/
lyapunov.html
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/
lyapunov.html
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<html>
<head>
<title>Lyapunov exponent</title>
</head>
<script type="x-shader/x-vertex" id="passThruVS">
attribute vec2 coord;
varying vec2 pos;
void main(void) {
pos = coord;
gl_Position = vec4(coord, 0, 1.0);
gl_PointSize = 1.0;
}
</script>
<script type="x-shader/x-fragment" id="lyapunovFS">
precision highp float;
varying vec2 pos;
uniform vec2 center, step;
const float positiveScaleFactor = 1.0;
const float negativeScaleFactor = -1.0;
const int preheatSteps = 10;
const int computeSteps = 10;
vec2 logisticStep(vec2 args, vec2 param);
float computeLyapunovExponent(vec2 pos) {
vec2 args = vec2(.5, 0.0);
// preheat
for(int cnt = 0; cnt < preheatSteps; ++cnt)
args = logisticStep(args, pos);
args.y = 0.0;
for(int cnt = 0; cnt < computeSteps; ++cnt)
args = logisticStep(args, pos);
return args.y;
}
void main(void) {
vec2 c = vec2(center.x + step.x*pos.x, center.y - step.y*pos.y);
float lambda = computeLyapunovExponent(c);
if (lambda > 0.0)
gl_FragColor = vec4(0.0, 0.0, positiveScaleFactor * lambda, 1.0);
else
gl_FragColor = vec4(negativeScaleFactor * lambda, negativeScaleFactor * lambda, 0.0, 1.0);
}
</script>
<script type="x-shader/x-fragment" id="solidColorFS">
precision highp float;
uniform vec4 color;
void main(void) {
gl_FragColor = color;
}
</script>
<script type="text/javascript">
function generateStepFunction(str) {
var rc = 'vec2 logisticStep(vec2 args, vec2 param) {';
for(var cnt = 0; cnt < str.length; ++cnt) {
const r = str[cnt] == 'A' ? 'param.x' : 'param.y';
rc += 'args.x = ' + r + ' * args.x * (1.0 - args.x);';
rc += 'args.y += log(abs(' + r + ' * (1.0 - 2.0 * args.x)));';
}
return rc + ' return args; }';
}
class GLContext {
constructor(canvas) {
if (canvas == null)
throw 'Can not find canvas';
const ctx = canvas.getContext('webgl');
if (ctx == null)
throw 'Can not get WebGL context...';
ctx.viewport(0, 0, canvas.clientWidth, canvas.clientHeight);
ctx.clearColor(0, 0, 0, 1.0);
ctx.clear(ctx.COLOR_BUFFER_BIT);
this._ctx = ctx;
this.PRIMITIVES = {
POINTS: ctx.POINTS,
LINE_STRIP: ctx.LINE_STRIP,
LINES: ctx.LINES,
TRIANGLE_STRIP: ctx.TRIANGLE_STRIP,
TRIANGLES: ctx.TRIANGLES,
};
this.VERTEX_SHADER = ctx.VERTEX_SHADER;
this.FRAGMENT_SHADER = ctx.FRAGMENT_SHADER;
}
getGLContext() {
if (!this._ctx) throw 'Missing context';
return this._ctx;
}
compileShader(type, source) {
const glCtx = this.getGLContext();
var rc = glCtx.createShader(type);
glCtx.shaderSource(rc, source);
glCtx.compileShader(rc);
if (!glCtx.getShaderParameter(rc, glCtx.COMPILE_STATUS)) {
throw glCtx.getShaderInfoLog(rc) + ' in ' + source;
}
return rc;
}
getElementById(id) {
const element = document.getElementById(id);
if (element == null) {
throw 'Can not find shader by element id ' + id;
}
return element;
}
compileShaderById(id) {
const glCtx = this.getGLContext();
const element = this.getElementById(id);
const source = element.innerHTML;
if (element.type === 'x-shader/x-vertex') {
return this.compileShader(glCtx.VERTEX_SHADER, source);
}
if (element.type === 'x-shader/x-fragment') {
return this.compileShader(glCtx.FRAGMENT_SHADER, source);
}
throw 'Unknown shader type ' + element.type;
}
linkProgram(shaders) {
const glCtx = this.getGLContext();
const rc = glCtx.createProgram();
for(var cnt = 0; cnt < shaders.length; cnt++) {
if (!shaders[cnt]) {
throw 'Can not link program with null shaders';
}
glCtx.attachShader(rc, shaders[cnt]);
}
glCtx.linkProgram(rc);
if (!glCtx.getProgramParameter(rc, glCtx.LINK_STATUS)) {
throw glCtx.getProgramInfoLog(rc);
}
return rc;
}
setUniform2f(name, a, b) {
const glCtx = this.getGLContext();
const prog = glCtx.getParameter(glCtx.CURRENT_PROGRAM);
const idx = glCtx.getUniformLocation(prog, name);
glCtx.uniform2f(idx, a, b);
}
setUniform4f(name, a, b, c, d) {
const glCtx = this.getGLContext();
const prog = glCtx.getParameter(glCtx.CURRENT_PROGRAM);
const idx = glCtx.getUniformLocation(prog, name);
glCtx.uniform4f(idx, a, b, c, d);
}
draw2DArray(type, name, arr) {
const glCtx = this.getGLContext();
const prog = glCtx.getParameter(glCtx.CURRENT_PROGRAM);
const idx = glCtx.getAttribLocation(prog, name);
var buf = glCtx.createBuffer();
glCtx.bindBuffer(glCtx.ARRAY_BUFFER, buf);
glCtx.bufferData(glCtx.ARRAY_BUFFER, new Float32Array(arr), glCtx.STATIC_DRAW);
glCtx.enableVertexAttribArray(idx);
glCtx.vertexAttribPointer(idx, 2, glCtx.FLOAT, false, 0, 0);
glCtx.drawArrays(type, 0, arr.length/2);
glCtx.deleteBuffer(buf);
}
}
class Point {
constructor(x, y) { this.x = x; this.y = y; }
sub(p) { return new Point(this.x-p.x, this.y-p.y); }
add(p) { return new Point(this.x+p.x, this.y+p.y); }
mul(a) { return new Point(a*this.x, a*this.y); }
len2() { return this.x*this.x + this.y*this.y;}
len() { return Math.sqrt(this.len2());}
}
function TouchState(event) {
const rc = {};
for(var cnt = 0; cnt < event.touches.length; ++cnt) {
const touch = event.touches[cnt];
rc[touch.identifier] = new Point(touch.clientX, touch.clientY);
}
return rc;
}
function comparableTouches(a, b) {
if (a == null || b == null) return false;
const akeys = Object.keys(a);
const bkeys = Object.keys(b);
for(var cnt = 0; cnt < akeys.length; ++cnt) {
if (!bkeys.includes(akeys[cnt])) return false;
}
return true;
}
class ZoomRenderer {
constructor(canvas) {
const ctx = new GLContext(canvas);
this._ctx = ctx;
this._halfCanvasDim = new Point(canvas.clientWidth, canvas.clientHeight).mul(.5);
this._scale = 2.0/Math.min(canvas.clientWidth, canvas.clientHeight);
this._center = new Point(3.0, 3.0);
this._configureMouseEventHandlers(canvas);
this._configureTouchEventHandlers(canvas);
const seqMatch = window.location.search.match(/sequence=([AB]+)/);
if (seqMatch)
this._compileProgram(seqMatch[1]);
else
this._compileProgram('AABAB');
}
_compileProgram(sequence) {
const ctx = this._ctx;
const gl = ctx.getGLContext();
const vertexShader = ctx.compileShaderById('passThruVS');
const numSteps = 300;
var fragmentShaderSource = ctx.getElementById('lyapunovFS').innerHTML
.replace('positiveScaleFactor = 1.0', 'positiveScaleFactor = ' + (3.0/numSteps))
.replace('negativeScaleFactor = -1.0', 'negativeScaleFactor = ' + (-2.5/numSteps))
.replace('preheatSteps = 10', 'preheatSteps = ' + Math.floor(50/sequence.length))
.replace('computeSteps = 10', 'computeSteps = ' + Math.floor(numSteps/sequence.length));
fragmentShaderSource += generateStepFunction(sequence);
const fragmentShader = ctx.compileShader(ctx.FRAGMENT_SHADER, fragmentShaderSource);
const prog = ctx.linkProgram([vertexShader, fragmentShader]);
gl.deleteShader(vertexShader);
gl.deleteShader(fragmentShader);
gl.useProgram(prog);
}
_configureMouseEventHandlers(canvas) {
canvas.addEventListener('click', (event) => {
const clickTime = Date.now();
// Doubleclick is two clicks less than .3 seconds apart
if (clickTime - this._prevClickTime > 300) {
this._prevClickTime = clickTime;
return;
}
this.adjustScaleWithInvariantPoint(.5, event.offsetX, event.offsetY);
this._prevClickTime = 0;
this.render();
});
canvas.addEventListener('wheel', (event) => {
const wheelTime = Date.now();
if (event.deltaY == 0) return;
// Limit number of scroll events to 20 per seconds
if (wheelTime - this._prevWheelTime < 50) {
event.preventDefault();
return;
}
this._prevWheelTime = wheelTime;
const factor = event.deltaY > 0 ? .8 : 1.25;
this.adjustScaleWithInvariantPoint(factor, event.offsetX, event.offsetY);
this.render();
event.preventDefault();
});
canvas.addEventListener('mousedown', (event) => {
this._dragStart = new Point(event.offsetX, event.offsetY);
this._dragStartCenter = new Point(this._center.x, this._center.y);
});
canvas.addEventListener('mousemove', (event) => {
const dragStart = this._dragStart;
if (dragStart == null) return;
const moveTime = Date.now();
if (moveTime - this._prevMoveTime < 50) return;
this._prevMoveTime = moveTime;
const offs = new Point(event.offsetX, event.offsetY).sub(dragStart);
this._center = this._dragStartCenter.sub(offs.mul(this._scale));
this.render();
});
canvas.addEventListener('mouseup', (event) => {
this._dragStart = null;
this._dragStartCenter = null;
});
this._prevClickTime = 0;
this._prevWheelTime = 0;
this._prevMoveTime = 0;
this._dragStart = null;
this._dragStartCenter = null;
}
_configureTouchEventHandlers(canvas) {
try { TouchEvent; } catch(e) {
return;
}
console.log("Configuring touch event handlers");
canvas.addEventListener('touchstart', (event) => {
this._touchStart = TouchState(event);
this._touchStartCenter = this._center;
this._touchStartScale = this._scale;
});
canvas.addEventListener('touchend', (event) => {
this._touchStart = null;
this._touchStartCenter = null;
});
canvas.addEventListener('touchmove', (event) => {
if (this._touchStart == null) return;
const state = TouchState(event);
if (!comparableTouches(state, this._touchStart)) return;
event.preventDefault();
const touchTime = Date.now();
if (touchTime - this._prevTouchTime < 50) return;
this._prevTouchTime = touchTime;
const touchKeys = Object.keys(this._touchStart);
if (touchKeys.length == 1) {
const key = touchKeys[0];
const offs = state[key].sub(this._touchStart[key]);
this._center = this._touchStartCenter.sub(offs.mul(this._scale));
this.render();
}
if (touchKeys.length == 2) {
const a = touchKeys[0];
const b = touchKeys[1];
const mid = this._touchStart[a].add(this._touchStart[b]).mul(.5);
const distStart = this._touchStart[a].sub(this._touchStart[b]).len();
const dist = state[a].sub(state[b]).len();
this._scale = this._touchStartScale;
this._center = this._touchStartCenter;
this.adjustScaleWithInvariantPoint(distStart/dist, mid.x, mid.y);
this.render();
}
});
this._prevTouchTime = 0;
this._touchStart = null;
this._touchStartCenter = null;
}
canvas2rendercoord(x, y) {
const offs = new Point(x, y).sub(this._halfCanvasDim);
return this._center.add(offs.mul(this._scale));
}
adjustScaleWithInvariantPoint(factor, invX, invY) {
const offs = new Point(invX, invY).sub(this._halfCanvasDim);
this._center = this._center.add(offs.mul((1-factor)*this._scale));
this._scale *= factor;
}
drawQuad(x0, y0, x1, y1) {
this._ctx.draw2DArray(this._ctx.PRIMITIVES.TRIANGLE_STRIP, 'coord', [x0, y0, x1, y0, x0, y1, x1, y1]);
}
render() {
const ctx = this._ctx;
const scale = this._scale;
const step = this._halfCanvasDim.mul(scale);
ctx.setUniform2f('center', this._center.x, this._center.y);
ctx.setUniform2f('step', step.x, step.y);
this.drawQuad(-1,-1, 1, 1);
}
}
var renderer = null;
function configureRenderer() {
const canvas = document.getElementById('canvas');
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
try {
renderer = new ZoomRenderer(canvas);
} catch (e) {
alert('Inialization failed: ' + e);
return;
}
renderer.render();
}
</script>
<body onLoad="configureRenderer();">
<H1>Lyapunov exponent rendered in fragment shader</H1>
<canvas id="canvas" width="1024px" height="1024px"></canvas>
</body>
</html>