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
2 ICS-FORTH - Institute of Computer Science [FORTH, Heraklion]
3 Department of Applied Mathematics [Heraklion]

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.

Domaines: Géométrie algorithmique [cs.CG]

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