the relation of the bezier Curve and ellipse?

Question

I want to draw a oval in html5 canvas,and i found a good method for it in stackoverflow.but I have another quesition.

function drawEllipse(ctx, x, y, w, h) {         


        

Answer 1

It can be mathematically proven, that circle can not be made with Bézier curve of any degree. You can make "almost circle" by approximating it.

Say you want to draw a quarter of circle around [0,0]. Cubic bézier coordinates are:

[0   , 1   ]
[0.55, 1   ]
[1   , 0.55]
[1   , 0   ]

It is a very good approximation. Transform it linearly to get an ellpise.