On the curvature of guided surfaces

Following [Karčiauskas, K., Peters, J., 2007. Concentric tessellation maps and curvature continuous guided surfaces. Computer Aided Geometric Design 24 (2) 99–111], we analyze surfaces arising as an infinite sequence of guided C2 surface rings. However, here we focus on constructions of a too low degree to be curvature continuous also at the extraordinary point. To characterize shape and smoothness of such surfaces, we track a sequence of quadratic functions anchored in a fixed coordinate system. These ‘anchored osculating quadratics’ are easily computed in terms of determinants of surface derivatives. Convergence of the sequence of quadratics certifies curvature continuity. Otherwise, the range of the curvatures of the limit quadratics gives a measure of deviation from curvature continuity.