Conformal freeform surfaces. (December 2016)

• Record Type: Journal Article
• Authors: Yang, Yi-Jun; Zeng, Wei; Meng, Xiang-Xu
• Is Part Of: Computer aided design. Volume 81(2016)
• Page Start: 48
• Page End: 60
• Publication Date: 2016-12
• Subjects: Hierarchical freeform surfaces -- Conformal surfaces -- Least square method; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2016.09.003
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: The conformality of freeform surfaces highly affects their rendering and tessellation results. To improve the conformality of freeform surfaces, a novel freeform surface representation named hierarchical freeform surfaces is presented in this paper. The conformality energy of hierarchical freeform surfaces is first formulated and its numerical approximation is then constructed using the composite Simpson's rule. By constructing the parameterization of the initial freeform transformation using the Ricci flow method, the optimal freeform transformation is obtained by the Levenberg–Marquardt method, which is further interleaved with the freeform refinement procedure to generate a hierarchical freeform surface with bounded conformality deviations. Examples are given to show the performance of our algorithm for rendering and tessellation applications. Highlights: This paper gives a novel freeform representation "hierarchical freeform surfaces". An optimization method is presented to improve the conformality of NURBS surfaces using the freeform transformations.