Using Images to create a Hierarchical Grid Spatial Index

This paper presents a hybrid approach to spatial indexing of two dimensional data. It sheds new light on the age old problem by thinking of the traditional algorithms as working with images. Inspiration is drawn from an analogous situation that is found in machine and human vision. Image processing techniques are used to assist in the spatial indexing of the data. A fixed grid approach is used and bins with too many records are sub-divided hierarchically. Search queries are pre-computed for bins that do not contain any data records. This has the effect of dividing the search space up into non rectangular regions which are based on the spatial properties of the data. The bucketing quad tree can be considered as an image with a resolution of two by two for each layer. The results show that this method performs better than the quad tree if there are more divisions per layer. This confirms our suspicions that the algorithm works better if it gets to look at the data with higher resolution images. An elegant class structure is developed where the implementation of concrete spatial indexes for a particular data type merely relies on rendering the data onto an image.Comment: In Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, Taiwan, 2006, pp. 1974-197

XOR-Based Compact Triangulations

Media, image processing, and geometric-based systems and applications need data structures to model and represent different geometric entities and objects. These data structures have to be time efficient and compact in term of space. Many structures in use are proposed to satisfy those constraints. This paper introduces a novel compact data structure inspired by the XOR-linked lists. The subject of this paper concerns the triangular data structures. Nevertheless, the underlying idea could be used for any other geometrical subdivision. The ability of the bitwise XOR operator to reduce the number of references is used to model triangle and vertex references. The use of the XOR combined references needs to define a context from which the triangle is accessed. The direct access to any triangle is not possible using only the XOR-linked scheme. To allow the direct access, additional information are added to the structure. This additional information permits a constant time access to any element of the triangulation using a local resolution scheme. This information represents an additional cost to the triangulation, but the gain is still maintained. This cost is reduced by including this additional information to a local sub-triangulation and not to each triangle. Sub-triangulations are calculated implicitly according to the catalog-based structure. This approach could be easily extended to other representation models, such as vertex-based structures or edge-based structures. The obtained results are very interesting since the theoretical gain is estimated to 38 % and the practical gain obtained from sample benches is about 34 %

Multirresolución adaptativa de mallas triangulares basado en criterios de textura

AbstractUsually, 3D models are composed by thousands of polygons. Some times, those representations can be obtained with the same visual quality but with a smaller number of polygons. In this paper, we present a method that reduces the size of 3D textured images based on triangular meshes, keeping the visual quality of the model. We introduced a texture criterion that controls the triangle decimation process. We used a polygonal algorithm of decimation that permits the structured point elimination without carrying out a new triangulation on the point cloud. In order to determine which points must to be removed, we used a 2D Sobel filter on the texture. We show that the algorithm can be used for reducing the load, rendering, transfer and storage times of 3D textured images.Los modelos 3D están generalmente compuestos por miles de polígonos. En ocasiones estas representaciones pueden obtenerse con la misma calidad visual pero con un menor número de polígonos. En este artículo se propone un método para reducir el tamaño de imágenes 3D texturadas basadas en mallas triangulares, conservando la calidad visual del modelo. Se introduce un criterio de textura que controla el proceso de decimación triangular. Para eliminar puntos sin necesidad de realizar una nueva triangulación, sobre la nube de puntos se usa un algoritmo poligonal de decimación. Para definir cuáles puntos deben ser removidos, se usa un filtro de Sobel 2D sobre la textura correspondiente. Se muestra que se puede usar el algoritmo para reducir los tiempos de carga, de renderización, de transferencia y de almacenamiento de una imagen 3D texturada

Unifying Geometry and Mesh Adaptive Refinement Using Loop Subdivision

RÉSUMÉ Cette thèse présente une nouvelle approche pour le raffinement de trois types de maillages : courbes, surfaces triangulaires et maillages tétraédriques tridimensionnels. Cette approche utilise des représentations par subdivisions afin de définir, modifier, analyser et visualiser des modèles géométriques de topologie arbitraire pour les applications de simulation numérique. Les représentations par subdivisions sont générées à l’aide des subdivisions de Loop. Après avoir étudié les inconvénients du manque de flexibilité dans le contrôle des niveaux de détails et du manque de précision dans les représentations de modèles géométriques utilisant les subdivisions itératives, approximatives et non-uniformes pour se rapprocher des modèles simulés, nous introduisons une nouvelle méthode de subdivision adaptative pour le raffinement de maillages. Cette méthode de raffinement à un seul niveau a été développée afin de supporter les subdivisions adaptatives pour les trois types de maillages. Cette méthode évite le stockage par hiérarchie et les problèmes d’assemblage rencontrés durant la génération des maillages multi-résolutions par subdivisions, surtout pour les maillages tétraédriques. La mise en œuvre de subdivisions pour les maillages adaptatifs tétraédriques amène deux innovations : la configuration de forme de fractionnement des tétraèdres et l’amélioration de la paramétrisation des surfaces de subdivision. La combinaison naturelle de ces deux innovations permet la génération par subdivision de maillages multi-résolutions tétraédriques dont les surfaces frontières sont exactement sur les limites de subdivision. Notre recherche contient cinq parties. Premièrement, nous développons un schéma de Loop pour la subdivision des solides, lequel permet d’intégrer le fractionnement topologique des arêtes avec le lissage géométrique des surfaces frontières. Deuxièmement, nous fusionnons les raffinements adaptatifs avec les techniques de subdivision, ce qui permet la subdivision adaptive complète du maillage tout en ayant les surfaces frontières projetées sur les limites de subdivision. Troisièmement, nous étudions et comparons des techniques existantes de paramétrisation des surfaces de subdivision, ce qui permet d’obtenir directement la limite de subdivision de toutes positions arbitraires sur les surfaces de subdivision de Loop. Quatrièmement, nous construisons les règles de création des sommets fixes et des arêtes vives du schéma de subdivision de Loop pour les modèles solides, ce qui permet de préserver les caractéristiques anguleuses des surfaces frontières des maillages tétraédriques. Finalement, nous utilisons un critère de qualité des maillages pour valider nos résultats et nous présentons la performance des calculs en ce qui a trait à la modélisation des solides.----------ABSTRACT In this thesis, we present a new refinement approach on three types of meshes: curves, triangular surfaces and 3D tetrahedral meshes. This approach utilizes subdivision-based representations to create, modify, analyze and visualize geometric models with arbitrary topology for numerical simulation applications. The subdivision-based representations are generated by utilizing Loop subdivisions. After studying the disadvantage of lack of flexibility in controlling LODs (Level Of Details) and accuracy in representing geometric models by using the non-uniform approximating subdivision iterations to approach simulated models, we introduce adaptive subdivisions in our refinement work. We develop a single-level refinement method to support adaptive subdivisions on the three types of meshes. This single-level method eliminates the hierarchy storage and the stitching issues encountered during the generation of multi-resolution subdivision meshes, especially 3D tetrahedral meshes. The implementation of adaptive tetrahedral mesh subdivisions brings up two innovations: the configuration of tetrahedron split patterns and the improvement in subdivision surface parameterizations. The natural combination of these two innovations fulfills generating multi-resolution subdivision tetrahedral meshes, whose boundary surfaces lie exactly on their subdivision limits. Our research work includes five parts. Firstly, we develop the Loop-based solid subdivision scheme, which permits integrating edge-based topological splits with geometrical smoothing on boundary surfaces. Secondly, we merge subdivision techniques with adaptive refinements with, which permits whole meshes to be adaptively subdivided and boundary meshes to be projected to their subdivision limits. Thirdly, we study and compare the existing subdivision surface parameterization techniques, which eventually permits obtaining the limit subdivision of any arbitrary position on Loop subdivision surfaces. Fourthly, we complete vertex and edge crease creation rules of the Loop-based solid subdivision scheme, which permits preserving sharp features on boundary surfaces of 3D tetrahedral meshes. Finally, we use a mesh quality evaluator to validate our results and we evaluate system performance in the context of solid modeling

Towards Predictive Rendering in Virtual Reality

The strive for generating predictive images, i.e., images representing radiometrically correct renditions of reality, has been a longstanding problem in computer graphics. The exactness of such images is extremely important for Virtual Reality applications like Virtual Prototyping, where users need to make decisions impacting large investments based on the simulated images. Unfortunately, generation of predictive imagery is still an unsolved problem due to manifold reasons, especially if real-time restrictions apply. First, existing scenes used for rendering are not modeled accurately enough to create predictive images. Second, even with huge computational efforts existing rendering algorithms are not able to produce radiometrically correct images. Third, current display devices need to convert rendered images into some low-dimensional color space, which prohibits display of radiometrically correct images. Overcoming these limitations is the focus of current state-of-the-art research. This thesis also contributes to this task. First, it briefly introduces the necessary background and identifies the steps required for real-time predictive image generation. Then, existing techniques targeting these steps are presented and their limitations are pointed out. To solve some of the remaining problems, novel techniques are proposed. They cover various steps in the predictive image generation process, ranging from accurate scene modeling over efficient data representation to high-quality, real-time rendering. A special focus of this thesis lays on real-time generation of predictive images using bidirectional texture functions (BTFs), i.e., very accurate representations for spatially varying surface materials. The techniques proposed by this thesis enable efficient handling of BTFs by compressing the huge amount of data contained in this material representation, applying them to geometric surfaces using texture and BTF synthesis techniques, and rendering BTF covered objects in real-time. Further approaches proposed in this thesis target inclusion of real-time global illumination effects or more efficient rendering using novel level-of-detail representations for geometric objects. Finally, this thesis assesses the rendering quality achievable with BTF materials, indicating a significant increase in realism but also confirming the remainder of problems to be solved to achieve truly predictive image generation