关于与多面体相交平面的 developement
计算几何
2009-09-25 v4 离散数学
摘要
定义“切片曲线”为平面与多面体表面相交得到的曲线，即三维中的凸多面体。我们证明了切片曲线在平面上发展且自身不相交。其关键工具是将 Cauchy 的臂引理推广，以容纳非凸的平面凸链的“开放”部分。
关键词
引用
@article{arxiv.cs/0006035,
title = {On the Development of the Intersection of a Plane with a Polytope},
author = {Joseph O'Rourke},
journal= {arXiv preprint arXiv:cs/0006035},
year = {2009}
}
备注
11 pages, 8 figures. Earlier version replaced after I discovered Schur's 1921 theorem, whose proof can be followed to establish the key generalization of Cauchy's arm lemma, my Theorem 1. Paper revised accordingly. New (2006) version corrects two errors in the proofs found by Raghavan Dhandapani