展开光滑棱柱体
Unfolding Smooth Prismatoids
摘要：
定义了光滑直纹曲面的展开概念，证明了每个光滑棱柱体（平行平面上两条光滑曲线的凸包）都有一个不重叠的“火山展开”。“这些展开保持基部完整，向外展开侧面，围绕基部张开，并将顶部连接到一些侧肋的尖端。我们的结果回答了一个问题，光滑prismatoids的模拟多面体prismatoids仍然没有解决。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
