Plane section of a subdivision surface ($g(u,v)=n\cdot S(u,v)-d=0$)

A plane section of a subdivision surface is a zero set of the plane functional evaluated on the limit parametric surface. Certified patch bounding volumes reject sign-definite patches. On a regular transverse section, $\nabla g\ne 0$ and the parameter tangent is $(-g_v,g_u)$; predictor-corrector continuation method traces a branch after every component has been isolated. Closed loops, tangencies, coplanar patches and extraordinary-vertex neighborhoods require more than corner-sign tests. Degenerate sections can contain isolated points or two-dimensional portions rather than only regular curves.