How do bezier handles work?

Question

On Wikipedia I found information about bezier curves and made a function to generate the inbetween points for a bezier polygon. I noticed that Expression Design uses bezier handles. This allows a circle to be made with 4 points each with a bezier handle.

I'm just not sure mathematically how this works in relation with the formula for bezier point at time T. How do these handle vectors work to modify the shape? Basically what's there relation to the bezier formula?

Thanks

Answer 1

Basically, the 4 points used in the cubic bezier formula are the 2 points the curve is between, plus the two points of the handles on that "side" of the first two points (1 handle from each of the first points). If there are double handles on each point, the handles on the "opposite" side of the points from the curve currently being calculated are ignored (they're used for generating the curve that comes out of the opposite side).

The actual generation method used for cubic bezier curves is outlined on the Wikipedia page you linked in your question.