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mandelbulb.html
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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta http-equiv="X-UA-Compatible" content="ie=edge">
<title>Frakal</title>
<style>
body { background: black; display: flex; justify-content: center; align-items: center; margin: 0; min-height: 100vh; overflow: hidden; }
.panel { display: flex; flex-direction: row-reverse; color: white }
.settings { margin-left: 20px; display: flex; flex-direction: column }
.field { margin-top: 20px; }
.keys { color: #666; }
input { border: white; }
#myCanvas { cursor: pointer }
#rayMinDist { background: black; color: #666;}
</style>
</head>
<body>
<div class="panel">
<canvas id="myCanvas" class="viewport" width=500 height=500></canvas>
<div class="settings">
<h1>Mandelbulb - Real-time 3d fractal<br> in Javascript</h1>
<small>Kamil Kiełczewski <a href="http://airavana.net">Airavana</a></small>
<div class="field">
<div>Instruction</div>
<div>Click on picture and <span class="keys">move mouse</span> around<br>
<span class="keys">A S D W E C</span> keys for change view point position <br>
Push ESC to stop move and unlock mouse
</div>
</div>
<div class="field">
<div>Calculate Light</div>
<div><input type="checkbox" onclick="settingsSetLight(event)" checked></div>
</div>
<div class="field">
<div>
Level of Details (and camera speed) <br>
<span class="keys">Mouse wheel</span> or <span class="keys">+/-</span> keys
</div>
<div>
<input id="rayMinDist" type="text" value="166" disabled >
</div>
</div>
<div class="field">
<div>Info</div>
<div>
<a href="http://blog.hvidtfeldts.net/index.php/2011/06/distance-estimated-3d-fractals-part-i/" class="c">Fraactals 3d/ray-marching</a>
</div>
<div><a href="http://iquilezles.org/www/articles/distfunctions/distfunctions.htm">Distance functions</a></div>
<div><a href="https://github.com/gpujs/gpu.js">GPU JS</a></div>
<div><a href="https://github.com/kamil-kielczewski/fractals">This project</a></div>
<div style="margin-top: 20px">If you like it <a href="https://www.buymeacoffee.com/kamilk">buy me a coffe</a>.</div>
</div>
</div>
</div>
<!-- <script src="https://cdn.rawgit.com/gpujs/gpu.js/87ccce51df9c7162f0f91fde20992268425e75fd/bin/gpu.js"></script> -->
<script src="https://unpkg.com/[email protected]/bin/gpu.js"></script>
<script>
// ----------------------------------------------------
//
// Init params
//
// ----------------------------------------------------
class RaytracerParams {
constructor() {
this.params = {
ray: {rayMaxSteps:512, rayMinDist:0.001, calcLight: 1 },
eye: { x:0, y:1, z:0 },
light: { x:-10, y:10, z:10 },
target: { x:0, y:0, z:1 },
vertical: { x:0, y:1, z: 0}, // wektor pionu
screen: { pxWidth: 0, pxHeight: 0 },
camera: { yaw: 0, pitch: 0, speed: 0.01, rotateSpeed: 0.01, fov: 90, locked: true }
}
}
getParams() {
return this.params;
}
setScreenSize(width, height) {
this.params.screen.pxWidth = width;
this.params.screen.pxHeight = height;
return this;
}
// yaw = left/right, pitch = up/down
// [x,y,z] = position
moveCamera(yawDelta, pitchDelta, forwardBackward, leftRight, upDown) {
let e = this.params.eye;
let t = this.params.target;
let v = this.params.vertical;
let d = this.sub(t,e);
this.params.camera.yaw += yawDelta * this.params.camera.rotateSpeed;
this.params.camera.pitch += pitchDelta * this.params.camera.rotateSpeed;
let yaw = this.params.camera.yaw;
let pitch = this.params.camera.pitch;
// rotate
t.x = e.x + Math.sin(yaw)*Math.cos(pitch);
t.z = e.z + Math.cos(yaw)*Math.cos(pitch);
t.y = e.y + Math.sin(pitch);
// move forward
let fb = this.scale( this.params.camera.speed * forwardBackward , d);
this.addInPlace(e,fb);
this.addInPlace(t,fb);
// move left-right
let lr = this.scale( this.params.camera.speed * leftRight , this.norm(this.cross(v, d)));
this.addInPlace(e,lr);
this.addInPlace(t,lr);
// move up-down
let ud = this.scale( this.params.camera.speed * upDown, v);
this.addInPlace(e,ud);
this.addInPlace(t,ud);
}
calcRayBase() {
let E = this.params.eye;
let T = this.params.target;
let w = this.params.vertical;
let t = this.sub(T,E); // = viewport center
let tn = this.norm(t);
let b = this.cross(w, t);
let bn = this.norm(b);
let vn = this.cross(tn,bn);
let m = this.params.screen.pxHeight;
let k = this.params.screen.pxWidth;
let gx = Math.tan((2*Math.PI*this.params.camera.fov/360)/2);
let gy = gx*m/k;
// P1M is left bottom viewport pixel
let P1M = this.add( tn, this.scale(-gx, bn), this.scale(-gy, vn) ) // chnage C to tn (tn= C-E)
let QX = this.scale(2*gx/(k-1), bn);
let QY = this.scale(2*gy/(m-1), vn);
// Pij = P1M + (i-1)*bnp + (j-1)*vnp
return {E, P1M, QX, QY};
}
cross(a,b) {
let x = a.y*b.z - a.z*b.y;
let y = a.z*b.x - a.x*b.z;
let z = a.x*b.y - a.y*b.x;
return {x,y,z};
}
norm(a) {
let size = 1/Math.sqrt(a.x*a.x + a.y*a.y + a.z*a.z);
return {x: a.x*size, y: a.y*size, z: a.z*size };
}
addInPlace(a,b) {
a.x += b.x;
a.y += b.y;
a.z += b.z;
return a;
}
add(...vs) {
return vs.reduce( (a,b) => ({ x: a.x+b.x, y: a.y+b.y, z: a.z+b.z }) )
// return {
// x: a.x + b.x,
// y: a.y + b.y,
// z: a.z + b.z
// }
}
sub(a,b) {
return this.add(a,this.scale(-1,b));
}
scale(s, a) {
return { x: a.x*s, y: a.y*s, z: a.z*s }
}
}
// ----------------------------------------------------
//
// GPU & Canvas
//
// ----------------------------------------------------
// T - target
// E - eye
// vvn - wektor pionu kamery (normalny)
// fov - kont widzenia (stopnie)
// ar - aspect ratio
// k - liczba pixeli widht
// m - liczba pixeli height
let kernelMarchingRays = function(calcLight, rayMaxSteps, rayMinDist, Ex,Ey,Ez, P1Mx, P1My, P1Mz, QXx, QXy, QXz, QYx, QYy,QYz, Lx, Ly, Lz)
{
let i = this.thread.x;
let j = this.thread.y;
let rx = P1Mx + QXx*(i-1) + QYx*(j-1);
let ry = P1My + QXy*(i-1) + QYy*(j-1);
let rz = P1Mz + QXz*(i-1) + QYz*(j-1);
let sr = 1/Math.sqrt(rx*rx + ry*ry + rz*rz);
let rnx = rx*sr;
let rny = ry*sr;
let rnz = rz*sr;
let totalDistance = 0.0;
let MaximumRaySteps= rayMaxSteps; //255;
let MinimumDistance= rayMinDist; //0.0001;
let stepsVal = 0;
let ppx = 0;
let ppy = 0;
let ppz = 0;
let distance = 0;
let hit = 0;
let dd= [0,0,0];
let hitObjectId = 0; // 0 = no hit
for (let steps=0 ; steps < MaximumRaySteps; steps++) {
ppx = Ex + totalDistance * rnx;
ppy = Ey + totalDistance * rny;
ppz = Ez + totalDistance * rnz;
dd = distScene(ppx,ppy,ppz)
distance = dd[0]; // --- Distance estimator
totalDistance += distance;
if (distance < MinimumDistance) {
stepsVal = steps;
hit=1;
hitObjectId = dd[2];
break
};
}
let iterFrac = dd[1];
let color_r = 0;
let color_g = 0;
let color_b = 0;
// --- calculate normals and light ---
if(calcLight==1) {
let eps = rayMinDist*10;
if(eps>0.00015) { eps = 0.00015; }
dd = distScene(ppx + eps, ppy, ppz);
let nx = dd[0] - distance; // - distScene(ppx - eps, ppy, ppz);
dd = distScene(ppx, ppy + eps, ppz);
let ny = dd[0] - distance; // - distScene(ppx, ppy - eps, ppz);
dd = distScene(ppx, ppy, ppz + eps);
let nz = dd[0] - distance; // - distScene(ppx, ppy, ppz - eps);
let sn = 1/Math.sqrt(nx*nx + ny*ny + nz*nz);
nx = nx * sn;
ny = ny * sn;
nz = nz * sn;
let lx = Lx - ppx;
let ly = Lz - ppy;
let lz = Lz - ppz;
let sl = 1/Math.sqrt(lx*lx + ly*ly + lz*lz);
lx *= sl;
ly *= sl;
lz *= sl;
//let colBcg = hsv2rgb(0.6,1,0.2*(0.4+((i+j))/(1024)));
//let colBcg = [j/4024,i/4024,0];
let colBcg = [0,0,0];
let light = lx * nx + ly*ny + lz*nz;
light = (light+1)/2;
//let col = hsv2rgb(((iterFrac*666)%100)/10, 1, light);
let distLight = -10/Math.log2(rayMinDist);///totalDistance; //1.0/(Math.pow(totalDistance,5));
//if(distLight>1) distLight=1;
let col = hsv2rgb(
(ppx+ppy+ppz),
1,
distLight*8*light*stepsVal/MaximumRaySteps
);
color_r = col[0];
color_g = col[1];
color_b = col[2];
if(hitObjectId==0) {
color_r = colBcg[0];
color_g = colBcg[1];
color_b = colBcg[2];
}
if(hitObjectId==1) {
color_r = 0;
color_g = 1*light;
color_b = 0;
}
//color_r = Math.max(light,0) + hit*0.2;
//color_g = light;
//color_b = light;
} else {
let trace= 2*stepsVal/MaximumRaySteps;
color_r = trace;
color_g = trace;
color_b = trace;
}
this.color(color_r, color_g, color_b ,1);
}
function hsv2rgb(h,s,v) {
//h = 3.1415*2*(h%360)/360;
// h=3.1415*2*h/100; // 100 is from max number of function mandelbulb iterations
let c = v*s;
let k = (h%1)*6;
let x = c*(1 - Math.abs(k%2-1));
let r=0;
let g=0;
let b=0;
if(k>=0 && k<=1) { r=c; g=x }
if(k>1 && k<=2) { r=x; g=c }
if(k>2 && k<=3) { g=c; b=x }
if(k>3 && k<=4) { g=x; b=c }
if(k>4 && k<=5) { r=x; b=c }
if(k>5 && k<=6) { r=c; b=x }
let m = v-c;
return [r+m,g+m,b+m]
}
// x,y,z - point on ray (marching)
function distScene(x,y,z)
{
//let p = sdPlane(x,y,z, 0,1,0,1);
let mm = mandelbulb(x,y,z);
let m = mm[0];
let letIter = mm[1];
let dis = m; //Math.min(p,m);
//let dis = Math.min(p,m);
let objId =1; // 1= plane
if(dis==m) objId =2; // 2= plane
return [ dis, letIter, objId ] ;
}
function sdPlane(px,py,pz, nx,ny,nz,nw)
{
return px*nx + py*ny + pz*nz + nw;
}
function mandelbulb(px,py,pz) {
let zx=px; let zy=py; let zz=pz;
let dr = 1;
let r = 0;
let iterations = 100;
let bailout = 2;
let power = 8;
let j=0;
for (let i=0 ; i < iterations ; i++) {
r = Math.sqrt(zx*zx + zy*zy + zz*zz);
if (r>bailout) break;
// convert to polar coordinates
let theta = Math.acos(zz/r);
let phi = Math.atan(zy,zx);
dr = Math.pow( r, power-1.0)*power*dr + 1.0;
// scale and rotate the point
let zzr = Math.pow( r,power);
theta = theta*power;
phi = phi*power;
// convert back to cartesian coordinates
zx = zzr * sin(theta) * cos(phi);
zy = zzr * sin(phi) * sin(theta);
zz = zzr * cos(theta);
zx+=px;
zy+=py;
zz+=pz;
j++;
}
return [0.5*Math.log(r)*r/dr, j];
}
// Pointer Locking enable
// https://www.html5rocks.com/en/tutorials/pointerlock/intro/
// https://w3c.github.io/pointerlock/
// continue this tommorow...
function canvasOnClick_enablePointerLocking(event) {
if(par.camera.locked) {
let canvas = event.target;
canvas.requestPointerLock = canvas.requestPointerLock ||
canvas.mozRequestPointerLock ||
canvas.webkitRequestPointerLock;
// Ask the browser to lock the pointer
canvas.requestPointerLock();
}
}
function lockChange(e) {
par = raytracerParams.getParams();
par.camera.locked = !par.camera.locked;
}
function initFractalGPU(raytracerParams) {
params = raytracerParams.getParams();
let pxWidth = params.screen.pxWidth;
let pxHeight = params.screen.pxHeight;
let canvas = document.getElementById("myCanvas");
if(canvas) { canvas.remove(); }
canvas = document.createElement('canvas');
canvas.id = 'myCanvas';
document.body.querySelector('.panel').appendChild(canvas);
//canvas.width = pxWidth;
//canvas.height = pxHeight;
canvas.addEventListener('click', canvasOnClick_enablePointerLocking);
document.addEventListener('pointerlockchange', lockChange, false);
const gl = canvas.getContext('webgl2', { premultipliedAlpha: false });
const gpu = new GPU({ canvas, webGl: gl });
const raytracer = gpu.createKernel(kernelMarchingRays)
.setConstants({ pxWidth, pxHeight })
.setOutput([pxWidth, pxHeight])
.setGraphical(true)
.setLoopMaxIterations(10000)
.setFunctions([
sdPlane,
]);
gpu.addFunction(mandelbulb, { returnType: 'Array(2)' });
gpu.addFunction(distScene, { returnType: 'Array(3)' });
gpu.addFunction(hsv2rgb, { returnType: 'Array(3)' });
return raytracer;
}
// ----------------------------------------------------
//
// UX
//
// ----------------------------------------------------
function initGui() {
raytracer.getCanvas().addEventListener('wheel',(event) => { mouseWheel(event); return false; }, false);
raytracer.getCanvas().addEventListener('mousemove',(event) => { mouseMove(event); return false; }, false);
document.onkeypress = (e) => {
if(e.key == "w") moveCamera(1,0,0);
if(e.key == "s") moveCamera(-1,0,0);
if(e.key == "a") moveCamera(0,-1,0);
if(e.key == "d") moveCamera(0,1,0);
if(e.key == "e") moveCamera(0,0,1);
if(e.key == "c") moveCamera(0,0,-1);
if(e.key == "+") mouseWheel({deltaY: -10});
if(e.key == "-") mouseWheel({deltaY: 10});
};
chceckScreenResize();
refresh();
}
function moveCamera(forwardBackward, leftRight, upDown) {
par = raytracerParams.getParams();
par.camera.locked
raytracerParams.moveCamera(0,0, forwardBackward, leftRight, upDown);
refresh();
}
function refresh()
{
// unlock on refresh demand
// (after changing some render parameter by key/mose move)
locked = false;
}
function refreshWindow(timestamp) {
// redraw only if some render parameter change (user move mose, push button etc.)
if(!locked) {
locked = true;
let par = raytracerParams.getParams();
let r = raytracerParams.calcRayBase(); // {E, P1M, Bn, Vn};
raytracer(
par.ray.calcLight, par.ray.rayMaxSteps, par.ray.rayMinDist,
r.E.x, r.E.y, r.E.z,
r.P1M.x, r.P1M.y, r.P1M.z,
r.QX.x, r.QX.y, r.QX.z,
r.QY.x, r.QY.y, r.QY.z,
par.light.x, par.light.y, par.light.z,
);
}
//
window.requestAnimationFrame(refreshWindow);
}
function mouseMove(e) {
par = raytracerParams.getParams();
//let canvas = document.getElementById("myCanvas");
//console.log('clock',canvas.requestPointerLock);
//raytracerParams.moveCamera(e.offsetX/100, e.offsetY/100); // yaw = left/right, pitch = up/down
if(!par.camera.locked) {
raytracerParams.moveCamera(e.movementX, -e.movementY, 0,0,0); // yaw = left/right, pitch = up/down
refresh();
}
}
function mouseWheel(e) {
tmpMouseWhellY += e.deltaY;
tmpMouseWhellY = tmpMouseWhellY>-2000 ? -2000 : tmpMouseWhellY;
tmpMouseWhellY = tmpMouseWhellY<-8000 ? -8000 : tmpMouseWhellY;
n = Math.pow(10, tmpMouseWhellY/1000);
par.ray.rayMinDist = n;
par.camera.speed = n*10;
document.querySelector("#rayMinDist").value = Math.floor((-tmpMouseWhellY-2000)/6);
refresh();
}
function chceckScreenResize() {
window.addEventListener("resize",() => {
//refreshScreenSize();
});
}
function refreshScreenSize() {
//raytracerParams.setScreenSize(window.innerWidth, window.innerHeight);
raytracerParams.setScreenSize(500, 500);
raytracer = initFractalGPU(raytracerParams);
refresh();
}
function settingsSetLight(e) {
par = raytracerParams.getParams();
par.ray.calcLight = 1-par.ray.calcLight;
refresh();
}
function settingsRayMinDist(e, direct=false) {
let n = ("0." + "0".repeat(e.target.value-1) + "1")*1;
par.ray.rayMinDist = n;
par.camera.speed = n*10;
document.querySelector("#rayMinDist").value = e.target.value;
refresh();
//rayMinDist
//par = raytracerParams.getParams();
}
function settingsRayMaxSteps(e) {
par = raytracerParams.getParams();
par.ray.rayMaxSteps = e.target.value;
document.querySelector("#rayMaxSteps").value = par.ray.rayMaxSteps;
refresh();
}
// ----------------------------------------------------
//
// Main
//
// ----------------------------------------------------
let raytracerParams = new RaytracerParams();
let tmpMouseWhellY = -3000;
let locked = false;
let start;
refreshScreenSize();
//let raytracer = initFractalGPU(raytracerParams);
initGui(raytracerParams);
window.requestAnimationFrame(refreshWindow);
</script>
</body>
</html>