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

A novel multidimensional model for the OLAP on documents : modeling, generation and implementation

International audienceAs the amount of textual information grows explosively in various kinds of business systems, it becomes more and more essential to analyze both structured data and unstructured textual data simultaneously. However information contained in non structured data (documents and so on) is only partially used in business intelligence (BI). Indeed On-Line Analytical Processing (OLAP) cubes which are the main support of BI analysis in decision support systems have focused on structured data. This is the reason why OLAP is being extended to unstructured textual data. In this paper we introduce the innovative “Diamond” multidimensional model that will serve as a basis for semantic OLAP on XML documents and then we describe the meta modeling, generation and implementation of a the Diamond multidimensional model

Letting Go of “Natural Kind”: Toward a Multidimensional Framework of Nonarbitrary Classification

This article uses the case study of ethnobiological classification to develop a positive and a negative thesis about the state of natural kind debates. On the one hand, I argue that current accounts of natural kinds can be integrated in a multidimensional framework that advances understanding of classificatory practices in ethnobiology. On the other hand, I argue that such a multidimensional framework does not leave any substantial work for the notion “natural kind” and that attempts to formulate a general account of naturalness have become an obstacle to understanding classificatory practices

Diamond multidimensional model and aggregation operators for document OLAP

International audienceOn-Line Analytical Processing (OLAP) has generated methodologies for the analysis of structured data. However, they are not appropriate to handle document content analysis. Because of the fast growing of this type of data, there is a need for new approaches abling to manage textual content of data. Generally, these data exist in XML format. In this context, we propose an approach of construction of our Diamond multidimensional model, which includes semantic dimension to better consider the semantics of textual data In addition, we propose new aggregation operators for textual data in OLAP environment