I worked at the Scientific Computing and Imaging (SCI) Institute in Salt Lake City, Utah as a graduate research assistant for Professor Mike Kirby. Our research focused on uncertainty quantification, and visualization of such uncertainties in simulation data (scalar/vector fields) generated from stochastic partial differential equations’ solutions.
Our project, that eventually led to my MS thesis, dealt with visualizing intrinsic variation in isosurfaces (level-set surface) due to input perturbation in a PDE simulation. This basically boils down to characterizing important changes in geometric features of the isosurface.
In order to tackle the question, we developed a framework that puts together ideas from shape analysis and high dimensional data analysis algorithms. The framework combines methods of geometry signatures and unsupervised machine learning techniques to answer the above question for any simulation dataset that satisfies certain criteria.
Mesh Deformation and Editing Tools
As part of this research effort, I developed several tools that aid the investigation of the above research question. One such tool is a particle-based simulation that helped us produce different perturbations of any mesh. This is important in experimenting with geometric feature change and evaluating the efficiency of our framework. This tool can also be used for any other mesh quality study and experimentation purpose.
The above figure shows two systematically deformed ellipsoid and sphere using my mesh deformation program.
Resources
MS Thesis (pdf)
Presentation Slides (pdf)
Code and data are available upon request.
Saquib 