Manifold splines

Constructing splines whose parametric domain is an arbitrary manifold and effectively computing such splines in realworld applications are of fundamental importance in solid and shape modeling, geometric design, graphics, etc. This paper presents a general theoretical and computational framework, in which spline surfaces defined over planar domains can be systematically extended to manifold domains with arbitrary topology with or without boundaries. We study the affine structure of domain manifolds in depth and prove that the existence of manifold splines is equivalent to the existence of a manifold’s affine atlas. Based on our theoretical breakthrough, we also develop a set of practical algorithms to generalize triangular B-spline surfaces from planar domains to manifold domains. We choose triangular B-splines mainly because of its generality and many of its attractive properties. As a result, our new spline surface defined over any manifold is a piecewise polynomial surface wit...

• Type: Conference
• Year: 2005
• Where: SMA
• Authors: Xianfeng Gu, Ying He 0001, Hong Qin
• Keywords: Arbitrary Manifold, Manifold, Manifold Splines, SMA 2005