Research Areas
Computer Graphics, Scientific Visualization, Geometric Modeling and Processing, and Computational Topology.

Research Description
I am interested in understanding how the geometry and topology of shapes affect the way we interact with them. For instance, figuring out the direction "North" is a relatively easy task everywhere on the Earth except at the South Pole where every direction is "North," and the North Pole, where you cannot go "North" from there. These points are so-called "singularities" and their appearances gives us some idea about the topology of the surface, i.e., how the surface is inner-connected. Geometry also plays an important role, such as curvature.

Application-dependent shape analysis is very important in Computer Graphics and Scientific Visualization. My research in this area has focused on feature-based surface parameterization and texture mapping, and visibility-guided simplification. In surface parameterization (building a "world map" for a curved surface, such as the Earth), one is concerned with minimizing distortion (Canada looks much bigger than the US) and discontinuity (Russia is split into two pieces, one on each side of the map). For an arbitrary surface, this problem becomes even more difficult. My algorithm minimizes distortion by dividing the surface based on its features (protrusions), which results in little distortion with relatively few "seams."

Vector field synthesis on a 3D surface is also an interesting problem. In one of my previous work, I built a system that lets a user design a vector field on an arbitrary surface. Such a tool is useful for not only graphics applications, such as texture synthesis and non-photorealistic rendering, but also teaching vector analysis. Extending this work further is still an ongoing research area.