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<title>Approximation of an arc with bezier</title>
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dojo.require("dojo.gfx.*");
makeShapes = function(){
var surface = dojo.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 = dojo.math.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 = dojo.gfx.matrix.normalize([dojo.gfx.matrix.scale(e.shape.rx, e.shape.ry), dojo.gfx.matrix.rotateg(startAngle + arcAngle / 2)]);
p1 = dojo.gfx.matrix.multiplyPoint(s, p1);
p2 = dojo.gfx.matrix.multiplyPoint(s, p2);
p3 = dojo.gfx.matrix.multiplyPoint(s, p3);
p4 = dojo.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([dojo.gfx.matrix.translate(250, 150), dojo.gfx.matrix.rotateg(axisAngle)]);
};
dojo.addOnLoad(makeShapes);
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<p>Approximation of an arc with bezier</p>
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<p>That's all Folks!</p>
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