Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

Wavelet representation of functions defined on tetrahedrical grids

In this paper, a method for representing scalar functions on volumes is presented. The method is based on wavelets and it can be used for representing volumetric data (geometric or scalar) defifined on non structured grids. The basic contribution is the extension of wavelets to represent scalar functions on volumetric domains of arbitrary topological type. This extension is made by constructing a wavelet basis defifined on any tetrahedrized volume. This basis construction is achieved using multiresolution analysis and the lifting schemeFacultad de Informátic

Cached Geometry Manager for View-dependent LOD Rendering

The new generation of commodity graphics cards with significant on-board video memory has become widely popular and provides high-performance rendering and flexibility. One of the features to be exploited with this hardware is the use of the on-board video memory to store geometry information. This strategy significantly reduces the data transfer overhead from sending geometry data over the (AGP) bus interface from main memory to the graphics card. However, taking advantage of cached geometry is not a trivial task because the data models often exceed the memory size of the graphics card. In this paper we present a dynamic Cached Geometry Manager (CGM) to address this issue. We show how this technique improves the performance of real-time view-dependent level-of-detail (LOD) selection and rendering algorithms of large data sets. Alternative caching approaches have been analyzed over two different view-dependent progressive mesh (VDPM) frameworks: one for rendering of arbitrary manifold 3D meshes, and one for terrain visualization

Wavelet Based Data-Hiding of DEM in the Context of Real Time 3D Visualization

International audienceThe use of aerial photographs, satellite images, scanned maps and digital elevation models necessitates the setting up of strategies for the storage and visualization of these data in an interactive way. In order to obtain a three dimensional visualization it is necessary to map the images, called textures, onto the terrain geometry computed with Digital Elevation Model (DEM). Practically, all of these informations are stored in three different files: DEM, texture and geo-localization of the data. In this paper we propose to save all this information in a single file for the purpose of synchronization. For this, we have developed a wavelet-based embedding method for hiding the data in a color image. The texture images containing hidden DEM data can then be sent from the server to a client in order to effect 3D visualization of terrains. The embedding method is integrable with the JPEG2000 coder to accommodate compression and multi-resolution visualization