Improved shape for refinable surfaces with singularly parameterized irregularities. (September 2017) - Karčiauskas, Kȩstutis; Peters, Jörg
Abstract: To date, singularly-parameterized surface constructions suffer from poor highlight line distributions, ruling them out as a surface representation of choice for primary design surfaces. This paper explores graded, many-piece, everywhere C 1 singularly-parameterized surface caps that mimic the shape of a high-quality guide surface. The approach illustrates the trade-off between polynomial degree and surface quality. For bi-degree 5, minor flaws in the highlight line distribution are still visible when zooming in on the singularity, but the distribution is good at the macroscopic level. Constructions of degree bi-4 or bi-3 may require one or more steps of guided subdivision to reach the same macroscopic quality. Akin to subdivision surfaces, singularly-parameterized functions on the surfaces are straightforward to refine. Highlights: Singularly-parameterized surfaces are known to suffer from poor highlight line distributions. A new family of graded, many-piece, everywhere singularly-parameterized constructions is defined. The highlight line distribution of the new constructions is good at the macroscopic level. Singularly-parameterized functions on the surfaces are refinable. Graphical abstract: