Unfolding Smooth Primsatoids

Computer Science – Computational Geometry

Scientific paper

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19 pages, 15 figures, 1st draft Revised version corrects an error in the proof of Lemma 3.3. The statement of the lemma remain

Scientific paper

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.

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