Pen Settings



CSS Base

Vendor Prefixing

Add External Stylesheets/Pens

Any URL's added here will be added as <link>s in order, and before the CSS in the editor. You can use the CSS from another Pen by using it's URL and the proper URL extention.

+ add another resource


Babel includes JSX processing.

Add External Scripts/Pens

Any URL's added here will be added as <script>s in order, and run before the JavaScript in the editor. You can use the URL of any other Pen and it will include the JavaScript from that Pen.

+ add another resource


Add Packages

Search for and use JavaScript packages from npm here. By selecting a package, an import statement will be added to the top of the JavaScript editor for this package.


Save Automatically?

If active, Pens will autosave every 30 seconds after being saved once.

Auto-Updating Preview

If enabled, the preview panel updates automatically as you code. If disabled, use the "Run" button to update.

Format on Save

If enabled, your code will be formatted when you actively save your Pen. Note: your code becomes un-folded during formatting.

Editor Settings

Code Indentation

Want to change your Syntax Highlighting theme, Fonts and more?

Visit your global Editor Settings.


                <canvas id="c"></canvas>


	background: #262626;
	position: absolute;
	top: 0;
	left: 0;
	width: 100%;
	height: 100%;


                // These have to be ordered by size (ascending) for them to be correctly drawn
var circles = [
	{ color: '#21a5ad', size: 84, angle: Math.PI / 3 },
	{ color: '#ffad10', size: 92, angle: - Math.PI / 3 },
	{ color: '#ef4239', size: 100, angle: 0 }
// To be able to "twist a circle", it has to be defined as a set of linked points
// This is the number of these points (you can see it if you set it to 3 or 4)
var segmentsPerCircle = 200;
// Time scaling factor : slower when closer to 0, faster when bigger than 1
var speed = .8;
// Easing function on the twist (indicates how fast the rotation goes at a given time)
// This is equivalent to an ease-in-out-quad
// A list of basic easings is available here
function twistEasing(t) {
	return (t < .5) ? 2 * t * t : 1 - 2 * (t = 1 - t) * t;

var c = document.getElementById('c'),
	ctx = c.getContext('2d');
Math.PI2 = 2 * Math.PI; // ¯\_(ツ)_/¯

// "3d" rotation functions, around base axes
// I didn't feel like using matrices so it uses basic 2d geometry and rotation algorithms (trigonometry, pythagore)
// rotateZ is a standard 2d rotation around [0,0] (measures the distance, the current angle and increases it, then goes back to X,Y coordinates)
// rotateX and rotateY are the same but as if we were viewing the scene from above (for rotateY, so y becomes z) or from the right
function rotateX(p, a) {
	var d = Math.sqrt(p[2] * p[2] + p[1] * p[1]),
		na = Math.atan2(p[1], p[2]) + a;
	return [p[0], d * Math.sin(na), d * Math.cos(na)];
function rotateY(p, a) {
	var d = Math.sqrt(p[2] * p[2] + p[0] * p[0]),
		na = Math.atan2(p[2], p[0]) + a;
	return [d * Math.cos(na), p[1], d * Math.sin(na)];
function rotateZ(p, a) {
	var d = Math.sqrt(p[1] * p[1] + p[0] * p[0]),
		na = Math.atan2(p[1], p[0]) + a;
	return [d * Math.cos(na), d * Math.sin(na), p[2]];

// Change the canvas size and restore other properties (lost when we resize)
function resize() {
	c.width = c.offsetWidth;
	c.height = c.offsetHeight;
	ctx.translate(c.width *.5, c.height * .5);
	ctx.lineWidth = 5;
	ctx.lineCap = 'round';
	ctx.lineJoin = 'round';
window.addEventListener('resize', resize);

// Variables enabling mouse control (just adds an extra rotation around Y based on the mouse positions)
// To get a nicer result we smoothly transition to the new mouse position, so we have to use 2 variables
// (one for the actual angle and one for the final one, where the mouse points)
var angleOffset = 0, angleOffsetGoal = 0;
c.addEventListener('mousemove', function(e) { angleOffsetGoal = Math.PI2 * (e.clientX / c.width - .5); });
c.addEventListener('mouseout', function(e) { angleOffsetGoal = 0; });

// This is one of the main elements I guess, it creates a regular polygon (so something close to a circle with enough points)
// but also rotates the points around the X axis progressively from 0 at the left up to `angle` at the right
// this creates the "twist". Here is what it would look like with twelve points and different `angle` values
function loxo(radius, angle, segments) {
	var r = [];
	for(var i = 0; i < segments; i++) {
		// We place the points regularly on a full circle so the angle increment is 2*PI (radians so 1 turn) divided by the number of segments
		// (and we multiply that by i to get the current one)
		var a = Math.PI2 * i / segments,
			c = Math.cos(a), s = Math.sin(a);
		var ax = Math.PI * .5;
		// c is the cosine, which is also the x position of the point on the circle with this angle
		// in [-1, 1], so (c + 1) * .5 gives the horizontal position from 0 (left) to 1 (right)
		// And the quantity of rotation around the X axis is basically `angle` multiplied by this 0 to 1 factor
		ax -= (c + 1) * .5 * angle;
		// Add the computed point to the list
		r.push([radius * c, radius * s * Math.sin(ax), radius * s * Math.cos(ax)]);
	return r;

// The computing and drawing loop, calling itself with requestAnimationFrame
// (basically runs 60 times per second when possible)
function loop() {
	// We move the mouse rotation towards its goal
	// (this formula makes it decelerate at the end, because it's always going 10% closer than what it was at the previous frame ; this gives a smooth transition)
	angleOffset += (angleOffsetGoal - angleOffset) * .1;
	// We get a number between 0 and PI based on the current time indicating the progress of the animation
	var t = ( * 1e-3 * speed) % Math.PI;
	// global rotation : the assembly does half of a turn around Y (if you look at the extremity starting facing us, it ends up on the back)
	// (it's actually offseted by PI/2 because the loxo function gives circles facing us and we want to start the animation looking at the side)
	var rotationY = -t - Math.PI * .5;
	// You can also see the extremity do this up and down and then back to the middle thing, which is basically a sine wave
	// It can be seen in multiple ways but I chose to do a rotateZ after the first Y rotation
	// You can try setting this variable to 0 to see what it does (it's like 2d-rotating the result)
	var rotationZ = Math.PI * .5 * Math.cos(t);
	// The "twist" quantity is how much between 0 and 1 the circles should be
	var twist = twistEasing((Math.cos(t * 2 + Math.PI) + 1) * .5),
		twistAngle = twist * 2 * Math.PI2, // and we multiply that by the max angle (2 full turns) to get the `angle` we must send to the loxo function
		twistSign = (t * 2 > Math.PI ? 1 : -1);
	var circlesPoints = [];
	var i, l, j;
	for(i = 0, l = circles.length; i < l; i++) {
		var pts = loxo(circles[i].size, twistAngle, segmentsPerCircle);
		for(j = 0; j < segmentsPerCircle; j++) {
			// Just rotates the circle by their own angle (as defined at the very top) but moves them together when they are twisted
			// You can comment this next line to see what it looks like without it
			pts[j] = rotateX(pts[j], circles[i].angle * (1 - twist) * twistSign);
			// And apply every other rotation as computed earlier (global Y and Z, and the mouse rotation)
			// (you should read this chain starting by the innermost function call btw, assuming you consider the XYZ axes don't move with the transformation)
			// (if you consider the axes to be moving and not absolute, you can read from left to right)
			// (this is basically the same difference as when you read CSS transformations, cf this post
			pts[j] = rotateY(rotateZ(rotateY(pts[j], rotationY), rotationZ), angleOffset);
		// Put the result in an array of arrays (array of circles and each circle is an array of points)
	// Draw the result in two steps to get a correct z-ordering
	// First we draw everything that is "behind" the middle (that should be further from you than the center of the sphere)
	// going from the biggest circle (farther lines) to the smallest
	drawCircles(circlesPoints, true);
	// Then we draw the other half (closer to you)
	// this time drawing the smaller circles first (because on this half they are farther away)
	drawCircles(circlesPoints, false);
// Function that draws one half of all the circles (called twice to draw the full thing)
function drawCircles(circlesPoints, behind) {
	var i, l = circles.length;
	// Connects the dots basically
	for(var i = behind ? l - 1 : 0; i >= 0 && i < l; behind ? i-- : i++) {
		ctx.strokeStyle = circles[i].color;
		for(var j = 0; j < segmentsPerCircle; j++) {
			var p = circlesPoints[i][j];
			// Gets rid of the points on the wrong half
			if(behind ? p[2] < 0 : p[2] > 0) continue;
			var prev = circlesPoints[i][(j || segmentsPerCircle) - 1];
			ctx.moveTo(prev[0], prev[1]);
			ctx.lineTo(p[0], p[1]);
// Starts the thing !