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 Author, Editor(s)
 Author(s): Berberich, Eric Kerber, Michael Sagraloff, Michael dblp dblp dblp
 BibTeX cite key*: bks-cgta-2009

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

 Journal
 Journal Title*: Computational Geometry: Theory and Applications (CGTA) Journal's URL: www.elsevier.com/locate/comgeo Download URL for the article: http://dx.doi.org/ Language: English

 Publisher
 Publisher's Name: Elsevier Publisher's URL: http://www.elsevier.com Publisher's Address: Amsterdam, Netherlands ISSN: 0925-7721

 Vol, No, pp, Date
 Volume*: 43 Number: 3 Publishing Date: April 2010 Pages*: 257-278 Number of VG Pages: 20 Page Start: 257 Page End: 278 Sequence Number: DOI: 10.1016/j.comgeo.2009.01.009

 Note: (LaTeX) Abstract: We present a method to compute the exact topology of a real algebraic surface $S$, implicitly given by a polynomial $f\in\mathbb{Q}[x,y,z]$ 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 $\Omega_S$ of $S$ into $O(N^5)$ nonsingular cells, including the complete adjacency information between these cells. This is done by a projection approach. We construct a special planar arrangement $\mathcal{A}_S$ 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 $\Omega_S$ 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 algebraic geometry. URL for the Abstract: Categories, Keywords: Algebraic surfaces, exact geometric computation, topology computation, cylindrical algebraic decomposition HyperLinks / References / URLs: Copyright Message: Personal Comments: Download Access Level: Public

 Correlation
 MPG Unit: Max-Planck-Institut für Informatik MPG Subunit: Algorithms and Complexity Group Audience: popular Appearance: MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort

BibTeX Entry:

@ARTICLE{bks-cgta-2009,
AUTHOR = {Berberich, Eric and Kerber, Michael and Sagraloff, Michael},
TITLE = {An efficient algorithm for the stratification and triangulation of an algebraic surface},
JOURNAL = {Computational Geometry: Theory and Applications (CGTA)},
PUBLISHER = {Elsevier},
YEAR = {2010},
NUMBER = {3},
VOLUME = {43},
PAGES = {257--278},