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

DOI10.1016/j.comgeo.2009.01.009zbMath1203.65037OpenAlexW2038780582MaRDI QIDQ1037650

Michael Sagraloff, Eric Berberich, Michael Kerber

Publication date: 16 November 2009

Published in: Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.comgeo.2009.01.009

zbMATH Keywords

cylindrical algebraic decompositionalgebraic surfacetopology computation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computational aspects of algebraic surfaces (14Q10) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Semialgebraic sets and related spaces (14P10) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (9)

CW Complexes for Complex Algebraic Surfaces ⋮ Cell decomposition of almost smooth real algebraic surfaces ⋮ Exact symbolic-numeric computation of planar algebraic curves ⋮ Root isolation of zero-dimensional polynomial systems with linear univariate representation ⋮ A general approach to isolating roots of a bitstream polynomial ⋮ A note on the complexity of real algebraic hypersurfaces ⋮ Computation of topological invariants for real projective surfaces with isolated singularities ⋮ Computational tools in weighted persistent homology ⋮ A worst-case bound for topology computation of algebraic curves

Uses Software

• CGAL
• 2D Arrangement
• insulate

Cites Work

• insulate
• An adjacency algorithm for cylindrical algebraic decompositions of three- dimensional space
• A cluster-based cylindrical algebraic decomposition algorithm
• Spline approximations of real algebraic surfaces
• Quantifier elimination and cylindrical algebraic decomposition. Proceedings of a symposium, Linz, Austria, October 6--8, 1993
• An efficient method for analyzing the topology of plane real algebraic curves.
• Local box adjacency algorithms for cylindrical algebraic decompositions
• Efficient topology determination of implicitly defined algebraic plane curves.
• Interval arithmetic in cylindrical algebraic decomposition
• Algorithms to compute the topology of orientable real algebraic surfaces
• An improved upper complexity bound for the topology computation of a real algebraic plane curve
• Advanced programming techniques applied to CGAL's arrangement package
• A delineability-based method for computing critical sets of algebraic surfaces
• Computation of the topology of real algebraic space curves
• Cylindrical algebraic decomposition using validated numerics
• Topology of real algebraic space curves
• Algorithmical determination of the topology of a real algebraic surface
• Exact geometric-topological analysis of algebraic surfaces
• Cylindrical Algebraic Decomposition I: The Basic Algorithm
• On the computation of the topology of a non-reduced implicit space curve
• An exact, complete and efficient implementation for computing planar maps of quadric intersection curves
• On the exact computation of the topology of real algebraic curves
• Mathematics of Surfaces XI
• Computer Algebra in Scientific Computing
• On the Kunneth Formula and Functorial Dependence in Algebraic Topology
• Algorithms in real algebraic geometry
• Improved projection for cylindrical algebraic decomposition
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: An efficient algorithm for the stratification and triangulation of an algebraic surface