Interpolatory quad/triangle subdivision schemes for surface design
文献类型：期刊论文
| 作者 | Jiang, Qingtang1; Li, Baobin2; Zhu, Weiwei1 |
| 刊名 | Computer aided geometric design
 |
| 出版日期 | 2009-11-01 |
| 卷号 | 26期号:8页码:904-922 |
| 关键词 | Quad/triangle subdivision Nonhomogeneous refinement equation Interpolatory quad/triangle scheme Matrix-valued subdivision Polynomial reproduction Smoothness analysis |
| ISSN号 | 0167-8396 |
| DOI | 10.1016/j.cagd.2009.07.002 |
| 通讯作者 | Jiang, qingtang(jiangq@umsl.edu) |
| 英文摘要 | Recently the study and construction of quad/triangle subdivision schemes have attracted attention. the quad/triangle subdivision starts with a control net consisting of both quads and triangles and produces finer and finer meshes with quads and triangles. the use of the quad/triangle structure for surface design is motivated by the fact that in cad modelling, the designers often want to model certain regions with quad meshes and others with triangle meshes to get better visual quality of subdivision surfaces. though the smoothness analysis tool for regular quad/triangle vertices has been established and c(1) and c(2) quad/triangle schemes (for regular vertices) have been constructed, there is no interpolatory quad/triangle schemes available in the literature. the problem for this is probably that since the template sizes of the local averaging rules of interpolatory schemes for either quad subdivision or triangle subdivision are big, an interpolatory quad/triangle scheme will have large sizes of local averaging rule templates. in this paper we consider matrix-valued interpolatory quad/triangle schemes. in this paper, first we show that both scalar-valued and matrix-valued quad/triangle subdivision scheme can be derived from a nonhomogeneous refinement equation. this observation enables us to treat polynomial reproduction of scalar-valued and matrix-valued quad/triangle schemes in a uniform way. then, with the result on the polynomial reproduction of matrix-valued quad/triangle schemes provided in our accompanying paper, we obtain in this paper a smoothness estimate for matrix-valued quad/triangle schemes, which extends the smoothness analysis of levin-levin from the scalar-valued setting to the matrix-valued setting. finally, with this smoothness estimate established in this paper, we construct c(1) matrix-valued interpolatory quad/triangle scheme (for regular vertices) with the same sizes of local averaging rule templates as those of stam-loop's quad/triangle scheme. we also obtain c(2) matrix-valued interpolatory quad/triangle scheme (for regular vertices) with reasonable sizes of local averaging rule templates. (c) 2009 elsevier b.v. all rights reserved. |
| WOS关键词 | NONHOMOGENEOUS REFINEMENT EQUATIONS ; 2-SCALE DIFFERENCE-EQUATIONS ; REFINABLE FUNCTIONS ; CASCADE ALGORITHMS ; DISTRIBUTIONAL SOLUTIONS ; FUNCTION VECTORS ; APPROXIMATION ; CONVERGENCE ; REGULARITY ; VERTICES |
| WOS研究方向 | Computer Science ; Mathematics |
| WOS类目 | Computer Science, Software Engineering ; Mathematics, Applied |
| 语种 | 英语 |
| WOS记录号 | WOS:000273349300007 |
| 出版者 | ELSEVIER SCIENCE BV |
| URI标识 | http://www.irgrid.ac.cn/handle/1471x/2404392 |
| 专题 | 中国科学院大学 |
| 通讯作者 | Jiang, Qingtang |
| 作者单位 | 1.Univ Missouri, Dept Math & Comp Sci, St Louis, MO 63121 USA 2.Chinese Acad Sci, Sch Informat Sci & Engn, Grad Univ, Beijing 100871, Peoples R China |
| 推荐引用方式 GB/T 7714 | Jiang, Qingtang,Li, Baobin,Zhu, Weiwei. Interpolatory quad/triangle subdivision schemes for surface design[J]. Computer aided geometric design,2009,26(8):904-922. |
| APA | Jiang, Qingtang,Li, Baobin,&Zhu, Weiwei.(2009).Interpolatory quad/triangle subdivision schemes for surface design.Computer aided geometric design,26(8),904-922. |
| MLA | Jiang, Qingtang,et al."Interpolatory quad/triangle subdivision schemes for surface design".Computer aided geometric design 26.8(2009):904-922. |
入库方式： iSwitch采集
来源：中国科学院大学
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。