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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
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- 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.