I have pursued my interest in physics-based modeling in three basic research areas, level set methods for graphics, particle-based modeling, and energy minimization solutions to 3-D geometric problems. (See Breen 1997). I have worked for several years with Ross Whitaker in the area of level set methods for computer graphics, visualization, and computer animation. Our major results include the development of a 3D metamorphosis technique and a framework for segmenting models from volume data. We are currently exploring interactive level set methods for geometric modeling and segmentation.
In particle-based modeling non-rigid materials are modeled with numerous small-scale primitives (particles) that represent the material's microstructure. By capturing the material's low-level structures and computationally aggregating the interactions of these structures, it is possible to model the mechanical behavior of complex flexible materials. My work in this area was first motivated by the challenge of modeling organic soft tissue for surgical simulation. Ultimately, my particle-based modeling research focused on cloth modeling.
The geometric structures and constraints of particle-based modeling are defined with energy functions. During simulation, these constraints are enforced by minimizing the energy functions. I have utilized this technique not only in my draping cloth work, but also in a project to extract closed geometric models from 3-D scalar data sets for visualization and analysis. Here, a Geometrically Deformed Model may be placed inside a volume data set and deformed by an energy minimization algorithm to find the 3-D features in the data set. I first studied energy minimization techniques while I was a visiting research engineer at Fraunhofer Institute in Darmstadt, Germany, where I used them to automatically generate motion paths for computer animation.