I need to write an OpenGL program to generate and display a piecewise quadratic Bézier curve that interpolates each set of data points:
$$(0.1, 0), (0, 0), (0, 5), (0.25, 5), (0.25, 0), (5, 0), (5, 5), (10, 5), (10, 0), (9.5, 0)$$
The curve should have continuous tangent directions, the tangent direction at each data point being a convex combination of the two adjacent chord directions.
I am not good at math, can anyone give me some suggestions about what formula I can use to calculate control point for Bézier curve if I have a starting point and an ending point.
Thanks in advance