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Research Homepage

This section is dedicated to my past and present research projects and their results.

Pages In This Section

Multi-Resolution Approximation

In many cases, data sets (images, 3D surfaces, digital elevation maps, etc.) are too large to transmit them across low-bandwidth connections, sometimes even too large to process them or store them. Compressing a data set is usually a trade-off between approximation error and space savings. Multi-resolution approximation offers a solution by providing a hierarchy of approximation to each data set with different levels of accuracy/compression. Then a user can select the most appropriate level for his/her needs. In the described techniques, data sets are interpreted as samples of multivariate functions, and are approximated by selecting subsets of samples. The selected samples specify an approximation function from a family of functions.
Linear Spline Approximation
For an approximated data set, the selected samples are connected to form a piecewise linear function (a polyline in 1D, a triangle mesh in 2D, a tetrahedral mesh in 3D). At each approximation level, the number of samples is prescribed, and the approximation algorithm attempts to find the best set of samples by using a global optimization method.
Voronoi-based Approximation
For an approximated data set, the selected samples define the approximating function by their Voronoi diagram. In one version of the algorithm, the Voronoi diagram defines a piecewise constant function; in another version, the Voronoi diagram defines a smooth approximation function (Sibson interpolant).

Interactive Previewing of Volume Data

This research project is a borderline case between multi-resolution approximation and volume rendering. To generate interactive previews of large volume data sets, we first generate a multi-resolution approximation by selecting subsets of samples, using a spatial decimation technique based on Delaunay complexes and maximum independent sets. We then render images of these approximations using a novel slicing approach.

Volume Visualization

High-quality Photo-realistic Rendering of Isosurfaces
Hardware-accelerated Volume Visualization
Volume Rendering Using Texture Hardware
Volume Rendering of Adaptive Mesh Refinement (AMR) Data
Volume Rendering of AMR Data
Research Project at Lawrence Berkeley National Laboratory.

Virtual Reality Development

The GLMotif User Interface Toolkit
The Vrui Virtual Reality Framework

Virtual Reality "Toy" Applications

Interactive Rigid Body Simulation
Interactive Crystal Structure Simulation ("Virtual Jell-O")

Virtual Reality Modelling

Virtual Reality Data Exploration

Scalar-valued Data Sets
Vector-valued Data Sets

Computational Steering

Particle-based Simulation
CFD Simulation of Weak Shocks
Joint project with Allen Tesdall.
Protein Folding Simulation
Research Project at Lawrence Berkeley National Laboratory.