Hierarchical and Geometrical Methods in Scientific Visualization: (Mathematics and Visualization)

The nature of the physical Universe has been increasingly better understood in recent years, and cosmological concepts have undergone a rapid evolution (see, e.g., [11], [2],or [5]). Although there are alternate theories, it is generally believed that the large-scale relationships and homogeneities that we see can only be explainedby having the universe expand suddenlyin a very early “in?ationary” period. Subsequent evolution of the Universe is described by the Hubble expansion, the observation that the galaxies are ?ying away from each other. We can attribute di?erent rates of this expansion to domination of di?erent cosmological processes, beginning with radiation, evolving to matter domination, and, relatively recently, to vacuum domination (the Cosmological Constant term)[4]. We assume throughout that we will be relying as much as possible on observational data, with simulations used only for limited purposes, e.g., the appearance of the Milky Wayfrom nearbyintergalactic viewpoints. The visualization of large-scale astronomical data sets using?xed, non-interactive animations has a long history. Several books and ?lms exist, ranging from “Cosmic View: The Universe in Forty Jumps” [3] by Kees Boeke to “Powers of 10” [6,13] by Charles and Ray Eames, and the recent Imax ?lm “Cosmic Voyage” [15]. We have added our own contribution [9], “Cosmic Clock,” which is an animation based entirely on the concepts and implementation described in this paper.

Table of Contents:
Dataflow and Remapping for Wavelet Compression and View-dependent Optimization of Biflion-triangle Isosurfaces.- Extraction of Crack-free Isosurfaces from Adaptive Mesh Refinement Data.- Edgebreaker on a Corner Table: A Simple Technique for Representing and Compressing Triangulated Surfaces.- Efficient Error Calculation for Multiresolution Texture-based Volume Visualization.- Hierarchical Spline Approximations.- Terrain Modeling Using Voronoi Hierarchies.- Multiresolution Representation of Datasets with Material Interfaces.- Approaches to Interactive Visualization of Large-scale Dynamic Astrophysical Environments.- Data Structures for Multiresolution Representation of Unstructured Meshes.- Scaling the Topology of Symmetric, Second-Order Planar Tensor Fields.- Simplification of Nonconvex Tetrahedral Meshes.- A Framework for Visualizing Hierarchical Computations.- Virtual-Reality Based Interactive Exploration of Multiresolution Data.- Hierarchical Indexing for Out-of-Core Access to Multi-Resolution Data.- Mesh Fairing Based on Harmonic Mean Curvature Surfaces.- Shape Feature Extraction.- Network-based Rendering Techniques for Large-scale Volume Data Sets.- A Data Model for Distributed Multiresolution Multisource Scientific Data.- Adaptive Subdivision Schemes for Triangular Meshes.- Hierarchical Image-based and Polygon-based Rendering for Large-Scale Visualizations.- Appendix: Color Plates.

Review :
From the reviews: "This work … introduce the first end-to-end multiresolution dataflow strategy that can effectively combine the top performing subdivision-surface wavelet compression and view-dependent optimization methods, thus increasing efficiency by several orders of magnitude over conventional processing pipelines. … Overall, this is the first effort to exploit semi-structured surface representations for a complete large-data visualization pipeline." (Wordtrade, July, 2008)