Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes
文献类型：期刊论文
| 作者 | Liu, Dan; Xu, Guoliang |
| 刊名 | COMPUTER-AIDED DESIGN
 |
| 出版日期 | 2007-06-01 |
| 卷号 | 39期号:6页码:506-517 |
| 关键词 | angle deficit Gaussian curvature quadrilateral mesh convergence |
| ISSN号 | 0010-4485 |
| DOI | 10.1016/j.cad.2007.01.007 |
| 英文摘要 | We propose a discrete approximation of Gaussian curvature over quadrilateral meshes using a linear combination of two angle deficits. Let g(ij) and b(ij) be the coefficients of the first and second fundamental forms of a smooth parametric surface F. Suppose F is sampled so that a surface mesh is obtained. Theoretically we show that for vertices of valence four, the considered two angle deficits are asymptotically equivalent to rational functions in g(ij) and b(ij) under some special conditions called the parallelogram criterion. Specifically, the numerators of the rational functions are homogenous polynomials of degree two in b(ij) with closed form coefficients, and the denominators are g(11g22) - g(12)(2). Our discrete approximation of the Gaussian curvature derived from the combination of the angle deficits has quadratic convergence rate under the parallelogram criterion. Numerical results which justify the theoretical analysis are also presented. (C) 2007 Elsevier Ltd. All rights reserved. |
| WOS研究方向 | Computer Science |
| 语种 | 英语 |
| WOS记录号 | WOS:000247850000007 |
| 出版者 | ELSEVIER SCI LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/4940]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Xu, Guoliang |
| 作者单位 | Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Liu, Dan,Xu, Guoliang. Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes[J]. COMPUTER-AIDED DESIGN,2007,39(6):506-517. |
| APA | Liu, Dan,&Xu, Guoliang.(2007).Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes.COMPUTER-AIDED DESIGN,39(6),506-517. |
| MLA | Liu, Dan,et al."Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes".COMPUTER-AIDED DESIGN 39.6(2007):506-517. |
入库方式： OAI收割
来源：数学与系统科学研究院
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