Pen Settings

HTML

CSS

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. If you link to another Pen, it will include the CSS from that Pen. If the preprocessor matches, it will attempt to combine them before processing.

+ add another resource

JavaScript

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

Packages

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.

Behavior

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.

HTML

              
                <button type="button" id="btnControl">control points on/off</button>
<button type="button" id="btnSplit">split curve on/off</button>
<div id="text">Check a more complete demo ported from Flash <a target="_blank" href="https://microbians.com/math/bezieroffseting.html">here →</a><br/>
  Also take a look the the math paper <a target="_blank" href="http://microbians.com/math/Gabriel_Suchowolski_Quadratic_bezier_offsetting_with_selective_subdivision.pdf">Quadratic bezier offsetting with selective subdivision →</a> <br/><br/>
  Gabriel Suchowolski (<a href="https://microbians.com" target="_blank">microbians</a>), Jul 10, 2012
</div>
<div id="little">Thanks to Bruno Imbrizi for the code (that I fork) implementing my paper at CodePen.</div>
              
            
!

CSS

              
                html, body { font-family: sans-serif; height: 100%; margin:0 }
canvas { display:block }
#btnControl { font-size:1em; position: absolute; top: 10px; left: 10px; }
#btnSplit { font-size:1em; position: absolute; top: 35px; left: 10px; }
#text { position: absolute; top: 75px; left: 10px; }
a {
  text-decoration: none;
  font-weight:700;
  color: #2f94e2;
}
#little { font-size:.7em; color:#a0a0a0; position: absolute; top: 775px; left: 10px; }
              
            
!

JS

              
                var canvas, ctx;
var drags;
var thickness = 60;
var drawControlPoints = true;
var useSplitCurve = true;

function init() {
	canvas = document.createElement('canvas');
	ctx = canvas.getContext('2d');
	document.body.appendChild(canvas);
  
	drags = [];
	
	window.addEventListener('resize', resize );
	window.addEventListener('mousedown', mousedown );
	window.addEventListener('mouseup', mouseup );
	window.addEventListener('mousemove', mousemove );

	document.getElementById('btnControl').addEventListener('click', function(e) { drawControlPoints = !drawControlPoints} );
	document.getElementById('btnSplit').addEventListener('click', function(e) { useSplitCurve = !useSplitCurve} );
	
	resize();
	draw();
  
  var positions = [ {x:canvas.width * 0.3, y:canvas.height * 0.4}, {x:canvas.width * 0.35, y:canvas.height * 0.85}, {x:canvas.width * 0.7, y:canvas.height * 0.25} ];
	for (var i = 0; i < positions.length; i++) {
		drags.push(new Drag(ctx, new Vec2D(positions[i].x, positions[i].y)));
	}
}

function draw() {
	requestAnimationFrame(draw);
	
	ctx.fillStyle = '#FFFFFF';
	ctx.fillRect(0, 0, canvas.width, canvas.height);
	ctx.lineWidth = 1;

	for (var i = 0; i < drags.length; i++) {
		d = drags[i];
		d.draw();
	}
  
	for (var i = 1; i < drags.length - 1; i++) {
   
    var p1 = drags[i - 1].pos;
		var p2 = drags[i + 1].pos;
		var c = drags[i].pos;

		var v1 = c.sub(p1);
		var v2 = p2.sub(c);

		var n1 = v1.normalizeTo(thickness).getPerpendicular();
		var n2 = v2.normalizeTo(thickness).getPerpendicular();

		var p1a = p1.add(n1);
		var p1b = p1.sub(n1);
		var p2a = p2.add(n2);
		var p2b = p2.sub(n2);

		var c1a = c.add(n1);
		var c1b = c.sub(n1);
		var c2a = c.add(n2);
		var c2b = c.sub(n2);

		var line1a = new Line2D(p1a, c1a);
		var line1b = new Line2D(p1b, c1b);
		var line2a = new Line2D(p2a, c2a);
		var line2b = new Line2D(p2b, c2b);

		var split = (useSplitCurve && v1.angleBetween(v2, true) > Math.PI / 2);

		if (!split) {
			var ca = line1a.intersectLine(line2a).pos;
			var cb = line1b.intersectLine(line2b).pos;
		}
		else {
			var t = MathUtils.getNearestPoint(p1, c, p2);
			var pt = MathUtils.getPointInQuadraticCurve(t, p1, c, p2);

			var t1 = p1.scale(1 - t).add(c.scale(t));
			var t2 = c.scale(1 - t).add(p2.scale(t));

			var vt = t2.sub(t1).normalizeTo(thickness).getPerpendicular();
			var qa = pt.add(vt);
			var qb = pt.sub(vt);

			var lineqa = new Line2D(qa, qa.add(vt.getPerpendicular()));
			var lineqb = new Line2D(qb, qb.add(vt.getPerpendicular()));

			var q1a = line1a.intersectLine(lineqa).pos;
			var q2a = line2a.intersectLine(lineqa).pos;
			var q1b = line1b.intersectLine(lineqb).pos;
			var q2b = line2b.intersectLine(lineqb).pos;
		}

		if (drawControlPoints) {
			// draw control points
			var r = 2;
			ctx.beginPath();
			if (!split) {
				ctx.rect(ca.x - r, ca.y - r, r * 2, r * 2);
				ctx.rect(cb.x - r, cb.y - r, r * 2, r * 2);
			}
			else {
				// ctx.rect(pt.x - r, pt.y - r, r * 2, r * 2);
				ctx.rect(p1a.x - r, p1a.y - r, r * 2, r * 2);
				ctx.rect(q1a.x - r, q1a.y - r, r * 2, r * 2);
				ctx.rect(p2a.x - r, p2a.y - r, r * 2, r * 2);
				ctx.rect(q2a.x - r, q2a.y - r, r * 2, r * 2);
				ctx.rect(qa.x - r, qa.y - r, r * 2, r * 2);

				ctx.rect(p1b.x - r, p1b.y - r, r * 2, r * 2);
				ctx.rect(q1b.x - r, q1b.y - r, r * 2, r * 2);
				ctx.rect(p2b.x - r, p2b.y - r, r * 2, r * 2);
				ctx.rect(q2b.x - r, q2b.y - r, r * 2, r * 2);
				ctx.rect(qb.x - r, qb.y - r, r * 2, r * 2);

				ctx.moveTo(qa.x, qa.y);
				ctx.lineTo(qb.x, qb.y);
			}
			ctx.closePath();
			ctx.strokeStyle = '#2f94e2';
			ctx.stroke();
			ctx.fillStyle = '#2f94e2';
			ctx.fill();

			// draw dashed lines
			ctx.beginPath();
			if (!split) {
				ctx.moveTo(p1a.x, p1a.y);
				ctx.lineTo(ca.x, ca.y);
				ctx.lineTo(p2a.x, p2a.y);

				ctx.moveTo(p1b.x, p1b.y);
				ctx.lineTo(cb.x, cb.y);
				ctx.lineTo(p2b.x, p2b.y);
			}
			else {
				ctx.moveTo(p1a.x, p1a.y);
				ctx.lineTo(q1a.x, q1a.y);
				ctx.lineTo(qa.x, qa.y);
				ctx.lineTo(q2a.x, q2a.y);
				ctx.lineTo(p2a.x, p2a.y);

				ctx.moveTo(p1b.x, p1b.y);
				ctx.lineTo(q1b.x, q1b.y);
				ctx.lineTo(qb.x, qb.y);
				ctx.lineTo(q2b.x, q2b.y);
				ctx.lineTo(p2b.x, p2b.y);
			}
			ctx.setLineDash([2,4]);
			ctx.stroke();
			ctx.closePath();
			ctx.setLineDash([]);
		}

		// central line
		ctx.beginPath();
		ctx.moveTo(p1.x, p1.y);
		ctx.quadraticCurveTo(c.x, c.y, p2.x, p2.y);
		ctx.strokeStyle = '#959595';
		ctx.stroke();

		// offset curve a
		ctx.beginPath();
		ctx.moveTo(p1a.x, p1a.y);
		if (!split) {
			ctx.quadraticCurveTo(ca.x, ca.y, p2a.x, p2a.y);
		}
		else {
			ctx.quadraticCurveTo(q1a.x, q1a.y, qa.x, qa.y);
			ctx.quadraticCurveTo(q2a.x, q2a.y, p2a.x, p2a.y);
		}
		ctx.strokeStyle = '#0072bc';
		ctx.lineWidth = 2;
		ctx.stroke();

		// offset curve b
		ctx.beginPath();
		ctx.moveTo(p1b.x, p1b.y);
		if (!split) {
			ctx.quadraticCurveTo(cb.x, cb.y, p2b.x, p2b.y);
		}
		else {
			ctx.quadraticCurveTo(q1b.x, q1b.y, qb.x, qb.y);
			ctx.quadraticCurveTo(q2b.x, q2b.y, p2b.x, p2b.y);
		}
		ctx.strokeStyle = '#0072bc';
		ctx.stroke();
	}
}

function resize() {
	canvas.width = window.innerWidth;
	canvas.height = window.innerHeight;
}

function mousedown(e) {
	e.preventDefault();
	
	var m = new Vec2D(e.clientX, e.clientY);

 	for (var i = 0; i < drags.length; i++) {
 		var d = drags[i];
 		var dist = d.pos.distanceToSquared(m);
 		if (dist < d.hitRadiusSq) {
 			d.down = true;
 			break;
 		}
 	}
}

function mouseup() {
  	for (var i = 0; i < drags.length; i++) {
 		var d = drags[i];
 		d.down = false;
 	}
}

function mousemove(e) {
	var m = new Vec2D(e.clientX, e.clientY);

  	for (var i = 0; i < drags.length; i++) {
 		var d = drags[i];
 		if (d.down) {
 			d.pos.x = m.x;
 			d.pos.y = m.y;
 			break;
 		}
 	}
}

function Drag(ctx, pos) {
	this.ctx = ctx;
	this.pos = pos;
	this.radius = 6;
	this.hitRadiusSq = 900;
	this.down = false;
}

Drag.prototype = {
	draw: function() {
		this.ctx.beginPath();
		this.ctx.arc(this.pos.x, this.pos.y, this.radius, 0, Math.PI * 2);
		this.ctx.closePath();
		this.ctx.strokeStyle = '#959595'
		this.ctx.stroke();
	}
}

// http://toxiclibs.org/docs/core/toxi/geom/Vec2D.html
function Vec2D(a,b) {
	this.x = a;
	this.y = b;
}

Vec2D.prototype = {
	add: function(a) {
	  return new Vec2D(this.x + a.x, this.y + a.y);
	},
	angleBetween: function(v, faceNormalize) {
	  if(faceNormalize === undefined){
		var dot = this.dot(v);
		return Math.acos(this.dot(v));
	  }
	  var theta = (faceNormalize) ? this.getNormalized().dot(v.getNormalized()) : this.dot(v);
	  return Math.acos(theta);
	},
	distanceToSquared: function(v) {
        if (v !== undefined) {
            var dx = this.x - v.x;
            var dy = this.y - v.y;
            return dx * dx + dy * dy;
        } else {
            return NaN;
        }
    },
	dot: function(v) {
	  return this.x * v.x + this.y * v.y;
	},
	getNormalized: function() {
	   return new Vec2D(this.x, this.y).normalize();
	},
	getPerpendicular: function() {
	  return new Vec2D(this.x, this.y).perpendicular();
	},
	interpolateTo: function(v, f) {
	   return new Vec2D(this.x + (v.x -this.x) * f, this.y + (v.y - this.y) * f);
	},
	normalize: function() {
		var mag = this.x * this.x + this.y * this.y;
		if (mag > 0) {
			mag = 1.0 / Math.sqrt(mag);
			this.x *= mag;
			this.y *= mag;
		}
		return this;
	},
	normalizeTo: function(len) {
	  var mag = Math.sqrt(this.x * this.x + this.y * this.y);
	  if (mag > 0) {
		mag = len / mag;
		this.x *= mag;
		this.y *= mag;
	  }
	  return this;
	},
	perpendicular: function() {
	  var t = this.x;
	  this.x = -this.y;
	  this.y = t;
	  return this;
	},
	scale: function(a) {
	  return new Vec2D(this.x * a, this.y * a);
	},
	sub: function(a,b){
	  return new Vec2D(this.x -a.x, this.y - a.y);
  },
}

// http://toxiclibs.org/docs/core/toxi/geom/Line2D.html
function Line2D(a, b) {
	this.a = a;
	this.b = b;
}

Line2D.prototype = {
	intersectLine: function(l) {
	var isec,
	  denom = (l.b.y - l.a.y) * (this.b.x - this.a.x) - (l.b.x - l.a.x) * (this.b.y - this.a.y),
	  na = (l.b.x - l.a.x) * (this.a.y - l.a.y) - (l.b.y - l.a.y) * (this.a.x - l.a.x),
	  nb = (this.b.x - this.a.x) * (this.a.y - l.a.y) - (this.b.y - this.a.y) * (this.a.x - l.a.x);
	if (denom !== 0) {
	  var ua = na / denom,
		ub = nb / denom;
	  if (ua >= 0.0 && ua <= 1.0 && ub >= 0.0 && ub <= 1.0) {
		isec =new Line2D.LineIntersection(Line2D.LineIntersection.Type.INTERSECTING,this.a.interpolateTo(this.b, ua));
	  } else {
		isec = new Line2D.LineIntersection(Line2D.LineIntersection.Type.NON_INTERSECTING, this.a.interpolateTo(this.b, ua));
	  }
	} else {
	  if (na === 0 && nb === 0) {
		isec = new Line2D.LineIntersection(Line2D.LineIntersection.Type.COINCIDENT, undefined);
	  } else {
		isec = new Line2D.LineIntersection(Line2D.LineIntersection.Type.COINCIDENT, undefined);
	  }
	}
	return isec;
  }
}

Line2D.LineIntersection = function(type, pos) {
  this.type = type;
  this.pos = pos;
}

Line2D.LineIntersection.Type = { COINCIDENT: 0, PARALLEL: 1, NON_INTERSECTING: 2, INTERSECTING: 3};


window.MathUtils = {
	getPointInQuadraticCurve: function(t, p1, pc, p2) {
		var x = (1 - t) * (1 - t) * p1.x + 2 * (1 - t) * t * pc.x + t * t * p2.x;
		var y = (1 - t) * (1 - t) * p1.y + 2 * (1 - t) * t * pc.y + t * t * p2.y;
		
		return new Vec2D(x, y);
	},

// http://microbians.com/math/Gabriel_Suchowolski_Quadratic_bezier_offsetting_with_selective_subdivision.pdf
	getNearestPoint: function (p1, pc, p2) {
    
    // Some years ago I found this little calc, tents to the nearest point as angle tents to 0... I have a wonderful demostratinon on this, but the space here is so little to expose...
    
   	var d1 = Math.sqrt(pc.distanceToSquared(p1));
	  var d2 = Math.sqrt(pc.distanceToSquared(p2));
  	var t=d1/(d1+d2);

/*
    var v0 = pc.sub(p1);
		var v1 = p2.sub(pc);

		var a = v1.sub(v0).dot(v1.sub(v0));
		var b = 3 * (v1.dot(v0) - v0.dot(v0));
		var c = 3 * v0.dot(v0) - v1.dot(v0);
		var d = -1 * v0.dot(v0);

		var p = -b / (3 * a);
		var q = p * p * p + (b * c - 3 * a * d) / (6 * a * a);
		var r = c / (3 * a);

		var s = Math.sqrt(q * q + Math.pow(r - p * p, 3));
		var t = MathUtils.cbrt(q + s) + MathUtils.cbrt(q - s) + p;
*/
		return t;
	},

	// http://stackoverflow.com/questions/12810765/calculating-cubic-root-for-negative-number
	cbrt: function (x) {
		var sign = x === 0 ? 0 : x > 0 ? 1 : -1;
		return sign * Math.pow(Math.abs(x), 1/3);
	}
}

init();
              
            
!
999px

Console