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HTML

              
                <canvas></canvas>
    <canvas></canvas>
    <canvas></canvas>
    <svg viewBox="0 0 10 10" version="1.1"
      xmlns="http://www.w3.org/2000/svg"
      id="dSprite">
      <circle cx="5" cy="5" r="5" style="fill: #db1313"/>
    </svg>
    <svg viewBox="0 0 10 10" version="1.1"
      xmlns="http://www.w3.org/2000/svg">
      <circle cx="5" cy="5" r="5" style="fill: #1313db"/>
    </svg>
    <div id="parameter"><i>t</i> = <span>0</span></div>
    <a href="/"><figure id="icon"></figure></a>
    
    <nav>
      <label for="number">Control points</label>
      <input name="number" id="number" type="number" value="3" min="2" max="14" step="1">
    </nav>
              
            
!

CSS

              
                html, body {
	height: 100%;
}

body {
	background: #111;
	color: white;
	margin:0;
}

canvas {
	width: 100%;
	height: 100%;
	position: absolute;
	left:0;
}

svg {
	position: absolute;
}
svg circle {
	opacity:0.8;
}

#parameter, .weight {
	position: absolute;
	font-size: 26px;
	color: white;
}

.weight {
	background: #909;
	padding: 5px;
	font-size: 13px;
	border-radius: 50%/25%;
}

figure#icon {
	position: fixed;

	opacity: .8;
	width: 70px;
	height: 70px;
	background: url("../images/icon.svg") no-repeat;
	background-size: contain;
	margin: 40px;
}

.draghelper {
	position: absolute;
}

nav {
	position: absolute;
	bottom: 25%;
}
nav #number {
	font-size: 24px;
}
              
            
!

JS

              
                
var ctx = [],
		bezier,
		slider,
		order = 3;

window.onload = function () {
	bezier = Bezier();
	slider = Slider();

	init();

	// Trouble with resizing the Draggable
	// You ought to look into that
	addEventListener('resize', init, false);

	var n = document.getElementById('number');
	var h = function () {
		order = n.value - 1;
  	var w = window.innerWidth,
				h = window.innerHeight;

		bezier.init(w, h);
		slider.draw(ctx[2]);
	};
	n.addEventListener('change', h );
	n.addEventListener('input', h );
};

function init () {
  var w = window.innerWidth,
			h = window.innerHeight;

	// Plural canvases
	// [1] is for the control points (so you can clear the canvas when dragging them
	// without interfering with the rest)
	// I'll have another canvas for the curve, so you can fade it a little when
	// you start a new one (after dragging a control point) (Not used)
	// [0] is for curve
	// [2] for chrome (slider)
	var canvases = document.getElementsByTagName('canvas');
	for (var i = 0; i < canvases.length; i++) {
		canvases[i].width = w;
		canvases[i].height = h;
		ctx[i] = canvases[i].getContext('2d');
		ctx[i].fillStyle = "#111";
	};
	ctx[1].strokeStyle = "#b98059";
	ctx[2].strokeStyle = "#fff";
	ctx[0].strokeStyle = "#fff";

	bezier.init(w, h);
	slider.init(ctx[2], bezier.update);
}

var Bezier = function () {
	var coordinateSprite, t, point_on_curve;
	var radius = 20;

	// each control point has a weight associated, and a basis function that detrmines the weight
	var cPoints = [];
	var basisF;
	var w = [];	
	
	var explicitFormula = function(t) {
		// Explicit Bezier formula for this curve
		
		var x = 0, y =0;
		
		for (var i = 0; i < cPoints.length; i++) {
			x += w[i] * cPoints[i].x;
			y += w[i] * cPoints[i].y;
		};

		return {x: x, y: y};
	}; 
	

	var init = function (w, h) {
		basisF = createBasis(order);

		// Create order + 1 more or less random control points
		var x, y, el, draghelper,
				offsetWeightSprite = {x: -15, y: 30};
		
		// Clean up DOM and old points, e.g when resizing, or picking a new order
		for (var i = 0; i < cPoints.length; i++) {
			document.body.removeChild(cPoints[i].weightSprite);
			document.body.removeChild(cPoints[i].dragsprite);
		}
		cPoints = [];

		for (var i = 0; i < order + 1; i++) {
			x = rand(200, w-2*radius);
			y = rand(radius, h * 3/5);

			// Create DOM sprite for parameter display
			el = document.createElement('div');
			
			el.className = "weight";
			el.style.left = x - offsetWeightSprite.x + "px";
			el.style.top = y + offsetWeightSprite.y + "px";
			
			document.body.appendChild(el);

			// And another DOM element for helping drag
			draghelper = document.createElement('div');
			draghelper.className = "draghelper";
			draghelper.style.left = x - radius + "px";
			draghelper.style.top = y -radius + "px";
			draghelper.style.width = 2*radius + "px";
			draghelper.style.height = 2*radius + "px";
			document.body.appendChild(draghelper);
			
			cPoints.push({x: x, y: y, weightSprite: el, dragsprite: draghelper});

			Draggable.create(draghelper,
				{	type: 'top,left', 
					onDrag: function(index, e) {
						// You might use e.target instead of cPoints[index].dragsprite

						// Update the corresponding control point
						cPoints[index].x = parseInt(cPoints[index].dragsprite.style.left, 10) + radius;
						cPoints[index].y = parseInt(cPoints[index].dragsprite.style.top, 10) + radius;
						
						// Update the weight display
						cPoints[index].weightSprite.style.left = cPoints[index].x - offsetWeightSprite.x + "px";
						cPoints[index].weightSprite.style.top = cPoints[index].y + offsetWeightSprite.y + "px";
						
						drawControlPoints();

						// You want to update the current Bezier coordinate too (its sprite).
						update(t);
					}.bind(this,i)
				}
			)

		};

		drawControlPoints();

		coordinateSprite = document.getElementsByTagName('svg')[1];
		coordinateSprite.style.width = 2*(radius/2) +"px";
		coordinateSprite.style.height = 2*(radius/2) +"px";	

		update(0);
	
	}

	function drawControlPoints() {
		// draw the control points and connection between 2 consecutive points

		// Erase the existing control points from the canvas

		ctx[1].clearRect ( 0 , 0 , ctx[1].canvas.width, ctx[1].canvas.height );


		for (var i = 0; i < cPoints.length; i++) {
			// First draw the line, you want to draw a filled circle over it
			if ( i < cPoints.length - 1 ) {
				drawLine(ctx[1], cPoints[i], cPoints[i+1]) ;
			}
			drawCircle(ctx[1], cPoints[i], radius/2, true);
			drawCircle(ctx[1], cPoints[i], radius, false);
		};
	}

	var update = function (t1) {
		// If t hasn't changed, assume we're only updating the controlpoints, not the
		// mark left by the coordinateSprite

		// Recalculate weights
		for (var i = 0; i < cPoints.length; i++) {
			w[i] = basisF(i,t1);

			// Display the weights per control point
			cPoints[i].weightSprite.innerHTML = w[i].toFixed(2);

		};
		
		var last_point;
		if (point_on_curve) {
			last_point = point_on_curve;
			point_on_curve = explicitFormula(t1);
		}
		else {
			point_on_curve = explicitFormula(t1);
			last_point = point_on_curve;
		}

		coordinateSprite.style.left = point_on_curve.x - radius/2 + "px";
		coordinateSprite.style.top = point_on_curve.y - radius/2 + "px";
		
		if ( t !== t1 ) {
			// Draw the points (line) of the curve
			ctx[0].beginPath();
			// ctx[0].arc(point_on_curve.x, point_on_curve.y, 0.7, 0, 2*Math.PI);
			ctx[0].moveTo(last_point.x, last_point.y)
			ctx[0].lineTo(point_on_curve.x, point_on_curve.y)
			ctx[0].stroke();
			// ctx[0].endPath();
		}

		t = t1;		
	};

	/**
	 * Create explicit formula for this Bezier curve.
	 * @return function
	 */
	var createExplicitFormula = function () {
		
		return (function(t) {
				var x = 0, y =0, m;

	 			for (var i = 0; i < cPoints.length; i++) {
					m = basisF(i,t);
					x += m * cPoints[i].x;
					y += m * cPoints[i].y;
				};

				return {x: x, y: y};
			}
		);
	};

	return {
		init: init,
		update: update
	};
}

var Slider = function() {
	var d, sprite,
			parameter_box_sprite,
			parameter_number_sprite,
			w, h, 
			minX, maxX;

	var init = function (ctx, callback) {
		// Only needed once at startup
		// After that use reset, to put the slider in it's original position
		// or redraw, to adjust the chrome to screen dimensions

		w = ctx.canvas.width,
		h = ctx.canvas.height;

		minX = floor(w/4);
		maxX = floor(3 * w/4);

		sprite = document.getElementsByTagName('svg')[0];
		parameter_box_sprite = document.getElementById('parameter');
		parameter_number_sprite = parameter_box_sprite.getElementsByTagName('span')[0];

		draw(ctx);

		//TODO
		radius_inner = 20;

		var d = new Draggable(sprite, 
				{	type: 'x', 
				bounds:{minX: 0, maxX:maxX - minX},
				onDrag: function() {
					var t = this.x / (maxX - minX);
					parameter_box_sprite.style.left = minX - radius_inner + this.x + "px";
					parameter_number_sprite.innerHTML = t.toPrecision(2);
					callback(t);
				}
			}
		);
	};

	var draw = function (ctx) {
		var radius_outer = 40,
				radius_inner = 20;
		
		var q1 = {x: minX, y: floor(h * 4/5) };
		var q2 = {x: maxX, y: floor(h * 4/5)};

		drawLine(ctx, q1,q2);

		drawCircle(ctx, q1, radius_inner, true);
		drawCircle(ctx, q1, radius_outer, false);
		drawCircle(ctx, q2, radius_inner, true);
		drawCircle(ctx, q2, radius_outer, false);

		// reset sprites
		sprite.style.left = q1.x - radius_inner + "px";
		sprite.style.top = q1.y - radius_inner + "px";
		sprite.style.width = 2*(radius_inner) +"px";
		sprite.style.height = 2*(radius_inner) +"px";

		// must reset transform in order to reset draggable
      TweenMax.set(sprite,{x:0})

		parameter_box_sprite.style.left = q1.x - radius_inner + "px";
		parameter_box_sprite.style.top = q1.y + radius_inner*3 +"px";

		// reset draggable
		if (typeof(d)!== 'undefined'){ 
			d[0].update();
		}
	}

	return {
		init: init,
		draw : draw
	};
};

// graphics
var drawCircle = function(ctx, p, radius, fill) {
	ctx.beginPath();
	ctx.arc(p.x, p.y, radius, 0, 2*Math.PI);
	ctx.lineWidth = 5;
	ctx.stroke();
	if ( fill === true ) ctx.fill();
}

var drawLine = function(ctx, p, q) {
	ctx.beginPath();
	ctx.moveTo(p.x, p.y);
	ctx.lineTo(q.x, q.y);
	ctx.lineWidth = 1;
	ctx.stroke();
}

// Util
var rand = function(min, max) {
	return min + random() * (max - min);
	// return floor(min + random() * (max+1 - min));	
};

/**
 * Calculate binomial coefficients
 * Recursion: Pascal's recurrence
 * Arguments must be integers >= 0, not checked
 * @param  {int} n 
 * @param  {int} k 
 * @return {int}  
 */
var binomial = function (n, k) {
	if (k == 0){
		return 1;
	}
	else if (n == 0) {
		return 0;
	}
	else {
		return binomial(n-1, k-1) + binomial(n-1,k);
	}
}


/**
 * Create basis function(s)
 * Also known as Bernstein basis polynomials
 * @param  {@int} order number of basis functions
 * @return {function} 
 */
function createBasis(order) {
	// Calculate and store binomial coefficients
	var b =[];
	for (var i = 0; i <= order; i++) {
		b[i] = binomial(order, i);
	}

	return (function(i,t){return b[i] * pow(1-t, order-i) * pow(t,i)});
}

Object.getOwnPropertyNames(Math).map(function(p) {
  window[p] = Math[p];
});

              
            
!
999px

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