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Qualitative Symbolic Perturbation: Two Applications of a New Geometry-based Perturbation Framework

Olivier Devillers 1 Menelaos Karavelas 2, 3 Monique Teillaud 1
1 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
2 ICS-FORTH - Institute of Computer Science
3 Department of Applied Mathematics [Heraklion]
Abstract : In a classical Symbolic Perturbation scheme, degeneracies are handled by substituting some polynomials in ε for the inputs of a predicate. Instead of a single perturbation, we propose to use a sequence of (simpler) perturbations. Moreover, we look at their effects geometrically instead of algebraically; this allows us to tackle cases that were not tractable with the classical algebraic approach.
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https://hal.inria.fr/hal-01586511
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Submitted on : Tuesday, September 12, 2017 - 11:05:48 PM
Last modification on : Wednesday, October 30, 2019 - 7:36:17 PM
Long-term archiving on: : Wednesday, December 13, 2017 - 6:49:37 PM

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Olivier Devillers, Menelaos Karavelas, Monique Teillaud. Qualitative Symbolic Perturbation: Two Applications of a New Geometry-based Perturbation Framework. Journal of Computational Geometry, Carleton University, Computational Geometry Laboratory, 2017, 8 (1), pp.282--315. ⟨10.20382/jocg.v8i1a11⟩. ⟨hal-01586511⟩

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