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[en] A TOPOLOGICAL APPROACH FOR MESH SIMPLIFICATION / [pt] UMA ABORDAGEM TOPOLÓGICA PARA SIMPLIFICAÇÃO DE MALHASANTONIO WILSON VIEIRA 17 December 2003 (has links)
[pt] Diversas aplicações, em matemática, computação gráfica,
medicina, geofísica e outras áreas, têm explorado a
representação de sólidos por superfícies de contorno, em
particular malhas poligonais. As malhas podem aproximar
com
muita precisão as propriedades geométricas da superfície
de
contorno de um sólido e ainda guardar importantes
propriedades topológicas das superfícies como gênero,
bordo
e conexidade. Devido à grande complexidade
dessas malhas, elas são geralmente processadas em meios
computacionais usando alguma estrutura de dados. Essas
estruturas guardam, além da geometria da malha,
informações de incidências e adjacências entre os
elementos da malha e exigem uma capacidade de
armazenamento e processamento em função da complexidade
da malha. Apesar da evolução dos recursos computacionais
disponíveis para a manipulação destas estruturas,
malhas extremamente complexas com milhões de elementos
inviabilizam o armazenamento, processamento e transmissão
de sua estrutura de dados nos meios computacionais.
Muitas pesquisas recentes estão voltadas para a obtenção
de processos de simplificação de malhas que permitam
representar a mesma superfície com menos elementos na
estrutura de dados e processos de compressão que
codifiquem os modelos em formatos menores para efeitos de
transmissão e armazenamento em mídia. Neste trabalho,
desenvolvemos operadores, em uma estrutura de dados
compacta, para a simplificação de malhas através da
decimação de células da superfície. Objetivamos, com
esses operadores, obter uma malha menos complexa que
preserve as propriedades topológicas da superfície
original e ainda, controlar as propriedades geométricas
como volume, área e aspecto visual da mesma. Apresentamos
ainda algumas aplicações para os processos de
simplificação desenvolvidos com esses operadores. / [en] Many applications, in mathematics, computer graphics,
medical imaging, geophysics and others, have used the
representation of solids by their boundary surface, usually
polygonal meshes. Those meshes can represent, with high
precision, the geometric properties of the boundary surface
of solid and also store important topological surface
properties as genus, boundary and connected components.
Because of the high complexity of such meshes, they are
usually processed by the computers using specific data
structures. These structures store, beyond the mesh
geometry, information about incidence and adjacency
relations among the mesh elements. They require
computational resources for storage and processing
according to the mesh complexity. Even with the development
of the computational resources available for handling such
structures, very large meshes with millions of elements are
hard to store, to process and to exchange through the web.
Many recent researches are looking for mesh simplification
process that allows to represent the same surface with
fewer elements and compression process to encode it in
compact ways for transmition and storage. In this work, we
develop topological operators, in a concise data structure,
for simplifying meshes by the decimation of its cells. One
of our goals, with these operators, is to obtain a mesh
with a low complexity that preserves the topological
properties from the original surface without loosing the
control of the geometric proprieties as volume, area and
visual aspect.
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Quadric-Based Polygonal Surface SimplificationGarland, Michael 09 May 1999 (has links)
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.
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3 D Modeling of elevation surfaces from voxel structured point clouds extracted from seismic cubes / 3D Modeling of elevation surfaces from voxel structured point clouds extracted from seismic cubesNguyen, Van sinh 25 October 2013 (has links)
Dans cette thèse, nous présentons des méthodes pour construire une surface géologique optimal à partir d’une quantité énorme de points 3D extraits de cubes sismiques. Appliquer le processus à l’ensemble des points induit un risque important de contraction de la surface de sorte que l’extraction de la frontière initiale est une étape importante permettant une simplification à l’intérieur de la surface. La forme globale de la surface sera alors mieux respectée pour la reconstruction de la surface triangulaire finale. Nos propositions sont basées sur la régularité des données qui permet, même si des données sont manquantes, d’obtenir facilement les informations de voisinage. Tout d’abord, nous présentons une nouvelle méthode pour extraire et simplifier la frontière d’une surface d’élévation définie par un ensemble de voxels dans un grand volume 3D où des données sont manquantes. Deuxièmement, une méthode pour simplifier la surface à l’intérieur de sa frontière est présentée. Elle comprend une étape de simplification grossière optionnelle suivie par une étape plus fine basée sur l’étude des courbures. Nous tenons également compte du fait que la densité de données doit changer graduellement afin de recevoir à la dernière étape d’une surface triangulée avec de meilleurs triangles. Troisièmement, nous avons proposé une nouvelle méthode rapide pour trianguler la surface après simplification. / Reconstructing surfaces with data coming from an automatic acquisition technique always entails the problem of mass of data. This implies that the usual processes cannot be applied directly. Therefore, it leads to a mandatory data reduction process. An effective algorithm for a rapid processing while keeping the original model is a valuable tool for constructing an optimal surface and managing the complex data.In this dissertation, we present methods for building an optimal geological surface from a huge amount of 3D points extracted from seismic cubes. Applying the process to the whole set of points induces an important risk of surface shrinking so that the initial boundary extraction is an important step permitting a simplification inside the surface. The global surface shape will then be better kept for the reconstruction of the final triangular surface. Our proposals are based on the regularity of data which permits, even if data are missing, to easily obtain the neighboring information. Firstly, we present a new method to extract and simplify the boundary of an elevation surface given as voxels in a large 3D volume having the characteristics to be sparse. Secondly, a method for simplifying the surface inside its boundary is presented with a rough optional simplification step followed by a finer one based on curvatures. We also keep into consideration that the density of data must gradually change in order to receive in the last step a triangulated surface with better triangles. Thirdly, we have proposed a new and fast method for triangulating the surface after simplification.
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Simplification, approximation and deformation of large modelsParadinas Salsón, Teresa 13 October 2011 (has links)
The high level of realism and interaction in many computer graphic applications requires techniques for processing complex geometric models. First, we present a method that provides an accurate low-resolution approximation from a multi-chart textured model that guarantees geometric fidelity and correct preservation of the appearance attributes. Then, we introduce a mesh structure called Compact Model that approximates dense triangular meshes while preserving sharp features, allowing adaptive reconstructions and supporting textured models. Next, we design a new space deformation technique called *Cages based on a multi-level system of cages that preserves the smoothness of the mesh between neighbouring cages and is extremely versatile, allowing the use of heterogeneous sets of coordinates and different levels of deformation. Finally, we propose a hybrid method that allows to apply any deformation technique on large models obtaining high quality results with a reduced memory footprint and a high performance. / L’elevat nivell de realisme i d’interacció requerit en múltiples aplicacions gràfiques fa que siguin necessàries tècniques pel processament de models geomètrics complexes. En primer lloc, presentem un mètode de simplificació que proporciona una aproximació precisa de baixa resolució d'un model texturat que garanteix fidelitat geomètrica i una correcta preservació de l’aparença. A continuació, introduïm el Compact Model, una nova estructura de dades que permet aproximar malles triangulars denses preservant els trets més distintius del model, permetent reconstruccions adaptatives i suportant models texturats. Seguidament, hem dissenyat *Cages, un esquema de deformació basat en un sistema de caixes multi-nivell que conserva la suavitat de la malla entre caixes veïnes i és extremadament versàtil, permetent l'ús de conjunts heterogenis de coordenades i diferents nivells de deformació. Finalment, proposem un mètode híbrid que permet aplicar qualsevol tècnica de deformació sobre models complexes obtenint resultats d’alta qualitat amb una memòria reduïda i un alt rendiment.
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