Single-Strip Triangulation of Manifolds with Arbitrary Topology

Triangle strips have been widely used for efficient rendering. It is NP-complete to test whether a given triangulated model can be represented as a single triangle strip, so many heuristics have been proposed to partition models into few long strips. In this paper, we present a new algorithm for creating a single triangle loop or strip from a triangulated model. Our method applies a dual graph matching algorithm to partition the mesh into cycles, and then merges pairs of cycles by splitting adjacent triangles when necessary. New vertices are introduced at midpoints of edges and the new triangles thus formed are coplanar with their parent triangles, hence the visual fidelity of the geometry is not changed. We prove that the increase in the number of triangles due to this splitting is 50% in the worst case, however for all models we tested the increase was less than 2%. We also prove tight bounds on the number of triangles needed for a single-strip representation of a model with holes on its boundary. Our strips can be used not only for efficient rendering, but also for other applications including the generation of space filling curves on a manifold of any arbitrary topology.Comment: 12 pages, 10 figures. To appear at Eurographics 200

Interactive ray tracing of massive and deformable models

Ray tracing is a fundamental algorithm used for many applications such as computer graphics, geometric simulation, collision detection and line-of-sight computation. Even though the performance of ray tracing algorithms scales with the model complexity, the high memory requirements and the use of static hierarchical structures pose problems with massive models and dynamic data-sets. We present several approaches to address these problems based on new acceleration structures and traversal algorithms. We introduce a compact representation for storing the model and hierarchy while ray tracing triangle meshes that can reduce the memory footprint by up to 80%, while maintaining high performance. As a result, can ray trace massive models with hundreds of millions of triangles on workstations with a few gigabytes of memory. We also show how to use bounding volume hierarchies for ray tracing complex models with interactive performance. In order to handle dynamic scenes, we use refitting algorithms and also present highly-parallel GPU-based algorithms to reconstruct the hierarchies. In practice, our method can construct hierarchies for models with hundreds of thousands of triangles at interactive speeds. Finally, we demonstrate several applications that are enabled by these algorithms. Using deformable BVH and fast data parallel techniques, we introduce a geometric sound propagation algorithm that can run on complex deformable scenes interactively and orders of magnitude faster than comparable previous approaches. In addition, we also use these hierarchical algorithms for fast collision detection between deformable models and GPU rendering of shadows on massive models by employing our compact representations for hybrid ray tracing and rasterization

Métricas para simplificaçao de malhas triangulares

Orientador: Hélio PedriniDissertaçao (mestrado) - Universidade Federal do Paraná, Setor de Ciencias Exatas, Programa de Pós-Graduaçao em Informática. Defesa: Curitiba, 2005Inclui bibliografia e apendiceResumo: Malhas triangulares são uma das representações de dados espaciais mais utilizadas, pois possibilitam a manipulação e visualização de superfícies de alta complexidade, além de apresentarem diversas vantagens, como suporte direto em software e hardware. O problema de como transformar conjuntos de dados espaciais distintos, entre eles modelos de terrenos, conjuntos de pontos tridimensionais e dados volumétricos, em malhas triangulares é amplamente estudado. Além disso, com o aumento da capacidade de coleta desse tipo de dados, torna-se cada vez mais comum a necessidade de manipulação de modelos com altíssima resolução. Uma abordagem para a solução desses dois problemas é a simplificação de malhas triangulares. Esta consiste em primeiramente transformar um determinado conjunto de dados em uma malha triangular e, então, simplificá-la reduzindo-se o número de vértices, arestas e triângulos, de forma que a malha simplificada aproxime a malha original com o menor erro possível. Assim, torna-se possível manipular os dados em questão e, aplicando-se o método de simplificação repetidamente com diferentes requisitos de qualidade, obtêm-se representações da malha triangular em diversas resoluções. Dentro do âmbito da simplificação de malhas triangulares, este trabalho se propõe a verificar experimentalmente quais métricas de caráter local existentes na literatura possibilitam uma simplificação rápida e gerando aproximações de alta qualidade. Além disso, este trabalho também propõe duas novas métricas que geram aproximações de grande qualidade e são uma alternativa mais adequada para certas aplicações. Outros aspectos dos métodos de simplificação de malhas triangulares também são investigados, bem como o seu efeito na qualidade das aproximações geradas. Para que as diferentes opções do método de simplificação pudessem ser investigadas sem a interferência de implementações distintas, um programa para a simplificação de malhas triangulares foi implementado, de forma que o resultado da mudança de apenas opções específicas do método de simplificação é adequadamente verificado. Também são discutidos os diversos trabalhos da literatura que utilizam as operações de simplificação para a construção de uma representação em múltiplas resoluções, da qual 'e possível então extrair uma malha triangular com determinado nível de detalhe, sem a necessidade da aplicação de um método de simplificação.Abstract: Triangle meshes are one of the mostly employed spatial data representations, since they allow the manipulation and visualization of highly complex surfaces, apart from presenting many advantages, including direct software and hardware support. The problem of converting distinct spatial datasets, among them terrain models, tridimensional point sets, and volumetric data, into triangle meshes is widely studied. Furthermore, with the increase in the collection capacity of such type of data, the manipulation of models with high resolution has become a common task. One approach for the solution of these two problems is triangle mesh simplification, which consists in firstly converting a specific dataset into a triangle mesh and then simplifying it to reduce the number of vertices, edges, and faces, in a way that the simplified mesh approximates the original mesh with the lowest error. Therefore, it is possible to manipulate the data and, by applying repeatedly the simplification method with different quality requirements, a representation in multiple resolutions is obtained. In the scope of triangle mesh simplification, this work presents an experimental study to establish which local metrics that exist in the literature allow fast simplification generating high quality approximations. This work also proposes two new metrics that are an adequate alternative for certain applications, and also generate great quality approximations. Other aspects of triangle mesh simplification are also studied, including their impact in the quality of the approximations. For the investigation of the different options of the simplification method, without the interference of distinct implementations, a program for triangle mesh simplification was implemented, allowing that the change in specific simplification options can be properly verified. Different works from the literature are also discussed, that employ the simplification operations for the creation of a multi-resolution representation, from which it is possible to extract a triangle mesh with a required level of detail, without the necessity of applying a simplification method

Hierarchical processing, editing and rendering of acquired geometry

La représentation des surfaces du monde réel dans la mémoire d’une machine peut désormais être obtenue automatiquement via divers périphériques de capture tels que les scanners 3D. Ces nouvelles sources de données, précises et rapides, amplifient de plusieurs ordres de grandeur la résolution des surfaces 3D, apportant un niveau de précision élevé pour les applications nécessitant des modèles numériques de surfaces telles que la conception assistée par ordinateur, la simulation physique, la réalité virtuelle, l’imagerie médicale, l’architecture, l’étude archéologique, les effets spéciaux, l’animation ou bien encore les jeux video. Malheureusement, la richesse de la géométrie produite par ces méthodes induit une grande, voire gigantesque masse de données à traiter, nécessitant de nouvelles structures de données et de nouveaux algorithmes capables de passer à l’échelle d’objets pouvant atteindre le milliard d’échantillons. Dans cette thèse, je propose des solutions performantes en temps et en espace aux problèmes de la modélisation, du traitement géométrique, de l’édition intéractive et de la visualisation de ces surfaces 3D complexes. La méthodologie adoptée pendant l’élaboration transverse de ces nouveaux algorithmes est articulée autour de 4 éléments clés : une approche hiérarchique systématique, une réduction locale de la dimension des problèmes, un principe d’échantillonage-reconstruction et une indépendance à l’énumération explicite des relations topologiques aussi appelée approche basée-points. En pratique, ce manuscrit propose un certain nombre de contributions, parmi lesquelles : une nouvelle structure hiérarchique hybride de partitionnement, l’Arbre Volume-Surface (VS-Tree) ainsi que de nouveaux algorithmes de simplification et de reconstruction ; un système d’édition intéractive de grands objets ; un noyau temps-réel de synthèse géométrique par raffinement et une structure multi-résolution offrant un rendu efficace de grands objets. Ces structures, algorithmes et systèmes forment une chaîne capable de traiter les objets en provenance du pipeline d’acquisition, qu’ils soient représentés par des nuages de points ou des maillages, possiblement non 2-variétés. Les solutions obtenues ont été appliquées avec succès aux données issues des divers domaines d’application précités.Digital representations of real-world surfaces can now be obtained automatically using various acquisition devices such as 3D scanners and stereo camera systems. These new fast and accurate data sources increase 3D surface resolution by several orders of magnitude, borrowing higher precision to applications which require digital surfaces. All major computer graphics applications can take benefit of this automatic modeling process, including: computer-aided design, physical simulation, virtual reality, medical imaging, architecture, archaeological study, special effects, computer animation and video games. Unfortunately, the richness of the geometry produced by these media comes at the price of a large, possibility gigantic, amount of data which requires new efficient data structures and algorithms offering scalability for processing such objects. This thesis proposes time and space efficient solutions for modeling, editing and rendering such complex surfaces, solving these problems with new algorithms sharing 4 fundamental elements: a systematic hierarchical approach, a local dimension reduction, a sampling-reconstruction paradigm and a pointbased basis. Basically, this manuscript proposes several contributions, including: a new hierarchical space subdivision structure, the Volume-Surface Tree, for geometry processing such as simplification and reconstruction; a streaming system featuring new algorithms for interactive editing of large objects, an appearancepreserving multiresolution structure for efficient rendering of large point-based surfaces, and a generic kernel for real-time geometry synthesis by refinement. These elements form a pipeline able to process acquired geometry, either represented by point clouds or non-manifold meshes. Effective results have been successfully obtained with data coming from the various applications mentioned

Compactaçao eficiente da geometria de malhas triangulares

Orientador: Hélio PedriniDissertaçao (mestrado) - Universidade Federal do Paraná, Setor de Ciencias Exatas, Programa de Pós-Graduaçao em Informática. Defesa: Curitiba, 2005Inclui bibliografi

Novel methods of image compression for 3D reconstruction

Data compression techniques are widely used in the transmission and storage of 2D image, video and 3D data structures. The thesis addresses two aspects of data compression: 2D images and 3D structures by focusing research on solving the problem of compressing structured light images for 3D reconstruction. It is useful then to describe the research by separating the compression of 2D images from the compression of 3D data. Concerning image compression, there are many types of techniques and among the most popular are JPEG and JPEG2000. The thesis addresses different types of discrete transformations (DWT, DCT and DST) thatcombined in particular ways followed by Matrix Minimization algorithm,which is achieved high compression ratio by converting groups of data into a single value. This is an essential step to achieve higher compression ratios reaches to 99%. It is demonstrated that the approach is superior to both JPEG and JPEG2000 for compressing 2D images used in 3D reconstruction. The approach has also been tested oncompressing natural or generic 2D images mainly through DCT followed by Matrix Minimization and arithmetic coding.Results show that the method is superior to JPEG in terms of compression ratios and image quality, and equivalent to JPEG2000 in terms of image quality. Concerning the compression of 3D data structures, the Matrix Minimization algorithm is used to compress geometry and connectivity represented by a list of vertices and a list of triangulated faces. It is demonstrated that the method can compress vertices very efficiently compared with other 3D formats. Here the Matrix Minimization algorithm converts each vertex (X, Y and Z) into a single value without the use of any prior discrete transformation (as used in 2D images) and without using any coding algorithm. Concerningconnectivity,the triangulated face data are also compressed with the Matrix Minimizationalgorithm followed by arithmetic coding yielding a stream of compressed data. Results show compression ratiosclose to 95% which are far superior to compression with other 3D techniques. The compression methods presented in this thesis are defined as per-file compression. The methods to generate compression keys depend on the data to be compressed. Thus, each file generates their own set of compression keys and their own set of unique data. This feature enables application in the security domain for safe transmission and storage of data. The generated keys together with the set of unique data can be defined as an encryption key for the file as, without this information, the file cannot be decompressed