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HTML

              
                .container
  h3.header Magnificent Trigonometry


.container
  .row
    #container.col-sm-6
    
    #side.col-sm-6
    
      h3 Options
      
      .row
        .col-sm-12
          label.custom-control.custom-checkbox
            input(type="checkbox" id="ce").custom-control-input
            span.custom-control-indicator
            span.custom-control-description Show circles
      
      .row
        label(for="n").col-sm-4 Circles
        input(type="number" id="n" step="1").col-sm-8.form-control
        
      .row
        label(for="s").col-sm-4 Speed
        input(type="number" id="s" step="0.001").col-sm-4.form-control
        input(type="button" id="p" value="Pause").col-sm-4.form-control
        
      .row
        label(for="k").col-sm-4 Multiplier
        input(type="number" id="k" step="0.2").col-sm-8.form-control
        
      .row
        label(for="aki").col-sm-4 Auto-adder
        input(type="number" id="aki" step="0.001").col-sm-4.form-control
        .col-sm-4
          label.custom-control.custom-checkbox
            input(type="checkbox" id="ake").custom-control-input
            span.custom-control-indicator
            span.custom-control-description Enable
        
      .row
        label.col-sm-4 Align view
        .btn-group(id="a")
          input(type="button" id="at" value="Top").btn
          input(type="button" id="af" value="Front").btn
          input(type="button" id="as" value="Side").btn
          input(type="button" id="ad" value="Default").btn
      
  
  h3 A few interesting combinations
  p
    i Note: it is recommended that you disable "Show circles" and set the speed to a very low value when the circle count is high.
  table.table
    thead
      tr
        th Comment
        th Circles
        th Multiplier
        th Speed
        th Action
    tbody#cbs
  
  
  h3 How does this work?
  p Coming soon...


  h3 Notes
  p Patterns seem to be proper to a multiplier. However, this seems untrue for higher multipliers, where increasing the number of circles also changes the pattern. Maybe a stable pattern emerges only after a certain precision in the number of circles. To investigate.
  
  
  h3 About  
  p This is a new version of this 
    a(href="https://codepen.io/ninivert/pen/LWXZaR/") pen
    | , after I realized that I was limiting myself to one view, the top view.
  p Powered by three.js
  p Made with 💗 by 
    a(href="codepen.io/ninivert") ninivert
              
            
!

CSS

              
                html,
body {
  margin: 0;
  padding: 0;
  width: 100%;
  height: 100%;
}

body {
  $base-font-size: 18px;
  $heading-scale: 8;
  @for $i from 1 through 6 {
    h#{$i} {
      margin: .5em 0;
      font-size: $base-font-size + $heading-scale * (6 - $i);
      color: #2c3e50;
    }
  }
  color: #34495e;
  
  .header {
    margin-top: .4em;
    padding: .4em 0;
    position: relative;
    &::after {
      content: '';
      position: absolute;
      bottom: 0;
      left: 0;
      display: block;
      width: 2em;
      height: 2px;
      background: #2980b9;
    }
    // border-bottom: 2px solid #2980b9;
  }
  
  .row {
    > #side {
      > .row {
        margin-bottom: .5em;
      }
    }
  }
  
  #container {
    // overflow: auto;
    > canvas {
      width: 100% !important;
      height: auto !important;
    }
  }
}


// * {
//   outline: 2px solid #aaa;
// }
              
            
!

JS

              
                // ORBIT CONTROLS LEGACY
// https://raw.githubusercontent.com/mrdoob/three.js/501c06b6cbf07ff72c82def54e2d39d5a7e3a7d6/examples/js/controls/OrbitControls.js

/**
 * @author qiao / https://github.com/qiao
 * @author mrdoob / http://mrdoob.com
 * @author alteredq / http://alteredqualia.com/
 * @author WestLangley / http://github.com/WestLangley
 * @author erich666 / http://erichaines.com
 */

// This set of controls performs orbiting, dollying (zooming), and panning.
// Unlike TrackballControls, it maintains the "up" direction object.up (+Y by default).
//
//    Orbit - left mouse / touch: one finger move
//    Zoom - middle mouse, or mousewheel / touch: two finger spread or squish
//    Pan - right mouse, or arrow keys / touch: three finger swipe

THREE.OrbitControls = function ( object, domElement ) {

	this.object = object;

	this.domElement = ( domElement !== undefined ) ? domElement : document;

	// Set to false to disable this control
	this.enabled = true;

	// "target" sets the location of focus, where the object orbits around
	this.target = new THREE.Vector3();

	// How far you can dolly in and out ( PerspectiveCamera only )
	this.minDistance = 0;
	this.maxDistance = Infinity;

	// How far you can zoom in and out ( OrthographicCamera only )
	this.minZoom = 0;
	this.maxZoom = Infinity;

	// How far you can orbit vertically, upper and lower limits.
	// Range is 0 to Math.PI radians.
	this.minPolarAngle = 0; // radians
	this.maxPolarAngle = Math.PI; // radians

	// How far you can orbit horizontally, upper and lower limits.
	// If set, must be a sub-interval of the interval [ - Math.PI, Math.PI ].
	this.minAzimuthAngle = - Infinity; // radians
	this.maxAzimuthAngle = Infinity; // radians

	// Set to true to enable damping (inertia)
	// If damping is enabled, you must call controls.update() in your animation loop
	this.enableDamping = false;
	this.dampingFactor = 0.25;

	// This option actually enables dollying in and out; left as "zoom" for backwards compatibility.
	// Set to false to disable zooming
	this.enableZoom = true;
	this.zoomSpeed = 1.0;

	// Set to false to disable rotating
	this.enableRotate = true;
	this.rotateSpeed = 1.0;

	// Set to false to disable panning
	this.enablePan = true;
	this.keyPanSpeed = 7.0;	// pixels moved per arrow key push

	// Set to true to automatically rotate around the target
	// If auto-rotate is enabled, you must call controls.update() in your animation loop
	this.autoRotate = false;
	this.autoRotateSpeed = 2.0; // 30 seconds per round when fps is 60

	// Set to false to disable use of the keys
	this.enableKeys = true;

	// The four arrow keys
	this.keys = { LEFT: 37, UP: 38, RIGHT: 39, BOTTOM: 40 };

	// Mouse buttons
	this.mouseButtons = { ORBIT: THREE.MOUSE.LEFT, ZOOM: THREE.MOUSE.MIDDLE, PAN: THREE.MOUSE.RIGHT };

	// for reset
	this.target0 = this.target.clone();
	this.position0 = this.object.position.clone();
	this.zoom0 = this.object.zoom;

	//
	// public methods
	//

	this.getPolarAngle = function () {

		return spherical.phi;

	};

	this.getAzimuthalAngle = function () {

		return spherical.theta;

	};

	this.saveState = function () {

		scope.target0.copy( scope.target );
		scope.position0.copy( scope.object.position );
		scope.zoom0 = scope.object.zoom;

	};

	this.reset = function () {

		scope.target.copy( scope.target0 );
		scope.object.position.copy( scope.position0 );
		scope.object.zoom = scope.zoom0;

		scope.object.updateProjectionMatrix();
		scope.dispatchEvent( changeEvent );

		scope.update();

		state = STATE.NONE;

	};

	// this method is exposed, but perhaps it would be better if we can make it private...
	this.update = function () {

		var offset = new THREE.Vector3();

		// so camera.up is the orbit axis
		var quat = new THREE.Quaternion().setFromUnitVectors( object.up, new THREE.Vector3( 0, 1, 0 ) );
		var quatInverse = quat.clone().inverse();

		var lastPosition = new THREE.Vector3();
		var lastQuaternion = new THREE.Quaternion();

		return function update() {

			var position = scope.object.position;

			offset.copy( position ).sub( scope.target );

			// rotate offset to "y-axis-is-up" space
			offset.applyQuaternion( quat );

			// angle from z-axis around y-axis
			spherical.setFromVector3( offset );

			if ( scope.autoRotate && state === STATE.NONE ) {

				rotateLeft( getAutoRotationAngle() );

			}

			spherical.theta += sphericalDelta.theta;
			spherical.phi += sphericalDelta.phi;

			// restrict theta to be between desired limits
			spherical.theta = Math.max( scope.minAzimuthAngle, Math.min( scope.maxAzimuthAngle, spherical.theta ) );

			// restrict phi to be between desired limits
			spherical.phi = Math.max( scope.minPolarAngle, Math.min( scope.maxPolarAngle, spherical.phi ) );

			spherical.makeSafe();


			spherical.radius *= scale;

			// restrict radius to be between desired limits
			spherical.radius = Math.max( scope.minDistance, Math.min( scope.maxDistance, spherical.radius ) );

			// move target to panned location
			scope.target.add( panOffset );

			offset.setFromSpherical( spherical );

			// rotate offset back to "camera-up-vector-is-up" space
			offset.applyQuaternion( quatInverse );

			position.copy( scope.target ).add( offset );

			scope.object.lookAt( scope.target );

			if ( scope.enableDamping === true ) {

				sphericalDelta.theta *= ( 1 - scope.dampingFactor );
				sphericalDelta.phi *= ( 1 - scope.dampingFactor );

			} else {

				sphericalDelta.set( 0, 0, 0 );

			}

			scale = 1;
			panOffset.set( 0, 0, 0 );

			// update condition is:
			// min(camera displacement, camera rotation in radians)^2 > EPS
			// using small-angle approximation cos(x/2) = 1 - x^2 / 8

			if ( zoomChanged ||
				lastPosition.distanceToSquared( scope.object.position ) > EPS ||
				8 * ( 1 - lastQuaternion.dot( scope.object.quaternion ) ) > EPS ) {

				scope.dispatchEvent( changeEvent );

				lastPosition.copy( scope.object.position );
				lastQuaternion.copy( scope.object.quaternion );
				zoomChanged = false;

				return true;

			}

			return false;

		};

	}();

	this.dispose = function () {

		scope.domElement.removeEventListener( 'contextmenu', onContextMenu, false );
		scope.domElement.removeEventListener( 'mousedown', onMouseDown, false );
		scope.domElement.removeEventListener( 'wheel', onMouseWheel, false );

		scope.domElement.removeEventListener( 'touchstart', onTouchStart, false );
		scope.domElement.removeEventListener( 'touchend', onTouchEnd, false );
		scope.domElement.removeEventListener( 'touchmove', onTouchMove, false );

		document.removeEventListener( 'mousemove', onMouseMove, false );
		document.removeEventListener( 'mouseup', onMouseUp, false );

		window.removeEventListener( 'keydown', onKeyDown, false );

		//scope.dispatchEvent( { type: 'dispose' } ); // should this be added here?

	};

	//
	// internals
	//

	var scope = this;

	var changeEvent = { type: 'change' };
	var startEvent = { type: 'start' };
	var endEvent = { type: 'end' };

	var STATE = { NONE: - 1, ROTATE: 0, DOLLY: 1, PAN: 2, TOUCH_ROTATE: 3, TOUCH_DOLLY: 4, TOUCH_PAN: 5 };

	var state = STATE.NONE;

	var EPS = 0.000001;

	// current position in spherical coordinates
	var spherical = new THREE.Spherical();
	var sphericalDelta = new THREE.Spherical();

	var scale = 1;
	var panOffset = new THREE.Vector3();
	var zoomChanged = false;

	var rotateStart = new THREE.Vector2();
	var rotateEnd = new THREE.Vector2();
	var rotateDelta = new THREE.Vector2();

	var panStart = new THREE.Vector2();
	var panEnd = new THREE.Vector2();
	var panDelta = new THREE.Vector2();

	var dollyStart = new THREE.Vector2();
	var dollyEnd = new THREE.Vector2();
	var dollyDelta = new THREE.Vector2();

	function getAutoRotationAngle() {

		return 2 * Math.PI / 60 / 60 * scope.autoRotateSpeed;

	}

	function getZoomScale() {

		return Math.pow( 0.95, scope.zoomSpeed );

	}

	function rotateLeft( angle ) {

		sphericalDelta.theta -= angle;

	}

	function rotateUp( angle ) {

		sphericalDelta.phi -= angle;

	}

	var panLeft = function () {

		var v = new THREE.Vector3();

		return function panLeft( distance, objectMatrix ) {

			v.setFromMatrixColumn( objectMatrix, 0 ); // get X column of objectMatrix
			v.multiplyScalar( - distance );

			panOffset.add( v );

		};

	}();

	var panUp = function () {

		var v = new THREE.Vector3();

		return function panUp( distance, objectMatrix ) {

			v.setFromMatrixColumn( objectMatrix, 1 ); // get Y column of objectMatrix
			v.multiplyScalar( distance );

			panOffset.add( v );

		};

	}();

	// deltaX and deltaY are in pixels; right and down are positive
	var pan = function () {

		var offset = new THREE.Vector3();

		return function pan( deltaX, deltaY ) {

			var element = scope.domElement === document ? scope.domElement.body : scope.domElement;

			if ( scope.object instanceof THREE.PerspectiveCamera ) {

				// perspective
				var position = scope.object.position;
				offset.copy( position ).sub( scope.target );
				var targetDistance = offset.length();

				// half of the fov is center to top of screen
				targetDistance *= Math.tan( ( scope.object.fov / 2 ) * Math.PI / 180.0 );

				// we actually don't use screenWidth, since perspective camera is fixed to screen height
				panLeft( 2 * deltaX * targetDistance / element.clientHeight, scope.object.matrix );
				panUp( 2 * deltaY * targetDistance / element.clientHeight, scope.object.matrix );

			} else if ( scope.object instanceof THREE.OrthographicCamera ) {

				// orthographic
				panLeft( deltaX * ( scope.object.right - scope.object.left ) / scope.object.zoom / element.clientWidth, scope.object.matrix );
				panUp( deltaY * ( scope.object.top - scope.object.bottom ) / scope.object.zoom / element.clientHeight, scope.object.matrix );

			} else {

				// camera neither orthographic nor perspective
				console.warn( 'WARNING: OrbitControls.js encountered an unknown camera type - pan disabled.' );
				scope.enablePan = false;

			}

		};

	}();

	function dollyIn( dollyScale ) {

		if ( scope.object instanceof THREE.PerspectiveCamera ) {

			scale /= dollyScale;

		} else if ( scope.object instanceof THREE.OrthographicCamera ) {

			scope.object.zoom = Math.max( scope.minZoom, Math.min( scope.maxZoom, scope.object.zoom * dollyScale ) );
			scope.object.updateProjectionMatrix();
			zoomChanged = true;

		} else {

			console.warn( 'WARNING: OrbitControls.js encountered an unknown camera type - dolly/zoom disabled.' );
			scope.enableZoom = false;

		}

	}

	function dollyOut( dollyScale ) {

		if ( scope.object instanceof THREE.PerspectiveCamera ) {

			scale *= dollyScale;

		} else if ( scope.object instanceof THREE.OrthographicCamera ) {

			scope.object.zoom = Math.max( scope.minZoom, Math.min( scope.maxZoom, scope.object.zoom / dollyScale ) );
			scope.object.updateProjectionMatrix();
			zoomChanged = true;

		} else {

			console.warn( 'WARNING: OrbitControls.js encountered an unknown camera type - dolly/zoom disabled.' );
			scope.enableZoom = false;

		}

	}

	//
	// event callbacks - update the object state
	//

	function handleMouseDownRotate( event ) {

		//console.log( 'handleMouseDownRotate' );

		rotateStart.set( event.clientX, event.clientY );

	}

	function handleMouseDownDolly( event ) {

		//console.log( 'handleMouseDownDolly' );

		dollyStart.set( event.clientX, event.clientY );

	}

	function handleMouseDownPan( event ) {

		//console.log( 'handleMouseDownPan' );

		panStart.set( event.clientX, event.clientY );

	}

	function handleMouseMoveRotate( event ) {

		//console.log( 'handleMouseMoveRotate' );

		rotateEnd.set( event.clientX, event.clientY );
		rotateDelta.subVectors( rotateEnd, rotateStart );

		var element = scope.domElement === document ? scope.domElement.body : scope.domElement;

		// rotating across whole screen goes 360 degrees around
		rotateLeft( 2 * Math.PI * rotateDelta.x / element.clientWidth * scope.rotateSpeed );

		// rotating up and down along whole screen attempts to go 360, but limited to 180
		rotateUp( 2 * Math.PI * rotateDelta.y / element.clientHeight * scope.rotateSpeed );

		rotateStart.copy( rotateEnd );

		scope.update();

	}

	function handleMouseMoveDolly( event ) {

		//console.log( 'handleMouseMoveDolly' );

		dollyEnd.set( event.clientX, event.clientY );

		dollyDelta.subVectors( dollyEnd, dollyStart );

		if ( dollyDelta.y > 0 ) {

			dollyIn( getZoomScale() );

		} else if ( dollyDelta.y < 0 ) {

			dollyOut( getZoomScale() );

		}

		dollyStart.copy( dollyEnd );

		scope.update();

	}

	function handleMouseMovePan( event ) {

		//console.log( 'handleMouseMovePan' );

		panEnd.set( event.clientX, event.clientY );

		panDelta.subVectors( panEnd, panStart );

		pan( panDelta.x, panDelta.y );

		panStart.copy( panEnd );

		scope.update();

	}

	function handleMouseUp( event ) {

		// console.log( 'handleMouseUp' );

	}

	function handleMouseWheel( event ) {

		// console.log( 'handleMouseWheel' );

		if ( event.deltaY < 0 ) {

			dollyOut( getZoomScale() );

		} else if ( event.deltaY > 0 ) {

			dollyIn( getZoomScale() );

		}

		scope.update();

	}

	function handleKeyDown( event ) {

		//console.log( 'handleKeyDown' );

		switch ( event.keyCode ) {

			case scope.keys.UP:
				pan( 0, scope.keyPanSpeed );
				scope.update();
				break;

			case scope.keys.BOTTOM:
				pan( 0, - scope.keyPanSpeed );
				scope.update();
				break;

			case scope.keys.LEFT:
				pan( scope.keyPanSpeed, 0 );
				scope.update();
				break;

			case scope.keys.RIGHT:
				pan( - scope.keyPanSpeed, 0 );
				scope.update();
				break;

		}

	}

	function handleTouchStartRotate( event ) {

		//console.log( 'handleTouchStartRotate' );

		rotateStart.set( event.touches[ 0 ].pageX, event.touches[ 0 ].pageY );

	}

	function handleTouchStartDolly( event ) {

		//console.log( 'handleTouchStartDolly' );

		var dx = event.touches[ 0 ].pageX - event.touches[ 1 ].pageX;
		var dy = event.touches[ 0 ].pageY - event.touches[ 1 ].pageY;

		var distance = Math.sqrt( dx * dx + dy * dy );

		dollyStart.set( 0, distance );

	}

	function handleTouchStartPan( event ) {

		//console.log( 'handleTouchStartPan' );

		panStart.set( event.touches[ 0 ].pageX, event.touches[ 0 ].pageY );

	}

	function handleTouchMoveRotate( event ) {

		//console.log( 'handleTouchMoveRotate' );

		rotateEnd.set( event.touches[ 0 ].pageX, event.touches[ 0 ].pageY );
		rotateDelta.subVectors( rotateEnd, rotateStart );

		var element = scope.domElement === document ? scope.domElement.body : scope.domElement;

		// rotating across whole screen goes 360 degrees around
		rotateLeft( 2 * Math.PI * rotateDelta.x / element.clientWidth * scope.rotateSpeed );

		// rotating up and down along whole screen attempts to go 360, but limited to 180
		rotateUp( 2 * Math.PI * rotateDelta.y / element.clientHeight * scope.rotateSpeed );

		rotateStart.copy( rotateEnd );

		scope.update();

	}

	function handleTouchMoveDolly( event ) {

		//console.log( 'handleTouchMoveDolly' );

		var dx = event.touches[ 0 ].pageX - event.touches[ 1 ].pageX;
		var dy = event.touches[ 0 ].pageY - event.touches[ 1 ].pageY;

		var distance = Math.sqrt( dx * dx + dy * dy );

		dollyEnd.set( 0, distance );

		dollyDelta.subVectors( dollyEnd, dollyStart );

		if ( dollyDelta.y > 0 ) {

			dollyOut( getZoomScale() );

		} else if ( dollyDelta.y < 0 ) {

			dollyIn( getZoomScale() );

		}

		dollyStart.copy( dollyEnd );

		scope.update();

	}

	function handleTouchMovePan( event ) {

		//console.log( 'handleTouchMovePan' );

		panEnd.set( event.touches[ 0 ].pageX, event.touches[ 0 ].pageY );

		panDelta.subVectors( panEnd, panStart );

		pan( panDelta.x, panDelta.y );

		panStart.copy( panEnd );

		scope.update();

	}

	function handleTouchEnd( event ) {

		//console.log( 'handleTouchEnd' );

	}

	//
	// event handlers - FSM: listen for events and reset state
	//

	function onMouseDown( event ) {

		if ( scope.enabled === false ) return;

		event.preventDefault();

		switch ( event.button ) {

			case scope.mouseButtons.ORBIT:

				if ( scope.enableRotate === false ) return;

				handleMouseDownRotate( event );

				state = STATE.ROTATE;

				break;

			case scope.mouseButtons.ZOOM:

				if ( scope.enableZoom === false ) return;

				handleMouseDownDolly( event );

				state = STATE.DOLLY;

				break;

			case scope.mouseButtons.PAN:

				if ( scope.enablePan === false ) return;

				handleMouseDownPan( event );

				state = STATE.PAN;

				break;

		}

		if ( state !== STATE.NONE ) {

			document.addEventListener( 'mousemove', onMouseMove, false );
			document.addEventListener( 'mouseup', onMouseUp, false );

			scope.dispatchEvent( startEvent );

		}

	}

	function onMouseMove( event ) {

		if ( scope.enabled === false ) return;

		event.preventDefault();

		switch ( state ) {

			case STATE.ROTATE:

				if ( scope.enableRotate === false ) return;

				handleMouseMoveRotate( event );

				break;

			case STATE.DOLLY:

				if ( scope.enableZoom === false ) return;

				handleMouseMoveDolly( event );

				break;

			case STATE.PAN:

				if ( scope.enablePan === false ) return;

				handleMouseMovePan( event );

				break;

		}

	}

	function onMouseUp( event ) {

		if ( scope.enabled === false ) return;

		handleMouseUp( event );

		document.removeEventListener( 'mousemove', onMouseMove, false );
		document.removeEventListener( 'mouseup', onMouseUp, false );

		scope.dispatchEvent( endEvent );

		state = STATE.NONE;

	}

	function onMouseWheel( event ) {

		if ( scope.enabled === false || scope.enableZoom === false || ( state !== STATE.NONE && state !== STATE.ROTATE ) ) return;

		event.preventDefault();
		event.stopPropagation();

		handleMouseWheel( event );

		scope.dispatchEvent( startEvent ); // not sure why these are here...
		scope.dispatchEvent( endEvent );

	}

	function onKeyDown( event ) {

		if ( scope.enabled === false || scope.enableKeys === false || scope.enablePan === false ) return;

		handleKeyDown( event );

	}

	function onTouchStart( event ) {

		if ( scope.enabled === false ) return;

		switch ( event.touches.length ) {

			case 1:	// one-fingered touch: rotate

				if ( scope.enableRotate === false ) return;

				handleTouchStartRotate( event );

				state = STATE.TOUCH_ROTATE;

				break;

			case 2:	// two-fingered touch: dolly

				if ( scope.enableZoom === false ) return;

				handleTouchStartDolly( event );

				state = STATE.TOUCH_DOLLY;

				break;

			case 3: // three-fingered touch: pan

				if ( scope.enablePan === false ) return;

				handleTouchStartPan( event );

				state = STATE.TOUCH_PAN;

				break;

			default:

				state = STATE.NONE;

		}

		if ( state !== STATE.NONE ) {

			scope.dispatchEvent( startEvent );

		}

	}

	function onTouchMove( event ) {

		if ( scope.enabled === false ) return;

		event.preventDefault();
		event.stopPropagation();

		switch ( event.touches.length ) {

			case 1: // one-fingered touch: rotate

				if ( scope.enableRotate === false ) return;
				if ( state !== STATE.TOUCH_ROTATE ) return; // is this needed?...

				handleTouchMoveRotate( event );

				break;

			case 2: // two-fingered touch: dolly

				if ( scope.enableZoom === false ) return;
				if ( state !== STATE.TOUCH_DOLLY ) return; // is this needed?...

				handleTouchMoveDolly( event );

				break;

			case 3: // three-fingered touch: pan

				if ( scope.enablePan === false ) return;
				if ( state !== STATE.TOUCH_PAN ) return; // is this needed?...

				handleTouchMovePan( event );

				break;

			default:

				state = STATE.NONE;

		}

	}

	function onTouchEnd( event ) {

		if ( scope.enabled === false ) return;

		handleTouchEnd( event );

		scope.dispatchEvent( endEvent );

		state = STATE.NONE;

	}

	function onContextMenu( event ) {

		event.preventDefault();

	}

	//

	scope.domElement.addEventListener( 'contextmenu', onContextMenu, false );

	scope.domElement.addEventListener( 'mousedown', onMouseDown, false );
	scope.domElement.addEventListener( 'wheel', onMouseWheel, false );

	scope.domElement.addEventListener( 'touchstart', onTouchStart, false );
	scope.domElement.addEventListener( 'touchend', onTouchEnd, false );
	scope.domElement.addEventListener( 'touchmove', onTouchMove, false );

	window.addEventListener( 'keydown', onKeyDown, false );

	// force an update at start

	this.update();

};

THREE.OrbitControls.prototype = Object.create( THREE.EventDispatcher.prototype );
THREE.OrbitControls.prototype.constructor = THREE.OrbitControls;

Object.defineProperties( THREE.OrbitControls.prototype, {

	center: {

		get: function () {

			console.warn( 'THREE.OrbitControls: .center has been renamed to .target' );
			return this.target;

		}

	},

	// backward compatibility

	noZoom: {

		get: function () {

			console.warn( 'THREE.OrbitControls: .noZoom has been deprecated. Use .enableZoom instead.' );
			return ! this.enableZoom;

		},

		set: function ( value ) {

			console.warn( 'THREE.OrbitControls: .noZoom has been deprecated. Use .enableZoom instead.' );
			this.enableZoom = ! value;

		}

	},

	noRotate: {

		get: function () {

			console.warn( 'THREE.OrbitControls: .noRotate has been deprecated. Use .enableRotate instead.' );
			return ! this.enableRotate;

		},

		set: function ( value ) {

			console.warn( 'THREE.OrbitControls: .noRotate has been deprecated. Use .enableRotate instead.' );
			this.enableRotate = ! value;

		}

	},

	noPan: {

		get: function () {

			console.warn( 'THREE.OrbitControls: .noPan has been deprecated. Use .enablePan instead.' );
			return ! this.enablePan;

		},

		set: function ( value ) {

			console.warn( 'THREE.OrbitControls: .noPan has been deprecated. Use .enablePan instead.' );
			this.enablePan = ! value;

		}

	},

	noKeys: {

		get: function () {

			console.warn( 'THREE.OrbitControls: .noKeys has been deprecated. Use .enableKeys instead.' );
			return ! this.enableKeys;

		},

		set: function ( value ) {

			console.warn( 'THREE.OrbitControls: .noKeys has been deprecated. Use .enableKeys instead.' );
			this.enableKeys = ! value;

		}

	},

	staticMoving: {

		get: function () {

			console.warn( 'THREE.OrbitControls: .staticMoving has been deprecated. Use .enableDamping instead.' );
			return ! this.enableDamping;

		},

		set: function ( value ) {

			console.warn( 'THREE.OrbitControls: .staticMoving has been deprecated. Use .enableDamping instead.' );
			this.enableDamping = ! value;

		}

	},

	dynamicDampingFactor: {

		get: function () {

			console.warn( 'THREE.OrbitControls: .dynamicDampingFactor has been renamed. Use .dampingFactor instead.' );
			return this.dampingFactor;

		},

		set: function ( value ) {

			console.warn( 'THREE.OrbitControls: .dynamicDampingFactor has been renamed. Use .dampingFactor instead.' );
			this.dampingFactor = value;

		}

	}

} );



/**
 * THREE.JS
 * TODO
 * add plane to see only one part of the sphere
 * add proper explanation of the pen
 * show a few interesting combinations
 * add gif export
 * KNOWN BUGS
 * n must be multiple of 2... for some reason
 * "incomplete" circle bug --> the camera has depth
 */
console.clear();


let scene, camera, renderer, controls;
const width = 500,
      height = 500;


/**
 * Camera setup
 */
scene = new THREE.Scene();

camera = new THREE.PerspectiveCamera(
  10,
  width/height,
  1,
  1000
);
camera.position.set(0, 12, 10);
camera.lookAt(scene.position);



/**
 * Renderer setup
 */
renderer = new THREE.WebGLRenderer({
  alpha: true,
  antialias: true
});
renderer.setPixelRatio(window.devicePixelRatio);
renderer.setSize(width, height);

document.getElementById('container').appendChild(renderer.domElement);



/**
 * Controller setup
 */
controls = new THREE.OrbitControls(camera, document.getElementById('container'));
controls.rotateSpeed = 0.5;
controls.enableZoom = false;
controls.enablePan = false;
controls.enableDamping = true;
controls.dampingFactor = 0.25;
controls.autoRotate = false;
controls.autoRotateSpeed = 1;



/**
 * UI objects
 */
// Options
let opts = {
  ce: true, // Circle enable
  n: 16, // Number of circles & dots
  s: 0.02, // Speed
  p: false, // Pause/Unpause
  k: 1, // Multiplier, full amplitude
  aki: 0.01, // Auto multiplier incrementation
  ake: false, // Auto multiplier enable
  at: [0, 16, 0], // Align view to top
  af: [16, 0, 0], // Align view to front
  as: [0, 0, 16], // Align view to side
  ad: [0, 12, 10], // Align view to default
  ENDOFOPTIONS: null, // Placeholder
  t: 0, // Time
  elmts: {
    ce: document.getElementById('ce'),
    n: document.getElementById('n'),
    s: document.getElementById('s'),
    p: document.getElementById('p'),
    k: document.getElementById('k'),
    aki: document.getElementById('aki'),
    ake: document.getElementById('ake'),
    at: document.getElementById('at'),
    af: document.getElementById('af'),
    as: document.getElementById('as'),
    ad: document.getElementById('ad')
  },
  handlers: {
    ce: function() {
      // Set the visibility of all circles
      opts.ce = this.checked;
      for (let i=0; i<circles.length; i++) {
        circles[i].visible = opts.ce;
      }
    },
    n: function() {
      let value = parseInt(this.value);
      // Set minimum value for k
      value = Math.max(1, Math.min(value, 10000));
      // Apply the value
      generateMeshes(value, opts.n);
      // Set the value
      opts.n = value;
      this.value = value;
    },
    s: function() {
      // Pause comes before speed modification
      if (opts.p === true) return;
      
      let value = parseFloat(this.value);
      // Clamp the value between 0.01 and 1
      value = Math.max(0.001, Math.min(1, value));
      // Set the value
      opts.s = value;
      this.value = value;
    },
    p: function() {
      // Toggle pause state
      opts.p = !opts.p;
      // Apply pause
      if (opts.p) {
        opts.s = 0;
        this.value = 'Unpause';
      } else {
        // Update the speed value
        // Call the event handler for the speed input with context
        opts.handlers.s.call(opts.elmts.s);
        this.value = 'Pause';
      }
    },
    k: function() {
      let value = parseFloat(this.value);
      // Set minimum value for k
      value = Math.max(0, value);
      // Set the value
      opts.k = value;
      this.value = value;
    },
    aki: function() {
      let value = parseFloat(this.value);
      // Set minimum value for k
      value = Math.max(0, Math.min(value, 1));
      // Set the value
      opts.aki = value;
      this.value = value;
    },
    ake: function() {
      opts.ake = this.checked;
    },
    at: function() {
      camera.position.set(...opts.at);
    },
    af: function() {
      camera.position.set(...opts.af);
    },
    as: function() {
      camera.position.set(...opts.as);
    },
    ad: function() {
      camera.position.set(...opts.ad);
    }
  },
  init: function() {
    let keys = Object.keys(this),
        elmt, type;
    
    for (let i of keys) {
      // Stop when you arrive at the end of the option list
      if (i === 'ENDOFOPTIONS') break;

      elmt = this.elmts[i];
      type = elmt.type;
      
      if (type === 'checkbox' || type === 'button') {
        elmt.checked = this[i];
        elmt.onclick = this.handlers[i];
      }
      if (type === 'number') {
        elmt.value = this[i];
        elmt.onchange = this.handlers[i];
      }
    }
  }
};

opts.init();

// Interesting combinations
let cbs = {
  values: [
    ['One synced arc', 16, 0, 0.02],
    ['Nearly a spiral', 16, 0.5, 0.02],
    ['Repulsive circle', 16, 43, 0.02],
    ['2 dancing arcs', 16, 47.8, 0.02],
    ['3 dancing arcs', 16, 42.8, 0.02],
    ['2 rotating circles', 32, 33, 0.02],
    ['Clover', 32, 34, 0.02],
    ['Rotor, 3 blades', 128, 3, 0.02],
    ['Rotor, 5 blades', 256, 5, 0.02],
    ['Rotating flower', 800, 43, 0.01],
    ['Rotating flower with waves', 800, 53, 0.01],
    ['Switching halves', 800, 64, 0.01],
    ['Glitchy flower, 4 petals', 800, 79.8, 0.01],
    ['Glitchy flower, 5 petals', 1000, 105, 0.01],
    ['Tripping flower', 1000, 33, 0.005]
  ],
  handler: function() {
    let i = this.i;
    opts.elmts.n.value = cbs.values[i][1];
    opts.elmts.k.value = cbs.values[i][2];
    opts.elmts.s.value = cbs.values[i][3];
    opts.handlers.n.call(opts.elmts.n);
    opts.handlers.k.call(opts.elmts.k);
    opts.handlers.s.call(opts.elmts.s);
  },
  init: function() {
    let tbody = document.getElementById('cbs');
    
    let value, tr, td, btn;
    for (let i=0; i<cbs.values.length; i++) {
      // Values
      value = cbs.values[i];
      tr = document.createElement('tr');
      for (let j=0; j<value.length; j++) {
        td = document.createElement('td');
        td.innerHTML = value[j];
        tr.appendChild(td);
      }
      // Button
      td = document.createElement('td');
      btn = document.createElement('button');
      btn.classList.add('btn');
      btn.innerHTML = 'Load';
      btn.i = i;
      btn.onclick = cbs.handler;
      td.appendChild(btn);
      tr.appendChild(td)
      // Append
      tbody.appendChild(tr);
    }
  }
};

cbs.init();



/**
 * Meshes
 */
// Global variables for the meshes
let dots = [], circles = [];
function generateMeshes(newN = 0, oldN = 0) {
  // Return if no changes have happened
  if (newN === oldN) return;
  
  // Construction variables
  let c = {}, d = {};
  c.material = new THREE.LineBasicMaterial({color: 0xcccccc});
  c.geometry = new THREE.CircleGeometry(1, 64);
  c.geometry.vertices.shift(); // Remove center vertex
  
  d.material = new THREE.MeshBasicMaterial({color: 0x000000});
  d.geometry = new THREE.SphereGeometry(.02, 8, 8);
  
  // Check if meshes need to be added or removed
  if (newN > oldN) {
    // Meshes need to be added
    let diff = newN - oldN; // # to be added
    
    for (let i=0; i<diff; i++) {
      c.mesh = new THREE.Line(c.geometry, c.material);
      c.mesh.visible = opts.ce; // Set visibility (while adding circles live)
      circles.push(c.mesh);
      scene.add(c.mesh);
    
      d.mesh = new THREE.Mesh(d.geometry, d.material);
      dots.push(d.mesh);
      scene.add(d.mesh);
    }
  } else {
    // Meshes need to be removed
    let diff = oldN - newN; // # to be removed
    
    let circle, dot;
    for (let i=0; i<diff; i++) {
      // Last elements of the arrays
      circle = circles[oldN-i-1];
      dot = dots[oldN-i-1];
      
      // Clean memory and remove meshes
      circle.material.dispose();
      circle.geometry.dispose();
      circles.pop();
      scene.remove(circle);
      dot.material.dispose();
      dot.geometry.dispose();
      dots.pop();
      scene.remove(dot);
    }
  }
  
  // Changes have been made, so we need to update the rotation
  for (let i=0, rot; i<newN; i++) {
    rot = i/newN*Math.PI;
    
    circles[i].rotation.y = rot;
    dots[i].delay = rot; // The dot's delay and rotation
  }
}
generateMeshes(opts.n, 0);



/**
 * Rendering
 */
let nextframe;
function loop() {
  opts.t += opts.s;
  
  let _time, _rot, _dot;
  for (let i=0; i<dots.length; i++) {
    _dot = dots[i]; // The current dot
    
    _time = opts.t + _dot.delay*opts.k; // The actual time for the dot
    _rot = _dot.delay; // The actual rotation of the dot
    
    _dot.position.x = Math.sin(_rot)*Math.sin(_time);
    _dot.position.y = Math.cos(_time);
    _dot.position.z = Math.cos(_rot)*Math.sin(_time);
  }
  
  if (opts.ake) {
    opts.k += opts.aki;
    opts.k = Math.round(opts.k*1000)/1000; // Because of rounding imprecisions
    opts.elmts.k.value = opts.k;
  }
  
  
  controls.update();
  renderer.render(scene, camera);
  
  nextframe = requestAnimationFrame(loop);
}

loop();
              
            
!
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Console