2004/07/28 by Nadia M. Benbernou, Benbernou, Nadia, Patricia Cahn +3
Mathematics · #Computational Geometry (cs.CG) #Discrete Mathematics (cs.DM) #F.2.2 #FOS: Computer and information sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.cs/0407063
openalex publication_date 2004/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.