论文标题
在平行切片中重建多边形之间的多面体
Reconstructing a Polyhedron between Polygons in Parallel Slices
论文作者
论文摘要
给定了两个$ n $ vertex多边形，$ p =（p_1，\ ldots，p_n）$位于$ xy $ - $ z = 0 $的$ xy $ - 平面，$ z = 0 $，$ p'=（p'_1，\ ldots，p'_n）$躺在$ z = 1 $的$ z = 1 $的$ z $ $ z $ $ z $ $ z $ $ z $ y的$ z $ ys triane ys trian and trian and trian and triane an $ p'$这样，三角剖分的边缘包含顶点不相交路径$π_i$连接$ p_i $ to $ i = 1，\ ldots，n $。然后，表面由频段组成，其中$ i $ th频段介于$π_i$和$π_{i+1} $之间。如果存在，我们给出了多项式时间算法以找到一个带状的表面，而无需施泰纳点。我们探索带状表面和线性变形之间的连接，其中的时间与$ z $方向相对应。特别是，我们表明，如果$ p $和$ p'$是凸，线性从$ p $到$ p'$（这将直线上的$ i $ th顶点从$ p_i $移动到$ p'_i $）一直是平面的，那么没有台面的表面没有台器。
Given two $n$-vertex polygons, $P=(p_1, \ldots, p_n)$ lying in the $xy$-plane at $z=0$, and $P'=(p'_1, \ldots, p'_n)$ lying in the $xy$-plane at $z=1$, a banded surface is a triangulated surface homeomorphic to an annulus connecting $P$ and $P'$ such that the triangulation's edge set contains vertex disjoint paths $π_i$ connecting $p_i$ to $p'_i$ for all $i =1, \ldots, n$. The surface then consists of bands, where the $i$th band goes between $π_i$ and $π_{i+1}$. We give a polynomial-time algorithm to find a banded surface without Steiner points if one exists. We explore connections between banded surfaces and linear morphs, where time in the morph corresponds to the $z$ direction. In particular, we show that if $P$ and $P'$ are convex and the linear morph from $P$ to $P'$ (which moves the $i$th vertex on a straight line from $p_i$ to $p'_i$) remains planar at all times, then there is a banded surface without Steiner points.
