The Bezier curves have the following properties:
- endpoints are interpolated
- tangents at endpoints point towards the interior control points;derivatives are 3(p1-p0) and 3(p3-p2) respectively;
- the curve is in the convex hull of control points.
The formula for the Bezier curve is
p(t) = (1-t)3 p0 + 3t(1-t)2 p1 + 3t2(1-t) p2 + t3 p3