KMS Of Academy of mathematics and systems sciences, CAS
| Combining complementary methods for implicitizing rational tensor product surfaces | |
| Shen, Li-Yong1,2,3; Goldman, Ron4 | |
| 2018-11-01 | |
| Source Publication | COMPUTER-AIDED DESIGN
 |
| ISSN | 0010-4485 |
| Volume | 104Pages:100-112 |
| Abstract | We present an algorithm to implicitize rational tensor product surfaces that works correctly and efficiently even in the presence of base points by combining three complementary approaches, some classical and some novel, to implicitization. One straightforward method is to implicitize these surfaces using the Dixon A-resultant of three obvious syzygies. For surfaces that cannot be implicitized using this resultant due, for example, to the presence of base points, we try the method of moving planes and moving quadrics. We show that this method works very well on surfaces with simple base points. For general rational surfaces that cannot be implicitized by these two methods, we refine the method that employs the resultant matrix of three low bidegree moving planes by providing a simple technique to construct this resultant matrix. To avoid computing the base points explicitly, we compute the extraneous factors associated to the base points by solving a system of polynomial equations with a finite number of solutions. (C) 2018 Elsevier Ltd. All rights reserved. |
| Keyword | Base point Implicitization A-resultant Moving plane Resultant Extraneous factor |
| DOI | 10.1016/j.cad.2018.07.002 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11731013] |
| WOS Research Area | Computer Science |
| WOS Subject | Computer Science, Software Engineering |
| WOS ID | WOS:000442979700008 |
| Publisher | ELSEVIER SCI LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31132 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Shen, Li-Yong |
| Affiliation | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Key Lab Big Data Min & Knowledge Management, Beijing 100190, Peoples R China 4.Rice Univ, Comp Sci Dept, 6100 Main St,MS 132, Houston, TX 77005 USA |
| Recommended Citation GB/T 7714 | Shen, Li-Yong,Goldman, Ron. Combining complementary methods for implicitizing rational tensor product surfaces[J]. COMPUTER-AIDED DESIGN,2018,104:100-112. |
| APA | Shen, Li-Yong,&Goldman, Ron.(2018).Combining complementary methods for implicitizing rational tensor product surfaces.COMPUTER-AIDED DESIGN,104,100-112. |
| MLA | Shen, Li-Yong,et al."Combining complementary methods for implicitizing rational tensor product surfaces".COMPUTER-AIDED DESIGN 104(2018):100-112. |
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