ellipse and circle for canvas 2d context

These days I am working inside an ExtJS panel to create some sophisticated drawing stuff, and I discovered (too late ...) that there is almost nothing in canvas 2d context to draw circle or ellipse.

That's why I have extended Google excanvas library and/or native canvas 2d context prototype to let us create circles and ellipse in the same simple way we can create rectangles.

Here the extended proto:

(function(){
// Andrea Giammarchi - Mit Style License
var extend = {
    // Circle methods
    circle:function(aX, aY, aDiameter){
        this.ellipse(aX, aY, aDiameter, aDiameter);
    },
    fillCircle:function(aX, aY, aDiameter){
        this.beginPath();
        this.circle(aX, aY, aDiameter);
        this.fill();
    },
    strokeCircle:function(aX, aY, aDiameter){
        this.beginPath();
        this.circle(aX, aY, aDiameter);
        this.stroke();
    },
    // Ellipse methods
    ellipse:function(aX, aY, aWidth, aHeight){
        var hB = (aWidth / 2) * .5522848,
            vB = (aHeight / 2) * .5522848,
            eX = aX + aWidth,
            eY = aY + aHeight,
            mX = aX + aWidth / 2,
            mY = aY + aHeight / 2;
        this.moveTo(aX, mY);
        this.bezierCurveTo(aX, mY - vB, mX - hB, aY, mX, aY);
        this.bezierCurveTo(mX + hB, aY, eX, mY - vB, eX, mY);
        this.bezierCurveTo(eX, mY + vB, mX + hB, eY, mX, eY);
        this.bezierCurveTo(mX - hB, eY, aX, mY + vB, aX, mY);
        this.closePath();
    },
    fillEllipse:function(aX, aY, aWidth, aHeight){
        this.beginPath();
        this.ellipse(aX, aY, aWidth, aHeight);
        this.fill();
    },
    strokeEllipse:function(aX, aY, aWidth, aHeight){
        this.beginPath();
        this.ellipse(aX, aY, aWidth, aHeight);
        this.stroke();
    }
};
for(var key in extend)
    CanvasRenderingContext2D.prototype[key] = extend[key];
if(!this.G_vmlCanvasManager)
    G_vmlCanvasManager = {init:function(){}, initElement:function(el){return el}};
})();

The last part is to obtain the same behavior with any browser and runtime create canvas:

var myCanvas = G_vmlCanvasManager.initElement(document.createElement("canvas"));

SImple and efficient? I hope so, since I spent more than a couple of minutes to be able to create a perfect circle via 1/4 of a rectangle (square ... but how could I remember the bloody constant to do that?) :P

P.S. I remind you that the simplest function to create a circle via a center is canvas.arc(x, y, radius, 0, Math.PI*2); and that this proto create a circle inside a specified square but ithout the same arc performances ( anyway, runtime rendering in IE and my personal version of excanvas even faster than FireFox 3 ... anybody interested? :-) )