We present a new method for simplifying simplicial complexes of any type embedded in Euclidean spaces of any dimension. At the heart of this system is a novel generalization of the quadric error metric used in surface simplification. We demonstrate that our generalized simplification system can produce high quality approximations of plane and space curves, triangulated surfaces, tetrahedralized volume data, and simplicial complexes of mixed type. Our method is both efficient and easy to implement. It is capable of processing complexes of arbitrary topology, including nonmanifolds, and can preserve intricate boundaries.

We describe a new dynamic level-of-detail (LOD) technique that allows real-time rendering of large tetrahedral meshes. Unlike approaches that require hierarchies of tetrahedra, our approach uses a subset of the faces that compose the mesh. No connectivity is used for these faces so our technique eliminates the need for topological information and hierarchical data structures. By operating on a simple set of triangular faces, our algorithm allows a robust and straightforward graphics hardware (GPU) implementation. Because the subset of faces processed can be constrained to arbitrary size, interactive rendering is possible for a wide range of data sets and hardware configurations.

Real-time rendering of large unstructured meshes is a major research goal in the scientific visualization community. While, for regular grids, texture-based techniques are well-suited for current Graphics Processing Units (GPUs), the steps necessary for rendering unstructured meshes are not so easily mapped to current hardware. This paper reviews volume rendering algorithm and techniques for unstructured grids aimed at exploiting high-performance GPUs. We discuss both the algorithms and their implementation details, including major shortcomings of existing approaches. Resumo: A visualização volumétrica de grandes malhas não estruturadas é uma das principais metas da comunidade de visualização científica. Enquanto que em grades regulares o uso de técnicas baseadas em textura são adequadas para as Unidades de Processamento Gráfico (GPUs) atuais, os passos necessários para exibir malhas não estruturas não são diretamente mapeadas para o hardware atual. Este artigo revisa algoritmos e técnicas de visualização volumétrica que exploram GPUs de alta performance. São discutidos tanto os algoritmos como seus detalhes de implementação, incluindo as principais dificuldades das abordagens atuais. 1

We describe a new progressive technique that allows real-time rendering of extremely large tetrahedral meshes. Our approach uses a client-server architecture to incrementally stream portions of the mesh from a server to a client which refines the quality of the approximate rendering until it converges to a full quality rendering. The results of previous steps are re-used in each subsequent refinement, thus leading to an efficient rendering. Our novel approach keeps very little geometry on the client and works by refining a set of rendered images at each step. Our interactive representation of the dataset is efficient, light-weight, and high quality. We present a framework for the exploration of large datasets stored on a remote server with a thin client that is capable of rendering and managing full quality volume visualizations. 1

Figure 1: Screen shots from interactive visualization of an unstructured 275Mb mesh with more than 5 million tetrahedra and 13 field values. Our method is the first to guarantee real-time performance regardless of rendering hardware (here a P4 1.7GHz, Radeon 8700) and size of the unstructured tetrahedral mesh. Images show real-time volumetric clipping by CSG intersection with a sphere probe (left), cutting plane (two center) and a box probe (right). We present a novel approach to interactive visualization and exploration of large unstructured tetrahedral meshes. These massive 3D meshes are used in mission-critical CFD and structural mechanics simulations, and typically sample multiple field values on several millions of unstructured grid points. Our method relies on the preprocessing of the tetrahedral mesh to partition it into non-convex boundaries and internal fragments that are subsequently encoded into compressed multi-resolution data representations. These compact hierarchical data structures are then adaptively rendered and probed in real-time on a commodity PC. Our point-based rendering algorithm, which is inspired by QSplat, employs a simple but highly efficient splatting technique that guarantees interactive frame-rates regardless of the size of the input mesh and the available rendering hardware. It furthermore allows for real-time probing of the volumetric data-set through constructive solid geometry operations as well as interactive editing of color transfer functions for an arbitrary number of field values. Thus, the presented visualization technique allows end-users for the first time to interactively render and explore very large unstructured tetrahedral meshes on relatively inexpensive hardware.

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Figure 1. Our novel point-based volume rendering technique is faster than the current state of the art while still generating high quality images. Left to right: baseline image rendered at full quality; our method with unshaped footprints, circular footprints and ellipsoidal footprints, respectively. The lower half (our method) shows the difference to the baseline exact image. Notice the increasing level of fidelity. Unstructured volume grids are ubiquitous in scientific computing, and have received substantial interest from the scientific visualization community. In this paper, we take a point-based approach to rendering unstructured grids. In particular, we present a novel method of approximating these irregular elements with point-based primitives amenable to existing hardware acceleration techniques. To improve interactivity to large datasets, we have adapted a level-of-detail strategy. We use a well-known quantitative metric to analyze the image quality achieved by the final rendering. 1.

Abstract—Efficient multiresolution representations for isosurfaces and interval volumes are becoming increasingly important as the gap between volume data sizes and processing speed continues to widen. Our multiresolution scalar field model is a hierarchy of tetrahedral clusters generated by longest edge bisection, that we call a hierarchy of diamonds. We propose two multiresolution models for representing isosurfaces, or interval volumes, extracted from a hierarchy of diamonds which exploit its regular structure. These models are defined by subsets of diamonds in the hierarchy, that we call isodiamonds, which are enhanced with geometric and topological information for encoding the relation between the isosurface, or interval volume, and the diamond itself. The first multiresolution model, called a relevant isodiamond hierarchy, encodes the isodiamonds intersected by the isosurface, or interval volume, as well as their non-intersected ancestors, while the second model, called a minimal isodiamond hierarchy, encodes only the intersected isodiamonds. Since both models operate directly on the extracted isosurface or interval volume, they require significantly less memory and support faster selective refinement queries than the original multiresolution scalar field, but do not support dynamic isovalue modifications. Moreover, since a minimal isodiamond hierarchy only encodes intersected isodiamonds, its extracted meshes require significantly less memory than those extracted from a relevant isodiamond hierarchy. We demonstrate the compactness of isodiamond hierarchies by comparing them to an indexed representation of the mesh at full resolution. Index Terms—Isosurfaces, interval volumes, multiresolution models, longest edge bisection, diamond hierarchies. 1

The Corner Table (CT) promoted by Rossignac et al. provides a simple and efficient representation of triangle meshes, storing 6 integer references per triangle (3 vertex references in the V table and 3 references to opposite corners in the O table that accelerate access to adjacent triangles). The Compact Half Face (CHF) proposed by Lage et al. extends CT to tetrahedral meshes, storing 8 references per tetrahedron (4 in the V table and 4 in the O table). We call it the Vertex Opposite Table (VOT) and propose a sorted variation, SVOT, which does not require any additional storage and yet provides, for each vertex, a reference to an incident corner from which an incident tetrahedron may be recovered and the star of the vertex may be traversed at a constant cost per visited element. We use a set of powerful wedge-based operators for querying and traversing the mesh. Finally, inspired by tetrahedral mesh encoding techniques used by Weiler et al. and by Szymczak and Rossignac, we propose our Sorted O Table (SOT) variation, which eliminates the V table completely and hence reduces storage requirements by 50 % to only 4 references and 9 bits per tetrahedron, while preserving the vertex-toincident-corner references and supporting our wedge operators with a linear average cost.