| On the curvature of guided surfaces (2009) | |||||||||||||||||
Abstract | |||||||||||||||||
| Following [KP07], we analyze surfaces arising as an infinite sequence of guided C 2 surface rings. However, here we focus on constructions of too low a 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. Key words: curvature continuity, anchored osculating quadratic, guided surface, 1 | |||||||||||||||||
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