论文标题
最小化Polyhedra的可见边缘
Minimizing Visible Edges in Polyhedra
论文作者
论文摘要
我们证明，给定$ \ mathbb {r}^3 $中的多面体$ \ mathcal p $，$ \ mathbb r^3 $中的每个点都看不到$ \ mathcal p $的任何顶点必须看到$ \ mathcal p $的八个或更多的边缘，并且此范围很紧。更一般而言，如果$ \ Mathcal P $是$ \ Mathbb {r}^3 $中内部不相交多边形的任何有限安排，这将是正确的。我们还证明，$ \ mathbb {r}^3 $中的每个点都可以看到$ \ mathcal {p} $的六个或更多边（可能只有某些边缘的端点），以及$ \ nathcal {p} $内部的每个点，至少可以看到$ \ mathcal {p} $的内部。这些边界也很紧。
We prove that, given a polyhedron $\mathcal P$ in $\mathbb{R}^3$, every point in $\mathbb R^3$ that does not see any vertex of $\mathcal P$ must see eight or more edges of $\mathcal P$, and this bound is tight. More generally, this remains true if $\mathcal P$ is any finite arrangement of internally disjoint polygons in $\mathbb{R}^3$. We also prove that every point in $\mathbb{R}^3$ can see six or more edges of $\mathcal{P}$ (possibly only the endpoints of some these edges) and every point in the interior of $\mathcal{P}$ can see a positive portion of at least six edges of $\mathcal{P}$. These bounds are also tight.
