Fairing Triangular B-splines of Arbitrary Topology

Triangular B-splines are powerful and flexible in modeling a broader class of geometric objects defined over arbitrary, non-rectangular domains. Despite their great potential and advantages in theory, practical techniques and computational tools with triangular B-splines are less-developed. This is mainly because users have to handle a large number of irregularly distributed control points over arbitrary triangulation. In this paper, we propose an automatic and efficient method to generate visually pleasing, high-quality triangular B-splines of arbitrary topology. Our experimental results on several real datasets show that triangular B-splines are powerful and effective in both theory and practice.