Implicit Quadric/Cubic Surface Fitting (Total-Least-Squares)

Fits an implicit polynomial surface p(y)=0 of increasing degree (affine, quadric, cubic) to a reduced-dimension point cloud via total-least-squares (SVD on the monomial design matrix), then compares held-out residual error across degrees and classifies the fitted quadric's type (ellipsoid, hyperboloid, paraboloid, cylinder, cone) to characterize local curvature.