So lets say I have a mesh and for each face I have the position of its $3$ vertices and the area of the face.
So let's say I have a point $p$ on this face and a vector $v$ that goes from $p$ to the camera/viewer. Let $x$ be its normalized projection onto the tangent plane to the surface $S$. What is the curvature at point $p$ in direction $x$?
First, how would I go about finding the tangent plane to this surface and projecting $v$ onto it? Then where do I go from there?