The Number of Views of Piecewise-Smooth Algebraic Objects

Abstract. A solid object in 3-dimensional space may be described by a collection of all its topologically distinct 2-dimensional appearances, its aspect graph. In this paper, we study the complexity of aspect graphs of piecewise-smooth algebraic objects using the modern tools of algebraic geometry, i.e. intersection theory, multiple-point theory and enumerative geometry. We give a bound on the number of different appearances of such objects, an indication of the computational complexity of aspect graphs.

• Type: Conference
• Year: 1995
• Where: STACS
• Authors: Sylvain Petitjean
• Keywords: Aspect Graphs, Distinct 2-dimensional Appearances, Piecewise-smooth Algebraic Objects, STACS 1995, Theoretical Computer Science