Combining complementary methods for implicitizing rational tensor product surfaces

doi:10.1016/j.cad.2018.07.002

	Combining complementary methods for implicitizing rational tensor product surfaces
	Shen, Li-Yong 1,2,3; Goldman, Ron 4
刊名	COMPUTER-AIDED DESIGN
	2018-11-01
卷号	104 页码:100-112
关键词	Base point Implicitization A-resultant Moving plane Resultant Extraneous factor
ISSN号	0010-4485
DOI	10.1016/j.cad.2018.07.002
英文摘要	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.
资助项目	National Natural Science Foundation of China[11731013]
WOS研究方向	Computer Science
语种	英语
出版者	ELSEVIER SCI LTD
WOS记录号	WOS:000442979700008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/31131]
专题	中国科学院数学与系统科学研究院
通讯作者	Shen, Li-Yong
作者单位	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
推荐引用方式 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.