Manifold splines with a single extraordinary point

Xianfeng Gu Ying He Miao Jin Feng Luo Hong Qin Shing-Tung Yau

Differential Geometry mathscidoc:1912.43542

Computer-Aided Design, 40, (6), 676-690, 2008.6
This paper develops a novel computational technique to define and construct manifold splines with only one singular point by employing the rigorous mathematical theory of Ricci flow. The central idea and new computational paradigm of manifold splines are to systematically extend the algorithmic pipeline of spline surface construction from any planar domain to an arbitrary topology. As a result, manifold splines can unify planar spline representations as their special cases. Despite its earlier success, the existing manifold spline framework is plagued by the topology-dependent, large number of singular points (ie,| 2 g 2| for any genus-g surface), where the analysis of surface behaviors such as continuity remains extremely difficult. The unique theoretical contribution of this paper is that we devise new mathematical tools so that manifold splines can now be constructed with only one singular point, reaching their
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  title={Manifold splines with a single extraordinary point},
  author={Xianfeng Gu, Ying He, Miao Jin, Feng Luo, Hong Qin, and Shing-Tung Yau},
  booktitle={Computer-Aided Design},
Xianfeng Gu, Ying He, Miao Jin, Feng Luo, Hong Qin, and Shing-Tung Yau. Manifold splines with a single extraordinary point. 2008. Vol. 40. In Computer-Aided Design. pp.676-690.
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