# Représentation géométrique des arrangements de droites du plan

Abstract : Lines arrangements in the plane are widely studied in computational geometry, for their geometric simplicity and combinatorial, or topological complexity. Our contribution is partially the search for relevant data structures and algorithms, efficient both for arrangements construction and explotation of the minimal information characterizing these arrangements. However, our main contribution is the study of the geometric representation of arrangements, by the definition of a geometric equivalence between two sets of lines in the euclidean plane, called isotopy. This is the theoretical justification of the geometric optimization algorithm we propose. This algorithm is based on several criteria to quantify the geometric niceness'' of an arrangement representation, that we present. We also give results on analytical optimization of arrangements with very few lines.
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Theses

https://tel.archives-ouvertes.fr/tel-00004631
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Submitted on : Wednesday, February 11, 2004 - 4:10:35 PM
Last modification on : Wednesday, March 10, 2021 - 1:50:03 PM
Long-term archiving on: : Friday, April 2, 2010 - 7:28:16 PM

### Identifiers

• HAL Id : tel-00004631, version 1

### Citation

Guillaume Allègre. Représentation géométrique des arrangements de droites du plan. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 2003. Français. ⟨tel-00004631⟩

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