Many applications in computer graphics and related fields can benefit fromautomatic simplification of complex polygonal surface models. Applications areoften confronted with either very densely over-sampled surfaces or models toocomplex for the limited available hardware capacity. An effective algorithmfor rapidly producing high-quality approximations of the original model is avaluable tool for managing data complexity. In this dissertation, I present my simplification algorithm, based on iterativevertex pair contraction. This technique provides an effective compromisebetween the fastest algorithms, which often produce poor quality results, andthe highest-quality algorithms, which are generally very slow. For example, a1000 face approximation of a 100,000 face model can be produced in about 10seconds on a PentiumPro 200. The algorithm can simplify both the geometryand topology of manifold as well as non-manifold surfaces. In addition toproducing single approximations, my algorithm can also be used to generatemultiresolution representations such as progressive meshes and vertex hierarchiesfor view-dependent refinement. The foundation of my simplification algorithm, is the quadric error metricwhich I have developed. It provides a useful and economical characterization oflocal surface shape, and I have proven a direct mathematical connection betweenthe quadric metric and surface curvature. A generalized form of this metric canaccommodate surfaces with material properties, such as RGB color or texturecoordinates. I have also developed a closely related technique for constructing a hierarchyof well-defined surface regions composed of disjoint sets of faces. This algorithminvolves applying a dual form of my simplification algorithm to the dual graphof the input surface. The resulting structure is a hierarchy of face clusters whichis an effective multiresolution representation for applications such as radiosity.

To decrease the rendering time of a mesh, Level of Detail can be generated by reducing the number of polygons based on some geometrical error. While this works well for most meshes, it is not suitable for meshes with an associated texture atlas. By iteratively collapsing edges based on an extended version of Quadric Error Metric taking both spatial and texture coordinates into account, textured meshes can also be simplified. Results show that constraining edge collapses in the seams of a mesh give poor geometrical appearance when it is reduced to a few polygons. By allowing seam edge collapses and by using a pull-push algorithm to fill areas located outside the seam borders of the texture atlas, the appearance of the mesh is better preserved.

Le CEA développe et utilise des logiciels de calcul, également appelés codes de calcul, dans différentes disciplines physiques pour optimiser les coûts de ses installations et de ses expérimentations. Lors d'une étude, plusieurs phénomènes physiques interagissent. Un couplage et des échanges de données entre plusieurs codes sont nécessaires.Chaque code réalise ses calculs sur une géométrie, généralement représentée sous forme d'un maillage contenant des milliers voire des millions de mailles. Cette thèse se focalise sur le transfert de déformations géométriques entre les maillages spécifiques de chacun des codes de calcul couplés. Pour cela, elle présente une méthode de couplage de plusieurs codes, dont le calcul des déformations est réalisé par l'un d'entre eux. Elle traite également de la mise en place d'un modèle commun aux différents codes de l'étude regroupant l'ensemble des données partagées. Enfin, elle porte sur les transferts de déformations entre des maillages représentant une même géométrie ou des géométries adjacentes. Les modifications géométriques sont de nature discrète car elles s'appuient sur un maillage. Afin de les rendre accessible à l'ensemble des codes de l'étude et pour permettre leur transfert, une représentation continue est calculée. Pour cela, deux fonctions sont développées : l'une à support global, l'autre à support local. Toutes deux combinent une méthode de simplification et un réseau de fonctions de base radiale. Un cas d'application complet est traité dans le cadre du réacteur Jules Horowitz. L'effet des dilatations différentielles sur le refroidissement d'un dispositif expérimental est étudié. / The CEA develops and uses scientific software, called physical codes, in various physical disciplines to optimize installation and experimentation costs. During a study, several physical phenomena interact, so a code coupling and some data exchanges between different physical codes are required.Each physical code computes on a particular geometry, usually represented by a mesh composed of thousands to millions of elements. This PhD Thesis focuses on the geometrical modification transfer between specific meshes of each coupled physical code. First, it presents a physical code coupling method where deformations are computed by one of these codes. Next, it discusses the establishment of a model, common to different physical codes, grouping all the shared data. Finally, it covers the deformation transfers between meshes of the same geometry or adjacent geometries. Geometrical modifications are discrete data because they are based on a mesh. In order to permit every code to access deformations and to transfer them, a continuous representation is computed. Two functions are developed, one with a global support, and the other with a local support. Both functions combine a simplification method and a radial basis function network. A whole use case is dedicated to the Jules Horowitz reactor. The effect of differential dilatations on experimental device cooling is studied.