| ON STABLE LINE SEGMENTS IN ALL TRIANGULATIONS OF A PLANAR POINT SET |
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| 作者姓名： | XuYINFENG |
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| 摘 要： | Abstract. Let S be a set of finite plauar points. A llne segment L(p, q) with p, q E Sis called a stable line segment of S, if there is no Line segment with two endpoints in S intersecting L(p, q). In this paper, some geometric properties of the set of all stable line segments
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| 关 键 词： | 平面点集 三角剖分 稳定线段 凸壳 算法 线性剖分 |
| 收稿时间： | 15 June 1994 |
On stable line segments in all triangulations of a planar point set |
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| XuYINFENG.ON STABLE LINE SEGMENTS IN ALL TRIANGULATIONS OF A PLANAR POINT SET[J].Applied Mathematics A Journal of Chinese Universities,1996,11(2):235-238. |
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| Authors: | Yinfeng Xu |
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| Institution: | (1) The School of Management, Xi’an Jiaotong University, 710049 Xi’an |
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| Abstract: | LetS be a set of finite planar points. A line segmentL(p,q) withp,q εS is called a stable line segment ofS, if there is no line segment with two endpoints inS intersectingL(p,q). In this paper, some geometric properties of the set of all stable line segments ofS are investigated. We show that (1) the set of all stable line segments ofS must be in any triangulation ofS, (2) ifM(n) is the maximum number of the stable line segments for anyn points in a plane, thenM(n) = 2(n − 1),n ≥ 4. |
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| Keywords: | 51A20 |
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