= Parametric surface interrogation
{title2=$S,S_u,S_v,S_{uu},S_{uv},S_{vv}$}
Core numerical enquiries return a surface point and its <derivatives> through second order, together with the parameter domain, patch boundaries and regularity information. At a regular point these determine its <tangent plane>, <normal vector>, first and <second fundamental forms> and <curvatures>. Subdivision and certified enclosing volumes provide spatial search and intersection support. Singular charts or discontinuity boundaries require one-sided or alternative-chart information; a zero <cross product> does not define a unique <normal vector>.
Back to article page
