I’d like to draw Bezier curves algorithmically, i.e. I’d like the control points to be functions of two data points. Assuming the following Bezier curve:

I imagine P0, P1, and P2 form an obtuse triangle where the angle at P1, say β, is somewhere around 115 degrees. How do I find point P1 given that points P0 and P2 are determined by my data?