An efficient algorithm for the stratification and triangulation of an algebraic surface

: We present a method to compute the exact topology of a real algebraic surface S, implicitly given by a polynomial f Q[x,y,z] of arbitrary total degree N. Additionally, our analysis provides geometric information as it supports the computation of arbitrary precise samples of S including critical points. We compute a stratification S of S into O(N5) nonsingular cells, including the complete adjacency information between these cells. This is done by a projection approach. We construct a special planar arrangement AS with fewer cells than a cad in the projection plane. Furthermore, our approach applies numerical and combinatorial methods to minimize costly symbolic computations. The algorithm handles all sorts of degeneracies without transforming the surface into a generic position. Based on S we also compute a simplicial complex which is isotopic to S. A complete C++-implementation of the stratification algorithm is presented. It shows good performance for many well-known examples from...

• Type: Journal
• Year: 2010
• Where: COMGEO
• Authors: Eric Berberich, Michael Kerber, Michael Sagraloff
• Keywords: Applied Computing, Arbitrary Precise Samples, COMGEO 2010, Compute, Real Algebraic Surface