个人信息Personal Information
教授
博士生导师
硕士生导师
主要任职:软件学院(大连理工大学-立命馆大学国际信息与软件学院)党委书记
性别:女
毕业院校:吉林大学
学位:博士
所在单位:软件学院、国际信息与软件学院
学科:软件工程. 计算数学. 计算机应用技术
办公地点:大连理工大学开发区校区信息楼309室
联系方式:nalei@dlut.edu.cn
电子邮箱:nalei@dlut.edu.cn
On Tetrahedralisations Containing Knotted and Linked Line Segments
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论文类型:会议论文
发表时间:2017-01-01
收录刊物:EI、CPCI-S
卷号:203
页面范围:323-335
摘要:This paper considers a set of twisted line segments in 3d such that they form a knot (a closed curve) or a link of two closed curves. Such line segments appear on the boundary of a family of 3d indecomposable polyhedra (like the SchOnhardt polyhedron) whose interior cannot be tetrahedralised without additional vertices added. On the other hand, a 3d (non-convex) polyhedron whose boundary contains such line segments may still be decomposable as long as the twist is not too large. It is therefore interesting to consider the question: when there exists a tetrahedralisation contains a given set of knotted or linked line segments?
In this paper, we studied a simplified question with the assumption that all vertices of the line segments are in convex position. It is straightforward to show that no tetrahedralisation of 6 vertices (the three-line-segments case) can contain a trefoil knot. Things become interesting when the number of line segments increases. Since it is necessary to create new interior edges to form a tetrahedralisation. We provided a detailed analysis for the case of a set of 4 line segments. This leads to a crucial condition on the orientation of pairs of new interior edges which determines whether this set is decomposable or not. We then prove a new theorem about the decomposability for a set of n (n >= 3) knotted or linked line segments. This theorem implies that the family of polyhedra generalised from the Schonhardt polyhedron by Rambau [1] are all indecomposable. (C) 2017 The Authors. Published by Elsevier Ltd.