Cylindrical algebraic decomposition I: the basic algorithm
SIAM Journal on Computing
Cylindrical algebraic decomposition II: an adjacency algorithm for the plane
SIAM Journal on Computing
An adjacency algorithm for cylindrical algebraic decompositions of three-dimenslonal space
Journal of Symbolic Computation
A cluster-based cylindrical algebraic decomposition algorithm
Journal of Symbolic Computation
An improved upper complexity bound for the topology computation of a real algebraic plane curve
Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
An efficient method for analyzing the topology of plane real algebraic curves
Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Spline approximations of real algebraic surfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Handbook of discrete and computational geometry
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Improved projection for cylindrical algebraic decomposition
Journal of Symbolic Computation
Local box adjacency algorithms for cylindrical algebraic decompositions
Journal of Symbolic Computation
Interval arithmetic in cylindrical algebraic decomposition
Journal of Symbolic Computation
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Algorithms to compute the topology of orientable real algebraic surfaces
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
On the exact computation of the topology of real algebraic curves
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Isotopic meshing of implicit surfaces
The Visual Computer: International Journal of Computer Graphics
A delineability-based method for computing critical sets of algebraic surfaces
Journal of Symbolic Computation
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
On the complexity of real solving bivariate systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Fast and exact geometric analysis of real algebraic plane curves
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Topology of real algebraic space curves
Journal of Symbolic Computation
Computation of the topology of real algebraic space curves
Journal of Symbolic Computation
Algorithmical determination of the topology of a real algebraic surface
Journal of Symbolic Computation
Determining the topology of real algebraic surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
A descartes algorithm for polynomials with bit-stream coefficients
CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Computer Aided Geometric Design
Isotopic triangulation of a real algebraic surface
Journal of Symbolic Computation
Isolating real roots of real polynomials
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An efficient algorithm for the stratification and triangulation of an algebraic surface
Computational Geometry: Theory and Applications
A deterministic algorithm for isolating real roots of a real polynomial
Journal of Symbolic Computation
Reliable and efficient geometric computing
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
The design of core 2: a library for exact numeric computation in geometry and algebra
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Journal of Symbolic Computation
Local generic position for root isolation of zero-dimensional triangular polynomial systems
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
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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 degree N. Additionally, our analysis provides geometric information as it supports the computation of arbitrary precise samples of S including critical points. We use a projection approach, similar to Collins' cylindrical algebraic decomposition (cad). In comparison we reduce the number of output cells to O(N5) by constructing a special planar arrangement instead of a full 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. We provide a complete implementation of the algorithm, written in C++. It shows good performance for many well known examples from algebraic geometry.