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# Etude et construction d'un modèle de surface fondé sur la représentation par un atlas de cartes

Abstract : In this thesis we study and design a surface modelling based on the representation of surfaces
with an atlas.
- The first part of it is dedicated to the study of our modelling.
Such a modelling allows to work locally on the surface without being afraid of any lose of global
consistency. Furthermore the representation with an atlas is a notion coming from differential
geometry. Our modelling inherits then good properties from this mathematical theory, and
especially to solve the continuity problem between the patches with which piecewise
parametric representation of surfaces meets frequently : our geometrical model
is a regular (or a quasi-regular) surface.
We present this modelling among those which are used in Computer Graphics and in its differential
geometric background.
- In the second part of this thesis, we propose an algorithm for designing such a modelling
from a triangular mesh.
This mesh is supposed to be a connected and compact 2-manifold.
The algorithm processes in three steps. Each steps reveals a geometrical problem
for which we propose an innovative solution. In particular we demonstrate that the nerve of a well-shaped covering is a combinatorial triangulation. We study also the
$C^1$-diffeomorphic parameterization of a planar crown, and finally the convex combination
as a smooth blending of surfaces.
Mots-clés :
Document type :
Theses
Domain :
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https://tel.archives-ouvertes.fr/tel-00097567
Contributor : Cédric Gérot <>
Submitted on : Thursday, September 21, 2006 - 6:36:03 PM
Last modification on : Friday, November 6, 2020 - 4:06:21 AM
Long-term archiving on: : Tuesday, April 6, 2010 - 1:07:04 AM

### Identifiers

• HAL Id : tel-00097567, version 1

### Citation

Cédric Gerot. Etude et construction d'un modèle de surface fondé sur la représentation par un atlas de cartes. domain_other. Université Joseph-Fourier - Grenoble I, 2001. Français. ⟨tel-00097567⟩

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