论文标题
球体上任意顺序的Voronoi图
Voronoi Diagrams of Arbitrary Order on the Sphere
论文作者
论文摘要
对于给定的一组点$ u $ $ s $ s $，$ k $ k $ gremical voronoi图$ sv_k（u）$将$ s $的表面分解为$ k $最接近$ u $的$ k $的区域。 Hyeon-Suk NA，Chung-Nim Lee和Otfried Cheong（Comput。Geom。，2002）应用反转来构建$ SV_1（U）$。我们将它们的构造从$ 1 $ $ 1 $到任何订单$ k $的订单中概括为球形沃罗诺伊图。我们使用该构造来证明$ SV_K（U）$的顶点，边缘和面的数量。这些公式以前尚不清楚。我们获得了$ SV_K（U）$的更多属性，并且还表明$ SV_K（U）$具有小的定向周期双盖。
For a given set of points $U$ on a sphere $S$, the order $k$ spherical Voronoi diagram $SV_k(U)$ decomposes the surface of $S$ into regions whose points have the same $k$ nearest points of $U$. Hyeon-Suk Na, Chung-Nim Lee, and Otfried Cheong (Comput. Geom., 2002) applied inversions to construct $SV_1(U)$. We generalize their construction for spherical Voronoi diagrams from order $1$ to any order $k$. We use that construction to prove formulas for the numbers of vertices, edges, and faces in $SV_k(U)$. These formulas were not known before. We obtain several more properties for $SV_k(U)$, and we also show that $SV_k(U)$ has a small orientable cycle double cover.
