On the curvature of guided surfaces

Following [KP07], we analyze surfaces arising as an infinite sequence of guided C2 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,

• Type: Journal
• Year: 2008
• Where: CAGD
• Authors: Kestutis Karciauskas, Jörg Peters
• Keywords: Analyze Surfaces, CAGD 2008, Curvature Continuity, Infinite Sequence