
Curvature of a Spheroid
Start with a continuous surface, parameterized in spherical coordinates, such that r(theta,phi) is defined uniquely for all points on the surface. Partial derivatives (first and second order) with respect to spherical bases (theta,phi) are known at every point on the surface. Given a point with a known position (r, theta, phi) and partial derivatives (dr/dphi, dr/dtheta, d2r/dphi2, d2r/dtheta2, d2r/dthetadphi), is it possible to calculate the principal curvature at this point? Is this possible for an arbitrary surface (no axis of revolution) ?