Applications of these technologies include the design and manufacture of car bodies, ship hulls, airplane wings, and a wide variety of mechanical components and assemblies. At the core of computer graphics and geometric design is the fundamental problem of defining, representing, and manipulating shape. As a result, the scope of computer graphics and geometric design is very broad. Related areas include automated design and manufacture, solid modeling, mesh generation, finite element analysis, computer animation, image and signal processing, computational geometry, computer vision, robotics, and scientific visualization. The Graphics and Geometric Design Group explores the fundamental mathematics associated with shape and applications of shape to areas such as those already discussed.
Piecewise polynomials are one of the most popular methods for representing shape.
One of the fundamental problems in visualization is creating a shape that interpolates observed data. Researchers in the group are investigating innovative techniques for creating such interpolating shapes. Multiresolution methods for representing shape. Most real-world shapes have a wealth of detail. Algorithms for manipulating such shapes are often overwhelmed by this detail.