Volume xx, (200y), Number z pp. 000–000 Multiresolution Surfaces Having Arbitrary Topologies by a Reverse Doo Subdivision Method

We have shown how to construct multiresolution structures for reversing subdivision rules using global least squares models 16. As a result, semiorthogonal wavelet systems have also been generated. To construct a multiresolution surface of an arbitrary topology, however, biorthogonal wavelets are needed. In 1 we introduced local least squares models for reversing subdivision rules to construct multiresolution curves and tensor product surfaces, noticing that the resulting wavelets were biorthogonal (under an induced inner product). Here, we construct multiresolution surfaces of arbitrary topologies by locally reversing the Doo subdivision scheme. In a Doo subdivision, a coarse surface is converted into a fine one by the contraction of coarse faces and the addition of new adjoining faces. We propose a novel reversing process to convert a fine surface into a coarse one plus an error. The conversion has the property that the subdivision of the resulting coarse surface is locally closest to the original fine surface, in the least squares sense, for two important face geometries. In this process, we first find those faces of the fine surface which might have been produced by the contraction of a coarse face in a Doo subdivision scheme. Then, we expand these faces. Since the expanded faces are not necessarily joined properly, several candidates are usually at hand for a single vertex of the coarse surface. To identify the set of candidates corresponding to a vertex, we construct a graph in such a way that any set of candidates corresponds to a connected component. Th

Etude et construction de schémas de subdivision quasi-linéaires sur des maillages bi-réguliers

Les schémas de subdivision et les schémas de subdivision inverse sont largement utilisés en informatiquegraphique; les uns pour lisser des objets 3D, et les autres pour minimiser le coût d encodagede l information. Ce sont les deux aspects abordés dans cette thèse.Les travaux présentés dans le cadre de la subdivision décrivent l études et la construction d un nouveautype de schémas de subdivision. Celui-ci unifie deux schémas de subdivision de type géométriquesdifférents. Cela permet de modéliser des objets 3D composés de zones issues de l applicationd un schéma approximant et de zones issues de l application d un schéma interpolant. Dans le cadrede la subdivision inverse, Nous présentons une méthode de construction des schémas de subdivisionbi-réguliers inverses (quadrilatères et triangles)Subdivision schemes are commonly used to generate a smooth shape from a much more coarseone. The reverse subdivision is designed to describe a high resolution mesh from a coarse one. Bothof these tools are used in numerous graphical modelisation domains. In this thesis, we focused ontwo distinct aspects: on one hand the construction of quasi-linear subdivision schemes and on theother hand the construction of reverse quad/triangle subdivision schemes. The work, presented inthe context of the subdivision, describes the construction of a new type of subdivision schemes, andtheirs applications to solve some problems coming from the application of linear subdivision schemes.The work presented in the context of the reverse subdivision describes a new method to reverse thequad/triangle subdivision schemesDIJON-BU Doc.électronique (212319901) / SudocSudocFranceF