PerfectEquation
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							<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" >
<head>
<title>Approximation of an arc with bezier</title>
<style type="text/css">
	@import "../../../dojo/resources/dojo.css";
	@import "../../../dijit/tests/css/dijitTests.css";
</style>
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<script type="text/javascript" src="../../../dojo/dojo.js" djConfig="isDebug: true"></script>
<script type="text/javascript" src="../_base.js"></script>
<script type="text/javascript" src="../shape.js"></script>
<script type="text/javascript" src="../path.js"></script>
<script type="text/javascript" src="../arc.js"></script>
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<script type="text/javascript">
dojo.require("dojox.gfx");

makeShapes = function(){
	var surface = dojox.gfx.createSurface("test", 500, 300);
	var g = surface.createGroup();
	
	// create a reference ellipse
	var rx = 200;
	var ry = 100;
	var startAngle = -30;
	var arcAngle = -90;
	var axisAngle = -30;
	var e = g.createEllipse({rx: rx, ry: ry}).setStroke({});
	
	// calculate a bezier
	var alpha = dojox.gfx.matrix._degToRad(arcAngle) / 2; // half of our angle
	var cosa  = Math.cos(alpha);
	var sina  = Math.sin(alpha);
	// start point
	var p1 = {x: cosa, y: sina};
	// 1st control point
	var p2 = {x: cosa + (4 / 3) * (1 - cosa), y: sina - (4 / 3) * cosa * (1 - cosa) / sina};
	// 2nd control point (symmetric to the 1st one)
	var p3 = {x: p2.x, y: -p2.y};
	// end point (symmetric to the start point)
	var p4 = {x: p1.x, y: -p1.y};
	
	// rotate and scale poins as appropriate
	var s = dojox.gfx.matrix.normalize([dojox.gfx.matrix.scale(e.shape.rx, e.shape.ry), dojox.gfx.matrix.rotateg(startAngle + arcAngle / 2)]);
	p1 = dojox.gfx.matrix.multiplyPoint(s, p1);
	p2 = dojox.gfx.matrix.multiplyPoint(s, p2);
	p3 = dojox.gfx.matrix.multiplyPoint(s, p3);
	p4 = dojox.gfx.matrix.multiplyPoint(s, p4);
	// draw control trapezoid
	var t = g.createPath().setStroke({color: "blue"});
	t.moveTo(p1.x, p1.y);
	t.lineTo(p2.x, p2.y);
	t.lineTo(p3.x, p3.y);
	t.lineTo(p4.x, p4.y);
	t.lineTo(p1.x, p1.y);
	t.moveTo((p1.x + p4.x) / 2, (p1.y + p4.y) / 2);
	t.lineTo((p2.x + p3.x) / 2, (p2.y + p3.y) / 2);
	t.moveTo((p1.x + p2.x) / 2, (p1.y + p2.y) / 2);
	t.lineTo((p3.x + p4.x) / 2, (p3.y + p4.y) / 2);
	// draw a bezier
	var b = g.createPath().setStroke({color: "red"});
	b.moveTo(p1.x, p1.y);
	b.curveTo(p2.x, p2.y, p3.x, p3.y, p4.x, p4.y);
	// move everything in a middle
	g.setTransform([dojox.gfx.matrix.translate(250, 150), dojox.gfx.matrix.rotateg(axisAngle)]);
};

dojo.addOnLoad(makeShapes);

</script>
</head>
<body>
<h1>Approximation of an arc with bezier</h1>
<!--<p><button onclick="makeShapes();">Make</button></p>-->
<div id="test" style="width: 500px; height: 300px;"></div>
<p>That's all Folks!</p>
</body>
</html>