# Bezier splines

## The 4 functions (Bernstein polynomials of order 3), P0(t), P1(t), P2(t), P3(t) are (almost) defined by the following properties:

- The sum is 1 for all t
- the endpoints have no influence on the position of the endpoint of the curve and on the tangents at opposite endpoints. This means that P0(1) = P0(1)´=0 , P3(0) = P3(0)´=0
- Two interior (blue) control points affect only the tangent and at the corresponding endpoint, not at the other endpoint, and do not affect the positions of the endpoints of the curve P1(0) =P1(1) = P1(1)´=0 , P2(1) =P2(0) = P2(0)´=0
- All polynomials are cubic and positive
- Symmetry w.r.t. t=1/2: P0(1-t) = P3(t), P1(1-t) = P2(t)