“Bezier Curve” is a method of generating smooth curve in computer graphics. Note that it is a method of curve representation, and not a curve in the usual sense in math contexts.

The Bezier Curve method is named after the engineer Pierre Bézier.

Given 4 points P0, P1, P2, P3, find a parametric formula in polynomial such that it passes P0 with tangent vector[P0,P1], and passes P2 with tangent vector[P3,P2].