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Free-form Shape Modeling Using Cyclides Splines

Thursday, November 17, 11AM – 1PM
ACE 4.304

Wenping Wang, University of Hong Kong

Cyclides, or Dupin cyclides, are classical surfaces discovered by the French mathematician Charles Dupin in the early 19th century. These surfaces have been extensively studied for surface representation for about three decades since Ralph Martin introduced them to surface modeling in early 1980s. Cyclides have several remarkable properties; for example, they are low-degree algebraic surfaces (degree 4 or less) and have rational bi-quadratic parameterization. Furthermore, the offsets of a cyclide are again cyclides. However, all previous attempts at using cyclides to model free-form surfaces have been unsuccessful because of the relative inflexibility of cyclides. Consequently, it is widely believed that cyclides do not have enough freedom to represent free-form shapes.

I shall present an effective approach to modeling free-form shapes using fair, smooth cyclide splines. The key ideas behind the approach are vertex relaxation and global optimization}. Specifically, we overcome the inflexibility of cyclides by relaxing the vertex positions of cyclide patches within a constrained optimization framework. Some preliminary results will be presented to demonstrate the feasibility of this approach.

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