Curvature-bounded guided subdivision: Biquartics vs bicubics. (September 2019) - Karčiauskas, Kȩstutis; Peters, Jörg
Abstract: A sequence of C 2 -connected nested subdivision rings of polynomial degree bi-4 can be made to follow a guide surface and completed by a tiny finite cap to serve as a refinable surface representation for design and analysis (Karčiauskas and Peters, 2018) . This raises the question, both of academic and practical interest, how much and at what cost to surface quality can the efficiency be improved by lowering the number of rings and/or the polynomial degree. In a systematic exploration, a new bi-4 construction is discovered that requires half the number of surface rings but matches the quality of (Karčiauskas and Peters, 2018). For this surface quality, numerous trials indicate that this number of surface rings is minimal and that the degree cannot be reduced. Bi-3 constructions with a similar layout have inferior highlight line distributions – although the best of the new bi-3 constructions visibly improve on Catmull–Clark subdivision and its curvature-bounded variants. Highlights: A systematic exploration of low-degree C 2 -connected subdivision rings. A bi-4 subdivision scheme halves the number of surface rings while matching the quality of its best predecessor. Numerous trials indicate that reducing the number of rings or the degree yield notably worse shape. Analogous bi-3 constructions have inferior highlight line distributions. but visibly improve on Catmull–Clark and curvature-bounded variants.