کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
414790 | 681038 | 2010 | 22 صفحه PDF | دانلود رایگان |
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 ΩS of S into O(N5) non-singular 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 ΩS 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 algebraic geometry.
Journal: Computational Geometry - Volume 43, Issue 3, April 2010, Pages 257-278