How to Exhibit Toroidal Maps in Space
How to Exhibit Toroidal Maps in Space
复制标题
如何在太空中展示环形地图
DOI：
10.1007/s00454-007-1354-3
复制
发表时间：
2007
影响因子：
0.8
通讯作者：
D. Archdeacon
中科院分区：
文献类型：
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作者：
D. Archdeacon
斯坦尼兹定理指出，一个图是凸多面体的1-骨架当且仅当它是3-连通的平面图。多面体被称为嵌入图的几何实现。它的面是由凸多边形，其点是共面的边界。环面上的映射不一定有这样的几何实现。本文放宽了面是共面点的凸船体的条件。相反，我们要求面上的点的凸船体可以投影到平面上，使得投影点的凸船体的边界是面的边界的图像。我们还要求不同面的凸包的内部不相交。 把这叫做地图的展览。一个地图是多面体的，如果任何两个封闭面的交点是单连通的。我们的主要结果是，每个多面体环面映射都可以显示出来。作为推论，每个环形三角剖分都有一个几何实现。
Steinitz's theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of the embedded graph. Its faces are bounded by convex polygons whose points are coplanar. A map on the torus does not necessarily have such a geometric realization. In this paper we relax the condition that faces are the convex hull of coplanar points. We require instead that the convex hull of the points on a face can be projected onto a plane so that the boundary of the convex hull of the projected points is the image of the boundary of the face. We also require that the interiors of the convex hulls of different faces do not intersect. Call this an exhibition of the map. A map is polyhedral if the intersection of any two closed faces is simply connected. Our main result is that every polyhedral toroidal map can be exhibited. As a corollary, every toroidal triangulation has a geometric realization.
投影平面上去除一个面的三角测量的几何实现
DOI：
--
发表时间：
2008
期刊：
Discrete Comput. Geom. 40 no.1
影响因子：
--
作者：
Yasunori;Okabe;岡部 靖憲;Atsuhiro Nakamoto and Yusuke Suzuki;C. Paul Bonnington and Atsuhiro Nakamoto
通讯作者：
C. Paul Bonnington and Atsuhiro Nakamoto
运动规划问题中的拓扑和组合方法
DOI：
--
发表时间：
2018
期刊：
影响因子：
--
作者：
Stolz Robert;Yoshida Masaaki;Brasher Reuben;Flanner Michelle;Ishihara Kai;Sherratt David J.;Shimokawa Koya;Vazquez Mariel;田中 康平
通讯作者：
田中 康平