/
mandelbrot.html
602 lines (547 loc) · 17.5 KB
/
mandelbrot.html
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<html>
<head>
<title>Mandelbrot set</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="dfMandelbrotFS">
precision highp float;
varying vec2 pos;
uniform vec2 center, step;
uniform int numSteps;
uniform int usePalette;
uniform float ONE;
const int maxNumSteps = 16384;
vec2 quickTwoSum(float a, float b) {
float s = (a + b) * ONE;
float e = b - (s - a);
return vec2(s, e);
}
vec4 twoSumComp(vec2 a_ri, vec2 b_ri) {
vec2 s = (a_ri + b_ri) * ONE;
vec2 v = s - a_ri;
vec2 e = (a_ri - (s - v)) + (b_ri - v);
return vec4(s.x, e.x, s.y, e.y);
}
vec2 df_add(vec2 a, vec2 b) {
vec4 st = twoSumComp(a, b);
st.y += st.z;
st.xy = quickTwoSum(st.x, st.y);
st.y += st.w;
st.xy = quickTwoSum(st.x, st.y);
return st.xy;
}
vec4 twoSubComp(vec2 a_ri, vec2 b_ri) {
vec2 s = a_ri - b_ri;
vec2 v = s - a_ri;
vec2 e = (a_ri - (s - v)) + (-b_ri - v);
return vec4(s.x, e.x, s.y, e.y);
}
vec2 df_sub(vec2 a, vec2 b) {
vec4 st = twoSubComp(a, b);
st.y += st.z;
st.xy = quickTwoSum(st.x, st.y);
st.y += st.w;
st.xy = quickTwoSum(st.x, st.y);
return st.xy;
}
vec4 splitComp(vec2 c)
{
vec2 t = c * 4097.0;
vec2 c_hi = t - (t - c);
vec2 c_lo = c - c_hi;
return vec4(c_hi.x, c_lo.x, c_hi.y, c_lo.y);
}
vec2 twoProd(float a, float b)
{
float p = a * b;
vec4 abS = splitComp(vec2(a,b));
float err = ((abS.x * abS.z - p)
+ abS.x * abS.w + abS.y * abS.z)
+ abS.y * abS.w;
return vec2(p, err);
}
vec2 df_mul(vec2 a, vec2 b) {
vec2 p = twoProd(a.x,b.x);
p.y += a.x * b.y;
p.y += a.y * b.x;
return quickTwoSum(p.x,p.y);
}
vec4 mandelbrotStep(vec4 z, vec4 c) {
vec2 zx = df_add(df_sub(df_mul(z.xy,z.xy), df_mul(z.zw, z.zw)), c.xy);
vec2 zy = df_add(df_mul(vec2(2.0,0), df_mul(z.xy,z.zw)), c.zw);
return vec4(zx, zy);
}
float sqrdistance(vec4 val) {
return val.x*val.x + val.z*val.z;
}
int mod(int a, int b) {
float af = float(a);
float bf = float(b);
return int(floor(af-floor(af/bf)*bf));
}
vec4 getPaletteColor(int steps) {
int idx = mod(steps, 7);
if (idx == 0)
return vec4(0, 0, 1, 1);
if (idx == 1)
return vec4(0, 1, 0, 1);
if (idx == 2)
return vec4(0, 1, 1, 1);
if (idx == 3)
return vec4(1, 0, 0, 1);
if (idx == 4)
return vec4(1, 0, 1, 1);
if (idx == 5)
return vec4(1, 1, 0, 1);
return vec4(1, 1, 1, 1);
}
vec4 assignColor(vec4 z, int steps, int numSteps) {
if (usePalette == 0)
return vec4(abs(.5*z.x), float(step)/float(numSteps), abs(.5*z.z), 1);
float nu = log(log(sqrdistance(z))/2.0)/log(2.0);
vec4 a = getPaletteColor(steps);
vec4 b = getPaletteColor(steps+1);
return a * nu + b * (1.0 - nu);
}
void main(void) {
vec4 z = vec4(0);
vec4 c = vec4(
df_add(vec2(center.x, 0), df_mul(vec2(step.x, 0), vec2(pos.x, 0))),
df_sub(vec2(center.y, 0), df_mul(vec2(step.y, 0), vec2(pos.y, 0))));
for(int cnt = 0; cnt < maxNumSteps; cnt++) {
if (cnt == numSteps) break;
if (sqrdistance(z) >= 4.0) {
gl_FragColor = assignColor(z, cnt, numSteps);
return;
}
z = mandelbrotStep(z, c);
}
gl_FragColor = vec4(0, 0, 0, 1.0);
}
</script>
<script type="x-shader/x-fragment" id="mandelbrotFS">
precision highp float;
varying vec2 pos;
uniform vec2 center, step;
uniform int numSteps;
uniform int usePalette;
const int maxNumSteps = 16384;
float sqrdistance(vec2 val) {
return val.x*val.x+val.y*val.y;
}
vec2 mandelbrotStep(vec2 z, vec2 c) {
return vec2(z.x*z.x-z.y*z.y+c.x, 2.0*z.x*z.y + c.y);
}
int mod(int a, int b) {
float af = float(a);
float bf = float(b);
return int(floor(af-floor(af/bf)*bf));
}
vec4 getPaletteColor(int steps) {
int idx = mod(steps, 7);
if (idx == 0)
return vec4(0, 0, 1, 1);
if (idx == 1)
return vec4(0, 1, 0, 1);
if (idx == 2)
return vec4(0, 1, 1, 1);
if (idx == 3)
return vec4(1, 0, 0, 1);
if (idx == 4)
return vec4(1, 0, 1, 1);
if (idx == 5)
return vec4(1, 1, 0, 1);
return vec4(1, 1, 1, 1);
}
vec4 assignColor(vec2 z, int steps, int numSteps) {
if (usePalette == 0)
return vec4(abs(.5*z.x), float(step)/float(numSteps), abs(.5*z.y), 1);
float nu = log(log(sqrdistance(z))/2.0)/log(2.0);
vec4 a = getPaletteColor(steps);
vec4 b = getPaletteColor(steps+1);
return a * nu + b * (1.0 - nu);
}
void main(void) {
vec2 z = vec2(0, 0);
vec2 c = vec2(center.x + step.x*pos.x, center.y - step.y*pos.y);
for(int cnt = 0; cnt < maxNumSteps; cnt++) {
if (cnt == numSteps) break;
if (sqrdistance(z) >= 4.0) {
gl_FragColor = assignColor(z, cnt, numSteps);
return;
}
z = mandelbrotStep(z, c);
}
gl_FragColor = vec4(0, 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">
class GLContext {
constructor(canvas) {
if (canvas == null)
throw 'Can not find canvas';
const ctx = canvas.getContext('webgl2');
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,
};
}
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;
}
compileShaderById(id) {
const glCtx = this.getGLContext();
const element = document.getElementById(id);
if (element == null) {
throw 'Can not find shader by element id ' + 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;
}
setUniform1i(name, a) {
const glCtx = this.getGLContext();
const prog = glCtx.getParameter(glCtx.CURRENT_PROGRAM);
const idx = glCtx.getUniformLocation(prog, name);
glCtx.uniform1i(idx, a);
}
setUniform1f(name, a) {
const glCtx = this.getGLContext();
const prog = glCtx.getParameter(glCtx.CURRENT_PROGRAM);
const idx = glCtx.getUniformLocation(prog, name);
glCtx.uniform1f(idx, a);
}
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());}
}
class Complex {
constructor(re, im) { this.re = re; this.im = im; }
sub(p) { return new Complex(this.re-p.re, this.im-p.im); }
add(p) { return new Complex(this.re+p.re, this.im+p.im); }
mul(x) {
if (x instanceof Complex)
return new Complex(x.re*this.re - x.im*this.im, x.re*this.im + x.im*this.re);
return new Complex(x*this.re, x*this.im);
}
}
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);
const prog = ctx.linkProgram(['passThruVS', 'mandelbrotFS'].map(_ => ctx.compileShaderById(_)));
const dprog = ctx.linkProgram(['passThruVS', 'dfMandelbrotFS'].map(_ => ctx.compileShaderById(_)));
const sprog = ctx.linkProgram(['passThruVS', 'solidColorFS'].map(_ => ctx.compileShaderById(_)));
this._ctx = ctx;
this._mandelProgram = prog;
this._dfMandelProgram = dprog;
this._solidProgram = sprog;
this._halfCanvasDim = new Point(canvas.clientWidth, canvas.clientHeight).mul(.5);
this._scale = 4.0/Math.min(canvas.clientWidth, canvas.clientHeight);
this._center = new Point(0.0, 0.0);
const stepsMatch = window.location.search.match(/[&?]numSteps=(\d+)/);
this._numSteps = stepsMatch ? Number(stepsMatch[1]) : 256;
if (window.location.search.indexOf('overfloat') >= 0) {
this._center = new Point(0.2807024158978315, -0.011177972555812295);
this._scale = 4.0/(2e6*Math.min(canvas.clientWidth, canvas.clientHeight));
}
this._forceDF = window.location.search.indexOf('forceDF') >= 0;
this._noDF = window.location.search.indexOf('noDF') >= 0;
this._usePalette = window.location.search.indexOf('usePalette') >= 0;
this._configureMouseEventHandlers(canvas);
this._configureTouchEventHandlers(canvas);
}
_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]);
}
renderOnCpu(sx,sy,ex,ey) {
if (sx == undefined) sx = -1;
if (sy == undefined) sy = -1;
if (ex == undefined) ex = 1;
if (ey == undefined) ey = 1;
const canvasDim = this._halfCanvasDim.mul(2.0);
const topLeft = this.canvas2rendercoord(0,0);
const bottomRight = this.canvas2rendercoord(canvasDim.x, canvasDim.y);
const dim = bottomRight.sub(topLeft);
const ctx = this._ctx;
ctx.getGLContext().useProgram(this._solidProgram);
for(var y = sy; y <= ey; y += 2.0/canvasDim.y)
for(var x = sx; x <= ex; x += 2.0/canvasDim.x) {
var z = new Complex(0, 0);
const c = new Complex(topLeft.x + dim.x*.5*(x+1.0), bottomRight.y - dim.y*.5*(y+1.0));
var cnt = 0;
while ( cnt < this._numSteps && z.re*z.re+z.im*z.im < 4.0) {
z = z.mul(z).add(c);
cnt += 1;
}
if (cnt == this._numSteps) {
ctx.setUniform4f('color', 0, 0, 0, 1);
} else {
ctx.setUniform4f('color', Math.abs(.5*z.re), cnt/256, Math.abs(.5*z.im), 1);
}
ctx.draw2DArray(ctx.PRIMITIVES.POINTS, 'coord', [x, y]);
}
}
render() {
const ctx = this._ctx;
const scale = this._scale;
const step = this._halfCanvasDim.mul(scale);
if (this._noDF)
ctx.getGLContext().useProgram(this._mandelProgram);
else if (this._forceDF)
ctx.getGLContext().useProgram(this._dfMandelProgram);
else
ctx.getGLContext().useProgram(scale >= 1e-7 ? this._mandelProgram : this._dfMandelProgram);
ctx.setUniform2f('center', this._center.x, this._center.y);
ctx.setUniform2f('step', step.x, step.y);
ctx.setUniform1i('numSteps', this._numSteps);
ctx.setUniform1i('usePalette', this._usePalette ? 1 : 0);
ctx.setUniform1f('ONE', 1.0);
this.drawQuad(-1,-1, 1, 1);
}
}
var renderer = null;
function configureRenderer() {
const runBenchmark = window.location.search.indexOf('benchmark') > 0;
const canvas = document.getElementById('canvas');
if (!runBenchmark) {
canvas.width = window.innerWidth;
canvas.height = window.innerHeight;
}
try {
renderer = new ZoomRenderer(canvas);
} catch (e) {
alert('Inialization failed: ' + e);
return;
}
if (!runBenchmark) {
return renderer.render();
}
var animCount = 0;
var lastTime = 0;
var avgFPS = 0;
const callback = function(animTime) {
if (lastTime > 0) {
const curFPS = 1000.0/(animTime - lastTime);
avgFPS += (curFPS - avgFPS) / animCount;
}
lastTime = animTime;
renderer.render();
renderer.adjustScaleWithInvariantPoint(.96, 591.7, 400);
if (animCount++ == 256) {
return console.log("Average FPS is " + avgFPS);
}
window.requestAnimationFrame(callback);
};
window.requestAnimationFrame(callback);
}
</script>
<body onLoad="configureRenderer();">
<H1>Mandelbrot Set rendered in fragment shader</H1>
<canvas id="canvas" width="1024px" height="1024px"></canvas>
</body>
</html>