On degenerate surface patches

A local construction of aGC¹ interpolating surface to given scattered data in ³ can give rise to degenerate Bernstein-Bézier patches. This means that the parametrization at vertices is not regular in the sense that the length of the tangent vector to any curve passing through a vertex is zero at that vertex. This implies that the curvature of these curves tends to infinity whenever one approaches a vertex. This fact seems not to have a negative influence on the shape of the surface.