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index.html
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<html>
<head>
<meta charset='UTF-8'/>
<title>Probability Distribution of Hydrogen Atom</title>
<link rel="stylesheet" type="text/css" href="./css/style.css">
</head>
<body>
<a id="github-link" href="https://github.com/cihadturhan/he-prob-density">
<img style="position: absolute; top: 0; left: 0; border: 0;" src="https://camo.githubusercontent.com/567c3a48d796e2fc06ea80409cc9dd82bf714434/68747470733a2f2f73332e616d617a6f6e6177732e636f6d2f6769746875622f726962626f6e732f666f726b6d655f6c6566745f6461726b626c75655f3132313632312e706e67" alt="Fork me on GitHub" data-canonical-src="https://s3.amazonaws.com/github/ribbons/forkme_left_darkblue_121621.png">
</a>
<p class="numParticles"></p>
<div class="explanation">
<h2>Probability density of a hydrogen atom </h2>
<h4>Use mouse drag to rotate, mouse wheel to zoom-in/out.</h4>
</div>
<a class="ref" href="http://en.wikipedia.org/wiki/File:Hydrogen_Density_Plots.png" target="_blank">See reference on Wikipedia</a>
<!-- THREE.min.js r60 and Orbit, GUI etc-->
<script type="text/javascript" src="js/THREE-r65.min.js"></script>
<script type="text/javascript" src="js/Stats.min.js"></script>
<script type="text/javascript" src="js/OrbitControls.js"></script>
<script type="text/javascript" src="js/dat.gui.min.js"></script>
<!--Mathematical Functions-->
<script type="text/javascript" src="js/MathLib/MathLib.js"></script>
<script type="text/javascript" src="js/MathLib/Complex.js"></script>
<script type="text/javascript" src="js/MathLib/Laguerre.js"></script>
<script type="text/javascript" src="js/MathLib/AssocLegendre.js"></script>
<script type="text/javascript" src="js/MathLib/SphericalHarmonic.js"></script>
<!-- ShaderParticles -->
<script type="text/javascript" src="js/ShaderParticleEngine/ShaderParticleUtils.js"></script>
<script type="text/javascript" src="js/ShaderParticleEngine/ShaderParticleGroup.js"></script>
<script type="text/javascript" src="js/ShaderParticleEngine/ShaderParticleEmitter.js"></script>
<script type="text/javascript">
gui = new dat.GUI();
parameters =
{
n: 2,
l: 1,
m: 0,
size: 10,
ppr: 60,
ppa: 30
};
var folder1 = gui.addFolder('Quantum numbers');
var folder2 = gui.addFolder('Resolution');
var guiN = folder1.add(parameters, 'n').min(1).max(10).step(1).listen();
var guiL = folder1.add(parameters, 'l').min(0).max(9).step(1).listen();
var guiM = folder1.add(parameters, 'm').min(-9).max(9).step(1).listen();
var guiSize = gui.add(parameters, 'size').min(1).max(30).step(1).name('Point Size').listen();
var guiPpr = folder2.add(parameters, 'ppr').min(10).max(100).step(1).name('Radial').listen();
var guiPpa = folder2.add(parameters, 'ppa').min(10).max(60).step(2).name('Angular').listen();
folder1.open();
folder2.open();
guiN.onChange(function(value)
{
guiL.max(value - 1);
((guiL.getValue()) > value - 1) && guiL.setValue(value - 1);
update();
});
guiL.onChange(function(value)
{
guiM.max(value).min(-value);
(guiM.getValue() < -value) && guiM.setValue(-value);
(guiM.getValue() > value) && guiM.setValue(value);
update();
});
guiM.onChange(function(value) {
update();
});
guiSize.onChange(function(value) {
update();
});
guiPpr.onChange(function(value) {
update();
});
guiPpa.onChange(function(value) {
update();
});
gui.open();
timer = null;
function update() {
clearTimeout(timer);
timer = setTimeout(function() {
scene.remove(particleGroup.mesh);
initParticles();
}, 1000);
}
function Ψ(n, l, m) {
var a0 = 100; // bohr radius
this.n = n;
this.l = l;
this.m = m;
this.const = Math.sqrt(
(2 / n / a0) * (2 / n / a0) * (2 / n / a0) *
MathLib.factorial(n - l - 1) /
(2 * this.n * MathLib.factorial(n + l))
);
var opts = {
lag: new Laguerre(n - l - 1, 2 * l + 1),
shr: new SphericalHarmonic(l, m),
eval: function(r, θ, φ) {
return this.const * this.evalRad(r) * this.evalAng(θ, φ);
},
evalRad: function(r) {
var ρ = 2 * r / (this.n * a0);
return Math.abs(Math.exp(-ρ / 2) * Math.pow(ρ, this.l) * this.lag.eval(ρ));
},
evalAng: function(θ, φ) {
return this.shr.eval(θ, φ).length();
}
};
extend(this, opts);
return this;
}
function randBtw(a, b) {
return (b - a) * Math.random() + a;
}
function randBtwVect(v1, v2) {
return new THREE.Vector3(randBtw(v1.x, v2.x), randBtw(v1.y, v2.y), randBtw(v1.z, v2.z));
}
function resetGridParams() {
rmin = 2,
rmax = Math.sqrt(parameters.n) * parameters.n * 300,
incr = (rmax - rmin) / parameters.ppr;
tmin = 0,
tmax = 2 * Math.PI + 0.01,
tincr = tmax / parameters.ppa;
angular = [], radial = [];
}
function createAngularGrid() {
angular = [];
angular = AntipodalPointSet(parameters.ppa * parameters.ppa);
}
function createRadialGrid() {
radial = [];
var index = 0;
for (var r = rmin; r < rmax; r += incr) {
radial[index++] = r;
}
}
function AntipodalPointSet(K2) {
// Ref. http://dx.doi.org/10.1016/j.jocs.2011.06.007
var K = K2 / 2;
var PI = Math.PI;
var n = Math.round(Math.sqrt(K * PI / 8.0));
var sc = new Array(K);
var L = PI / Math.sin(PI / (4.0 * n));
var phi, theta, k;
var sum = 0;
var index = 0;
for (var i = 1; i < n; i++) {
phi = (i - 0.5) * 0.5 * PI / n;
k = Math.round(2.0 * PI * Math.sin(phi) * K / L);
sum += k;
for (var j = 1; j <= k; j++) {
theta = (j - 0.5) * 2.0 * PI / k;
sc[index] = new THREE.Vector2(theta, PI / 2 - phi);
index++;
}
}
phi = (n - 0.5) * 0.5 * PI / n;
k = K - sum;
for (var j = 1; j <= k; j++) {
theta = (j - 0.5) * 2.0 * PI / k;
sc[index] = new THREE.Vector2(theta, PI / 2 - phi);
index++;
}
for (var k = 0; k < K; k++) {
sc[index] = new THREE.Vector2(sc[K - k - 1].x, PI + sc[K - k - 1].y);
index++;
}
return sc;
}
// variables used in init()
var scene, camera, renderer, clock;
// Used in initParticles()
var emitter, particleGroup, numEmitters = 1;
// Setup the scene
function init() {
scene = new THREE.Scene();
camera = new THREE.PerspectiveCamera(75, window.innerWidth / window.innerHeight, 0.1, 100000);
camera.lookAt(scene.position);
renderer = new THREE.WebGLRenderer();
renderer.setSize(window.innerWidth, window.innerHeight);
renderer.setClearColor(0x000000);
clock = new THREE.Clock();
document.body.appendChild(renderer.domElement);
}
function getRandomNumber(base) {
return base * Math.random() - (base / 2);
}
// Create particle group and emitter
function initParticles() {
resetGridParams();
createAngularGrid();
createRadialGrid();
particleGroup = new SPE.Group({
texture: THREE.ImageUtils.loadTexture('./img/particle3.png'),
maxAge: 2
});
for (var i = 0; i < numEmitters; ++i) {
emitter = new SPE.Emitter({
type: 'function',
func: new Ψ(parameters.n, parameters.l, parameters.m), //n,l,m
increment: incr,
sizeStart: parameters.size,
particleCount: Math.floor((rmax - rmin) / incr) * Math.floor((tmax - tmin) / tincr) * Math.floor((tmax - tmin) / tincr),
colorStartSpread: new THREE.Vector3(1, 1, 1),
opacityStart: 1,
opacityEnd: 0,
isStatic: 1
});
emitter.tincr = tincr;
particleGroup.updateEmitter(emitter);
}
scene.add(particleGroup.mesh);
}
function initAxes() {
function buildAxes(length) {
var axes = new THREE.Object3D();
axes.add(buildAxis(new THREE.Vector3(0, 0, 0), new THREE.Vector3(length, 0, 0), 0xEE5555, false)); // +X
axes.add(buildAxis(new THREE.Vector3(0, 0, 0), new THREE.Vector3(-length, 0, 0), 0xEE5555, true)); // -X
axes.add(buildAxis(new THREE.Vector3(0, 0, 0), new THREE.Vector3(0, length, 0), 0x55EE55, false)); // +Y
axes.add(buildAxis(new THREE.Vector3(0, 0, 0), new THREE.Vector3(0, -length, 0), 0x55EE55, true)); // -Y
axes.add(buildAxis(new THREE.Vector3(0, 0, 0), new THREE.Vector3(0, 0, length), 0x5555EE, false)); // +Z
axes.add(buildAxis(new THREE.Vector3(0, 0, 0), new THREE.Vector3(0, 0, -length), 0x5555EE, true)); // -Z
return axes;
}
function buildAxis(src, dst, colorHex, dashed) {
var geom = new THREE.Geometry(),
mat;
if (dashed) {
mat = new THREE.LineDashedMaterial({linewidth: 3, color: colorHex, dashSize: 50, gapSize: 50});
} else {
mat = new THREE.LineBasicMaterial({linewidth: 3, color: colorHex});
}
geom.vertices.push(src.clone());
geom.vertices.push(dst.clone());
geom.computeLineDistances(); // This one is SUPER important, otherwise dashed lines will appear as simple plain lines
var axis = new THREE.Line(geom, mat, THREE.LinePieces);
return axis;
}
var axes = buildAxes(10000);
scene.add(axes);
}
function setCount(count) {
document.querySelector('.numParticles').textContent = 'Total particles: ' + count;
}
function animate() {
requestAnimationFrame(animate);
// Using a fixed time-step here to avoid pauses
render(clock.getDelta());
}
function render(dt) {
//particleGroup.tick(dt);
renderer.render(scene, camera);
}
SPE.ready(function() {
init();
initParticles();
initAxes();
animate();
controls = new THREE.OrbitControls(camera, renderer.domElement);
camera.position.z = rmax * 2.5;
camera.position.y = 0;
camera.position.x = 0;
controls.addEventListener('change', render);
window.addEventListener('resize', function() {
var w = window.innerWidth,
h = window.innerHeight;
camera.aspect = w / h;
camera.updateProjectionMatrix();
renderer.setSize(w, h);
}, false);
}
);
</script>
</body>
</html>