Rational Spherical Splines for Genus Zero Shape Modeling

Traditional approaches for modeling a closed manifold surface with either regular tensor-product or triangular splines (defined over an open planar domain) require decomposing the acquired geometric data into a group of charts, mapping each chart to a planar parametric domain, fitting an open surface patch of certain degree to each chart, and finally, trimming the patches (if necessary) and stitching all of them together to form a closed manifold. In this paper, we develop a novel modeling method which does not need any cutting or patching operations for genus zero surfaces. Our new approach is founded upon the concept of spherical splines proposed by Pfeifle and Seidel. Our work is strongly inspired by the fact that, for genus zero surfaces, it is both intuitive and necessary to employ spheres as their natural domains. Using this framework, we can convert genus zero mesh to a single rational spherical spline whose maximal error deviated from the original data is less than a user-...

• Type: Conference
• Year: 2005
• Where: SMI
• Authors: Ying He 0001, Xianfeng Gu, Hong Qin
• Keywords: Genus Zero Surfaces, Rational Spherical Splines, SMI 2005, Spherical Splines