The Curved Triangle Problem
As the starting point for a little machine learning project, I chose the following geometric problem. We are given a curved triangle in 3D space. It’s specified via its three vertices plus three additional vector-valued coefficients associated to its three edges. These coefficients are interpreted as control points of a quadratic triangular Bezier surface. Such representations are commonly used in CAD systems to represent curved surfaces. Mathematically speaking, we map parameters \((u,v)\) which lie in the parameter-space triangle \( 0 \le u, v;\ u+v \le 1\) to ...