Fairing triangular B-splines of arbitrary topology

show a degree 5 ( C continuous) spherical spline and its mean curvature plot. Note that the spline surface has high curvature concentration along the image of edges of the spherical triangles. (e), (f) and (g) show the spline generated by our automatic fairing method. The computational time is 8 seconds on a 3GHz Pentium IV PC. Compared to the surface in (b), the shape of the smooth spline (e) does not change too much, but the curvature distribution improves significantly. The red curves in (c) and (f) correspond to the edges in the spherical triangulation. 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 for shape fairing. Our experimental results on several real datasets show that triangular B-splines are powerful and effective in both theory and practice. Keywords: Triangular B-splines, fairing algorithm. 1