) {
if(this.checked) {
eval(this.value).draw(ctx);
}
});
}
canvas.redraw();
$("#canvas").mousemove(function (e){
var p = $(this).position();
cursor.positionX = e.pageX - Math.round(p.left);
cursor.positionY = e.pageY - Math.round(p.top);
canvas.redraw();
});
$("#canvas").mousedown(function (e) {
var p = new Point(cursor.valueX(), cursor.valueY(), coordSys);
var needAdd = true;
for( var k in points) {
if( points[k].x == p.x) {
points[k].y = p.y;
needAdd = false;
break;
}
}
if(needAdd) {
points.push(p);
}
points.sort(function (a, b) {
return a.x - b.x;
});
canvas.redraw();
});
$("input[type=checkbox]").click(function() {
canvas.redraw();
})
});
})();
</script>
</head>
<body>
<div>
<header>
<h1>Interpolations</h1>
</header>
<nav>
<span style="color:BurlyWood ; background-color: black"><input type="checkbox" checked="true" value="linearInter" />Linear Interpolation</span>
<span style="color:Chartreuse ; background-color: black"><input type="checkbox" checked="true" value="lagrangeInter" />Lagrange Interpolation</span>
<span style="color:Red ; background-color: black"><input type="checkbox" checked="true" value="hermiteInter" />Hermite Interpolation</span>
<span style="color:Gold ; background-color: black"><input type="checkbox" checked="true" value="splineInter" />Spline3 Interpolation</span>
</nav>
<div>
<canvas id="canvas"></canvas>
</div>
<footer>
<p>
© Copyright 2012 by Alex Cheng
</p>
</footer>
</div>
</body>
</html>