论文标题
$ l_p $ voronoi图的限制为$ p \ rightarrow 0 $是边界盒-Box-area voronoi图
The limit of $L_p$ Voronoi diagrams as $p \rightarrow 0$ is the bounding-box-area Voronoi diagram
论文作者
论文摘要
当$ l_p（a-b）$中给出$ l_p（（（x，y））=（| x | x |^p+| y |^p）^{1/p}时，我们考虑实际飞机中的Voronoi点图。功能$ l _*（（x，y））= | xy | $。在此图中，两个点的两点的一致性由一条线和双曲线的两个分支组成，它们将平面分成每个点三个面。我们建议将$ l _*$命名为“几何$ l_0 $距离”上方。
We consider the Voronoi diagram of points in the real plane when the distance between two points $a$ and $b$ is given by $L_p(a-b)$ where $L_p((x,y)) = (|x|^p+|y|^p)^{1/p}.$ We prove that the Voronoi diagram has a limit as $p$ converges to zero from above or from below: it is the diagram that corresponds to the distance function $L_*((x,y)) = |xy|$. In this diagram, the bisector of two points in general position consists of a line and two branches of a hyperbola that split the plane into three faces per point. We propose to name $L_*$ as defined above the "geometric $L_0$ distance".
