= Plane section of a subdivision surface
{title2=$g(u,v)=n\cdot S(u,v)-d=0$}
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, $\nabla g\ne0$ 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.
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