Optimizing conformality of NURBS surfaces by general bilinear transformations. (June 2015)

• Record Type: Journal Article
• Authors: Yang, Yi-Jun; Zeng, Wei; Song, Tian-Qi
• Is Part Of: Computer aided design. Volume 63(2015)
• Page Start: 12
• Page End: 25
• Publication Date: 2015-06
• Subjects: NURBS surfaces -- General bilinear transformation -- Conformal mapping -- Rendering -- Tessellation; 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.2015.01.004
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: The conformality of NURBS surfaces greatly affects the results of rendering and tessellation applications. To improve the conformality of NURBS surfaces, an optimization algorithm using general bilinear transformations is presented in this paper. The conformality energy is first formulated and its numerical approximation is then constructed using the composite simpson's rule. The initial general bilinear transformation is obtained by approximating the conformal mapping of its 3D discretized mesh using a least square method, which is further optimized by the Levenberg–Marquardt method. Examples are given to show the performance of our algorithm for rendering and tessellation applications. Highlights: We give explicit representations of the general bilinear reparameterized surfaces. A scheme is given to construct the general bilinear reparameterized NURBS surfaces. An optimization method is given to improve the conformality of NURBS surfaces.