Subareas: Geometric Modeling and Computation, Solid Modeling

In our research we look for fast algorithms for problems from physically-based simulation, robot motion planning, CAD/CAM, and virtual prototyping: problems include collision and interference detection, collision-free path computation, motion planning, and computing Boolean operations and offsets. We also investigate frameworks to ensure that algorithms are robust to numerical error and to test geometric consistency for applications across the length scales: from molecular modeling to geographic information systems. By studying geometric problems in an abstract setting, we learn techniques that can be applied in many application domains.