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HTML

              
                <h1>Quadratic bezier throw 3 points</h1>
<div>
  
  Also take a look the the math paper <a target="_blank" href="https://microbians.com/mathcode">Quadratic bezier through three points! →</a> <br/><br/>
  Gabriel Suchowolski (<a href="https://microbians.com" target="_blank">microbians</a>), December, 2012
</div>
<div id="little">Thanks to 艾蔓草 xhhjin for the code (that I fork) implementing my math paper.</div>
  <br/>
</div>
<input type="checkbox" id="cbThrough" name="through"/>Primitive quadratic Bezier (as control points)</input><br/><br/>
<canvas id="canvas" height="500" width="800" class="through" style="cursor: default; background-color: #FFF;"></canvas>
              
            
!

CSS

              
                html, body { background-color: #DDD;font-family: sans-serif; height: 100%; margin:0;
padding:10px;
}
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

              
                (function() {

	var canvas, ctx, point, style, drag = null, dPoint;

	// define initial points
	function Init() {
		point = {
			p1: { x:200, y:350 },
			p2: { x:600, y:350 }
		};
		point.cp1 = { x: 500, y: 200 };
		
		// default styles
		style = {
			curve:	{ width: 2, color: "#333" },
			cpline:	{ width: 1, color: "#C00" },
			curve1:	{ width: 1, color: "#2f94e2" },
			curve2: { width: 1, color: "#2f94e2" },
			point: { radius: 10, width: 2, color: "#2f94e2", fill: "rgba(200,200,200,0.5)", arc1: 0, arc2: 2 * Math.PI }
		}
		
		// line style defaults
		ctx.lineCap = "round";
		ctx.lineJoin = "round";

		// event handlers
		canvas.onmousedown = DragStart;
		canvas.onmousemove = Dragging;
		canvas.onmouseup = canvas.onmouseout = DragEnd;
		
		DrawCanvas();
	}
	
	
	// draw canvas
	function DrawCanvas() {
		ctx.clearRect(0, 0, canvas.width, canvas.height);
		
		// control lines
		ctx.lineWidth = style.cpline.width;
		ctx.strokeStyle = style.cpline.color;
		ctx.beginPath();
		ctx.moveTo(point.p1.x, point.p1.y);
		ctx.lineTo(point.cp1.x, point.cp1.y);
		ctx.lineTo(point.p2.x, point.p2.y);
		ctx.stroke();
		
		// curve
		ctx.lineWidth = style.curve.width;
		ctx.strokeStyle = style.curve.color;
		ctx.beginPath();
		ctx.moveTo(point.p1.x, point.p1.y);

		through = !document.getElementById("cbThrough").checked;
		if(through)
		{
			tmpx1 = point.p1.x-point.cp1.x;
			tmpx2 = point.p2.x-point.cp1.x;
			tmpy1 = point.p1.y-point.cp1.y;
			tmpy2 = point.p2.y-point.cp1.y;
			dist1 = Math.sqrt(tmpx1*tmpx1+tmpy1*tmpy1);
			dist2 = Math.sqrt(tmpx2*tmpx2+tmpy2*tmpy2);
			tmpx = point.cp1.x-Math.sqrt(dist1*dist2)*(tmpx1/dist1+tmpx2/dist2)/2;
			tmpy = point.cp1.y-Math.sqrt(dist1*dist2)*(tmpy1/dist1+tmpy2/dist2)/2;
			ctx.quadraticCurveTo(tmpx, tmpy, point.p2.x, point.p2.y);
		}
		else
		{
			ctx.quadraticCurveTo(point.cp1.x, point.cp1.y, point.p2.x, point.p2.y);
		}
		
		ctx.stroke();
		
		//new, t range is [0, 1]
		ctx.beginPath();
		ctx.lineWidth = style.curve1.width;
		ctx.strokeStyle = style.curve1.color;
		
		ctx.moveTo(point.p1.x, point.p1.y);
		
		// control points
		for (var p in point) {
			ctx.lineWidth = style.point.width;
			ctx.strokeStyle = style.point.color;
			ctx.fillStyle = style.point.fill;
			ctx.beginPath();
			ctx.arc(point[p].x, point[p].y, style.point.radius, style.point.arc1, style.point.arc2, true);
			ctx.fill();
			ctx.stroke();
		}
	}
	
	// start dragging
	function DragStart(e) {
		e = MousePos(e);
		var dx, dy;
		for (var p in point) {
			dx = point[p].x - e.x;
			dy = point[p].y - e.y;
			if ((dx * dx) + (dy * dy) < style.point.radius * style.point.radius) {
				drag = p;
				dPoint = e;
				canvas.style.cursor = "move";
				return;
			}
		}
	}
	
	
	// dragging
	function Dragging(e) {
		if (drag) {
			e = MousePos(e);
			point[drag].x += e.x - dPoint.x;
			point[drag].y += e.y - dPoint.y;
			dPoint = e;
			DrawCanvas();
		}
	}
	
	
	// end dragging
	function DragEnd(e) {
		drag = null;
		canvas.style.cursor = "default";
		DrawCanvas();
	}

	
	// event parser
	function MousePos(event) {
		event = (event ? event : window.event);
		return {
			x: event.pageX - canvas.offsetLeft,
			y: event.pageY - canvas.offsetTop
		}
	}
	
	
	// start
	canvas = document.getElementById("canvas");
	if (canvas.getContext) {
		ctx = canvas.getContext("2d");
		Init();
	}
	
})();

 





              
            
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