Curvature computations for degenerate surface patches
In modeling surfaces with rational \(B\)-spline patches one encounters frequently situations where the parametric representation is singular at a boundary point. The authors develop formulas for the computation of principal curvatures at such a point if the surface admits a representation \((x,y,g(x,y))\) near the point in question and \(g\) has a regular 2-jet. \{Many problems in computer graphics arise from the use of modern texts on differential geometry that are not adapted to computational problems. There is no problem in computer graphics that cannot be treated by methods presented, e.g., by \textit{G. Salmon} and \textit{W. Fiedler} [Analytische Geometrie des Raumes (2nd ed., Leipzig 1874)]\}.
scientific article; zbMATH DE number 97030