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Symbolic treatment of geometric degeneracies

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Linear Algebra
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Algorithms in Combinatorial Geometry
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On condition numbers and the distance to the nearest ill-posed problem
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Edge-skeletons in arrangements with applications
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Simultaneous computation of functions, partial derivatives and estimates of rounding errors —Complexity and practicality—
inferredcites →https://doi.org/10.1016/0004-3702(88)90061-6openalex-snapshot
Verifiable implementations of geometric algorithms using finite precision arithmetic
inferredcites →https://doi.org/10.1016/0020-0255(89)90037-6openalex-snapshot
Notes on Gröbner bases
inferredcites →https://doi.org/10.1016/0022-0000(90)90016-eopenalex-snapshot
A geometric consistency theorem for a symbolic perturbation scheme
inferredcites →https://doi.org/10.1016/0196-6774(85)90021-5openalex-snapshot
A “retraction” method for planning the motion of a disc
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On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds
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Computing a ham-sandwich cut in two dimensions
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On computational geometry
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The Probability That a Numerical Analysis Problem is Difficult
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Finite-resolution computational geometry
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Catastrophe Theory and Its Applications
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Evaluating Polynomials at Fixed Sets of Points
inferredcites →https://doi.org/10.1137/0205008openalex-snapshot
On the Evaluation of Powers
inferredcites →https://doi.org/10.1137/0209022openalex-snapshot
On the Evaluation of Powers and Monomials
inferredcites →https://doi.org/10.1145/73393.73406openalex-snapshot
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
inferredcites →https://doi.org/10.1145/77635.77639openalex-snapshot
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
inferredcites →https://doi.org/10.2307/1907845openalex-snapshot
Optimality and Degeneracy in Linear Programming
inferredcites →https://doi.org/10.2307/2325168openalex-snapshot
Algorithms in Combinatorial Geometry.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Constrained pose refinement of parametric objects
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Fast theorem-proving and Wu’s Method
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The Nature and Meaning of Perturbations in Geometric Computing
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Efficient Perturbations for Handling Geometric Degeneracies
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A geometric consistency theorem for a symbolic perturbation scheme
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Towards exact geometric computation
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Robustness and Precision Issues in Geometric Computation**Work on this survey was partially supported by the ESPRIT IV Long Term Research Project No. 21957 (CGAL).
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Sliver-free perturbation for the Delaunay tetrahedrization
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Analytical aspects of tie breaking
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An efficient approach to removing geometric degeneracies
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Triangulating topological spaces
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Computational geometry
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Polyhedral modelling with exact arithmetic
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How good are convex hull algorithms?
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Linear-time triangulation of a simple polygon made easier via randomization
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Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
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General Tiebreaking Schemes for Computational Social Choice
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