RESEARCH

Geometric Computing Initiative

We are exploring issues such as how techniques for solving problems can be discovered, improved, analyzed, and demonstrated to be correct or optimal. We expect to make leading contributions in computational geometry, geometric modeling, data structures, high-performance computing, I/O-efficiency for external memory, geographic information systems (GIS), biological computing, and data compression.

Because of the geometric nature of the physical world in which we live, geometric problems arise in any area that interacts with the physical world. Geometric computing focuses on designing, analyzing, and implementing efficient algorithms for geometric problems. The geometric computing group of the department is internationally renowned for its contributions to the fundamental problems in computational geometry, addressing massive data management issues in geometric problems, and applying geometric techniques to a variety of areas, including molecular biology, geometric modeling, robotics, geographic information systems, ecology, and photonics.

The group actively collaborates with other groups within the department and with the researchers in other departments at Duke. They collaborate with faculty in Mathematics, Biology, Biochemistry, Electrical and Computer Engineering, and the Nicholas School of Environment. Beyond Duke, the group also collaborates with researchers at various top institutes. Because of its depth and breadth, the geometric computing group at Duke is arguably the top geometric computing group in the nation.

Geometric computing research at Duke works under the common rationalization of the field of computational geometry, often given in the past, that the world around us is three-dimensional and questions how things in this world relate to each other are inherently geometric. Take moving a piano through a door-frame and planning a flight-path that avoids collisions with other airplanes as two examples. It should therefore not surprise that computing properties about these geometric things and their interaction are common-place and important. While this is still a valid argument, we would like to amend that most of the geometric questions people concern themselves with have to do with how things are connected. It is important that highways are sufficiently straight and smooth to support the driving of fast cars, but another essential property, which we usually take for granted, is that highways are continuous, indeed connecting A to B, and not just approximately. The corresponding subfield of computational geometry is often referred to as computational topology. A good portion of our efforts may be classified to belong to this subfield and are driven by applications in a variety of other fields, the prediction of the structure of folded proteins and the reconstruction of human organs being two. The hallmark of our work is fast algorithms that implement mathematical models to offer insights into and answers to such questions.