Parametric curve with an implicit domain

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• 作者：WeiHong Zhang (1) (2)
  JianSong Deng (1)
  ZhouWang Yang (1)
  LiGang Liu (1)
  
• 关键词：parametric curve with an implicit domain ; regularity ; quadratic programming ; image deformation ; 65D18 ; 65D17 ; 65D15
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：57
• 期：12
• 页码：2621-2634
• 全文大小：1,362 KB
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• 作者单位：WeiHong Zhang (1) (2)
  JianSong Deng (1)
  ZhouWang Yang (1)
  LiGang Liu (1)
  
  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China
  2. School of Mathematics and Statistics, Hefei Normal University, Hefei, 230601, China
  
• ISSN：1869-1862

文摘

In this paper we present a new representation of curve, named parametric curve with an implicit domain (PCID), which is a curve that exists in parametric form defined on an implicit domain. PCID provides a bridge between parametric curve and implicit curve because the conversion of parametric form or implicit form to PCID is very convenient and efficient. We propose a framework model for mapping given points to the implicit curve in a homeomorphic manner. The resulting map is continuous and does not overlap. This framework can be used for many applications such as compatible triangulation, image deformation and fisheye views. We also present some examples and experimental results to demonstrate the effectiveness of the framework of our proposed model.