Unfolding Smooth Prismatoids
计算几何
2015-03-12 v3 离散数学
摘要
We define a notion for unfolding smooth, ruled surfaces, and prove that every smooth prismatoid (the convex hull of two smooth curves lying in parallel planes), has a nonoverlapping "volcano unfolding." These unfoldings keep the base intact, unfold the sides outward, splayed around the base, and attach the top to the tip of some side rib. Our result answers a question for smooth prismatoids whose analog for polyhedral prismatoids remains unsolved.
关键词
引用
@article{arxiv.cs/0407063,
title = {Unfolding Smooth Prismatoids},
author = {Nadia Benbernou and Patricia Cahn and Joseph O'Rourke},
journal= {arXiv preprint arXiv:cs/0407063},
year = {2015}
}
备注
19 pages, 15 figures, 1st draft Revised version corrects an error in the proof of Lemma 3.3. The statement of the lemma remains unchanged. Second revised version: corrected a typo in the title