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fractal.htm
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fractal.htm
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<!DOCTYPE html>
<html>
<head>
<script>
var GRAPH1 = null;
var GRAPH2 = null;
function ComplexGraph(canvas, origin)
{
this.Color = "#0000ff";
this.Origin = origin;
this.Scale = 100.0; // Unit
this.Canvas = canvas;
this.Context = null;
this.R=1.0;
this.I=0.5;
this.Dragable = true;
this.Active = false;
this.Dragging = false;
}
ComplexGraph.prototype.RelativeMouseCoordinates = function (event) {
var totalOffsetX = 0;
var totalOffsetY = 0;
var canvasX = 0;
var canvasY = 0;
var currentElement = this.Canvas;
do{
totalOffsetX += currentElement.offsetLeft - currentElement.scrollLeft;
totalOffsetY += currentElement.offsetTop - currentElement.scrollTop;
}
while(currentElement = currentElement.offsetParent)
canvasX = event.pageX - totalOffsetX;
canvasY = event.pageY - totalOffsetY;
graphX = canvasX - this.Origin[0];
graphY = -(canvasY - this.Origin[1]);
return {x:graphX, y:graphY}
}
ComplexGraph.prototype.MouseMove = function(event) {
coords = this.RelativeMouseCoordinates(event);
if (this.Dragging) {
// Just move the tip to the mouse.
this.R = coords.x / this.Scale;
this.I = coords.y / this.Scale;
this.Draw();
} else {
// Haw far is the event away from the tip (in pixels).
var tx = this.R*100.0;
var ty = this.I*100.0;
tx = tx - coords.x;
ty = ty - coords.y;
// Distance squared
dist = tx * tx + ty * ty;
if (dist <= 25.0 && ! this.Active) {
this.Active = true;
this.Draw();
}
if (dist > 25.0 && this.Active) {
this.Active = false;
this.Draw();
}
}
}
ComplexGraph.prototype.MouseDown = function() {
if (this.Active) {
this.Dragging = true;
}
}
ComplexGraph.prototype.MouseUp = function() {
this.Dragging = false;
}
ComplexGraph.prototype.Draw = function () {
var c=this.Canvas;
var r = this.R;
var i = this.I;
var canvOK=1;
try {c.getContext("2d");}
catch (er) {canvOK=0;}
if (canvOK==1) {
this.Radius = Math.sqrt(r*r + i*i);
this.Theta = Math.atan2(i,r) * 180 / Math.PI;
if (this.Theta < 0.0) {
this.Theta += 360.0;
}
var ctx=c.getContext("2d");
ctx.clearRect (this.Origin[0]-200 , this.Origin[1]-200, 400 , 410);
// Draw the unit circle.
ctx.beginPath();
ctx.arc(this.Origin[0],this.Origin[1],100,0,2*Math.PI);
ctx.strokeStyle="#A0A0A0";
ctx.stroke();
ctx.closePath();
// Draw the Axes vector
ctx.beginPath();
ctx.moveTo(this.Origin[0]-180,this.Origin[1]);
ctx.lineTo(this.Origin[0]+180,this.Origin[1]);
ctx.strokeStyle="#000000";
ctx.stroke();
ctx.moveTo(this.Origin[0],this.Origin[1]-180);
ctx.lineTo(this.Origin[0],this.Origin[1]+180);
ctx.strokeStyle="#000000";
ctx.stroke();
ctx.closePath();
// Draw the complex vector
ctx.beginPath();
ctx.moveTo(this.Origin[0],this.Origin[1]);
ctx.lineTo(this.Origin[0] + r*this.Scale, this.Origin[1] - i*this.Scale);
ctx.strokeStyle=this.Color;
ctx.stroke();
ctx.closePath();
// Draw the angle theta arc.
if (this.Dragable) {
ctx.beginPath();
ctx.strokeStyle=this.Color;
ctx.arc(this.Origin[0],this.Origin[1],20,-this.Theta * Math.PI/ 180.0, 0.0);
ctx.stroke();
ctx.closePath();
}
if (this.Dragable) {
// Active end spot
ctx.beginPath();
ctx.arc(this.Origin[0] + r*this.Scale, this.Origin[1] - i*this.Scale, 5, 0, 2*Math.PI);
ctx.closePath();
if (this.Active) {
ctx.fillStyle="#FFFF00";
} else {
ctx.fillStyle=this.Color;
}
ctx.fill();
} else {
// Draw an arrow tip.
ctx.beginPath();
var tx = this.Origin[0] + r*this.Scale;
var ty = this.Origin[1] - i*this.Scale;
// Tip is origin. end point of barb.
var x = -15;
var y = +8;
// sin and cos from normalized complex vector
s = -i/this.Radius; // Rotation is opposite because y is flipped.
c = r/this.Radius;
// Rotate barb
var t1x = tx + x*c - y*s;
var t1y = ty + x*s + y*c;
var t2x = tx + x*c + y*s;
var t2y = ty + x*s - y*c;
// draw the barb
ctx.beginPath();
ctx.strokeStyle=this.Color;
ctx.moveTo(tx,ty);
ctx.lineTo(t1x,t1y);
ctx.stroke();
ctx.moveTo(tx,ty);
ctx.lineTo(t2x,t2y);
ctx.stroke();
ctx.closePath();
}
// Draw the complex coordinates label
ctx.font="30px Arial";
var coordStr = "";
ctx.fillStyle=this.Color;
coordStr = coordStr + r.toFixed(1);
coordStr = coordStr + " + ";
coordStr = coordStr + i.toFixed(1) + "i";
ctx.fillText(coordStr, this.Origin[0]-195, this.Origin[1]-170);
// Draw the polar coordinates
var coordStr = "Radius: ";
coordStr = coordStr + this.Radius.toFixed(1);
coordStr = coordStr + ", Theta: ";
coordStr = coordStr + this.Theta.toFixed(1);
ctx.font="20px Arial";
ctx.fillStyle=this.Color;
ctx.fillText(coordStr, this.Origin[0]-195, this.Origin[1]+205);
}
}
// I should really make draw use this method.
// For drawing the multiplcation composition.
ComplexGraph.prototype.DrawVector = function (r,i, color, startTheta, endTheta) {
var c=this.Canvas;
var ctx=c.getContext("2d");
// Draw the complex vector
ctx.beginPath();
ctx.moveTo(this.Origin[0],this.Origin[1]);
ctx.lineTo(this.Origin[0] + r*this.Scale, this.Origin[1] - i*this.Scale);
ctx.strokeStyle=color;
ctx.stroke();
ctx.closePath();
if (this.Dragable) {
// Active end spot
ctx.beginPath();
ctx.arc(this.Origin[0] + r*this.Scale, this.Origin[1] - i*this.Scale, 5, 0, 2*Math.PI);
ctx.closePath();
if (this.Active) {
ctx.fillStyle="#FFFF00";
} else {
ctx.fillStyle=color;
}
ctx.fill();
} else {
// Draw an arrow tip.
ctx.beginPath();
var tx = this.Origin[0] + r*this.Scale;
var ty = this.Origin[1] - i*this.Scale;
// Tip is origin. end point of barb.
var x = -15;
var y = +8;
// sin and cos from normalized complex vector
var radius = Math.sqrt(i*i + r*r);
s = -i/radius; // Rotation is opposite because y is flipped.
c = r/radius;
// Rotate barb
var t1x = tx + x*c - y*s;
var t1y = ty + x*s + y*c;
var t2x = tx + x*c + y*s;
var t2y = ty + x*s - y*c;
// draw the barb
ctx.beginPath();
ctx.strokeStyle=color;
ctx.moveTo(tx,ty);
ctx.lineTo(t1x,t1y);
ctx.stroke();
ctx.moveTo(tx,ty);
ctx.lineTo(t2x,t2y);
ctx.stroke();
ctx.closePath();
}
}
// I should really make draw use this method.
// For drawing the multiplcation composition.
ComplexGraph.prototype.DrawArc = function (color, startTheta, endTheta) {
var c=this.Canvas;
var ctx=c.getContext("2d");
// Draw the angle theta arc.
ctx.beginPath();
ctx.strokeStyle=color;
ctx.arc(this.Origin[0],this.Origin[1],20, -endTheta*Math.PI/ 180.0, -startTheta*Math.PI/ 180.0);
ctx.stroke();
ctx.closePath();
}
function updateResult() {
x = (GRAPH1.R * GRAPH2.R) - (GRAPH1.I * GRAPH2.I);
y = (GRAPH1.R * GRAPH2.I) + (GRAPH1.I * GRAPH2.R);
GRAPH3.R = x;
GRAPH3.I = y;
}
function mouseMove(event)
{
if (GRAPH1) GRAPH1.MouseMove(event);
if (GRAPH2) GRAPH2.MouseMove(event);
if (GRAPH1.Dragging || GRAPH2.Dragging) {
updateResult();
GRAPH3.Draw();
GRAPH3.DrawVector(GRAPH1.R,GRAPH1.I, GRAPH1.Color, 0, GRAPH1.Theta);
GRAPH3.DrawArc(GRAPH1.Color, 0, GRAPH1.Theta);
GRAPH3.DrawArc(GRAPH2.Color, GRAPH1.Theta, GRAPH1.Theta + GRAPH2.Theta);
}
}
function mouseDown()
{
if (GRAPH1) GRAPH1.MouseDown();
if (GRAPH2) GRAPH2.MouseDown();
}
function mouseUp()
{
if (GRAPH1) GRAPH1.MouseUp();
if (GRAPH2) GRAPH2.MouseUp();
}
function main()
{
var canvas = document.getElementById("myCanvas")
var canvOK=1;
try {canvas.getContext("2d");}
catch (er) {
alert("Could not initialize canvas");
return;
}
var ctx=canvas.getContext("2d");
GRAPH1=new ComplexGraph(canvas, [200, 250]);
GRAPH1.Color = "#0000FF"
GRAPH2=new ComplexGraph(canvas, [600, 250]);
GRAPH2.Color = "#00A000"
GRAPH3=new ComplexGraph(canvas, [1000, 250]);
GRAPH3.Color = "#000000"
GRAPH3.Dragable = false;
GRAPH1.Draw();
GRAPH2.Draw();
updateResult();
GRAPH3.Draw();
GRAPH3.DrawVector(GRAPH1.R,GRAPH1.I, GRAPH1.Color, 0, GRAPH1.Theta);
GRAPH3.DrawArc(GRAPH1.Color, 0, GRAPH1.Theta);
GRAPH3.DrawArc(GRAPH2.Color, GRAPH1.Theta, GRAPH1.Theta + GRAPH2.Theta);
// Draw titles on the graphs
ctx.beginPath();
ctx.font="30px Arial";
ctx.fillStyle=GRAPH1.Color;
ctx.fillText("A", GRAPH1.Origin[0]-10, GRAPH1.Origin[1]-225);
ctx.fillStyle=GRAPH2.Color;
ctx.fillText("B", GRAPH2.Origin[0]-10, GRAPH2.Origin[1]-225);
ctx.fillStyle=GRAPH3.Color;
ctx.fillText("A*B", GRAPH3.Origin[0]-20, GRAPH3.Origin[1]-225);
ctx.closePath();
}
</script>
<body onload="main()">
<canvas id="myCanvas" width="1200" height="470" style="border:1px solid #d3d3d3;"
onmousemove="mouseMove(event)"
onmousedown="mouseDown()"
onmouseup="mouseUp()"
>
Your browser does not support the HTML5 canvas tag.</canvas>
</br>
<a href="mandelbrot.htm">Mandelbrot</a>
</body>
</html>