A Note on the Complexity of Real Algebraic Hypersurfaces

Given an algebraic hypersurface O in Êd, how many simplices are necessary for a simplicial complex isotopic to O? We address this problem and the variant where all vertices of the complex must lie on O. We give asymptotically tight worst-case bounds for algebraic plane curves. Our results gradually improve known bounds in higher dimensions; however, the question for tight bounds remains unsolved for d ≥ 3. Key words. Algebraic curves, algebraic surfaces, triangulation, isotopy

• Type: Journal
• Year: 2011
• Where: GC
• Authors: Michael Kerber, Michael Sagraloff
• Keywords: Algebraic Curves, Algebraic Surfaces, Applied Computing, GC 2011, Plane Curves