Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration

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Torsten Möller, Bernd Hamann, Robert D. Russell
Springer Science & Business Media, Jun 12, 2009 - Computers - 350 pages
The goal of visualization is the accurate, interactive, and intuitive presentation of data. Complex numerical simulations, high-resolution imaging devices and incre- ingly common environment-embedded sensors are the primary generators of m- sive data sets. Being able to derive scienti?c insight from data increasingly depends on having mathematical and perceptual models to provide the necessary foundation for effective data analysis and comprehension. The peer-reviewed state-of-the-art research papers included in this book focus on continuous data models, such as is common in medical imaging or computational modeling. From the viewpoint of a visualization scientist, we typically collaborate with an application scientist or engineer who needs to visually explore or study an object which is given by a set of sample points, which originally may or may not have been connected by a mesh. At some point, one generally employs low-order piecewise polynomial approximationsof an object, using one or several dependent functions. In order to have an understanding of a higher-dimensional geometrical “object” or function, ef?cient algorithms supporting real-time analysis and manipulation (- tation, zooming) are needed. Often, the data represents 3D or even time-varying 3D phenomena (such as medical data), and the access to different layers (slices) and structures (the underlying topology) comprising such data is needed.
 

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Contents

Maximizing Adaptivity in Hierarchical Topological Models Using Cancellation Trees
1
Computation and Presentation of Multiresolution Topology
19
Isocontour Based Visualization of TimeVarying Scalar Fields
41
DeBruijn Counting for Visualization Algorithms
69
Topological Methods for Visualizing Vortical Flows
89
A StateoftheArt Report
109
An Ants Perspective
126
TensorFields Visualization Using a Fabriclike Texture Applied to Arbitrary Twodimensional Surfaces
139
Constructing 3D Elliptical Gaussians for Irregular Data
212
From Sphere Packing to the Theory of Optimal Lattice Sampling
227
Reducing Interpolation Artifacts by Globally Fairing Contours
256
Time and SpaceEfficient Error Calculation for Multiresolution Direct Volume Rendering
271
A Survey
284
Compression and Occlusion Culling for Fast Isosurface Extraction from Massive Datasets
303
Volume Visualization of Multiple Alignment of Large Genomic DNA
325
Computing Perceptually Optimal Visualizations
343

Flow Visualization via Partial Differential Equations
156
Iterative Twofold Line Integral Convolution for TextureBased Vector Field Visualization
191

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