Computer Graphics/Geometric Design Group

Overview

Scientists and engineers often model and analyze the physical world. Computer graphics and geometric design are vital tools in this task. Consider the problem of designing mechanical parts for industrial applications such as automobile manufacturing. Computer models are replacing physical models. They are cheaper to construct, easier to change, and simpler to analyze. They enable a broad range of automated technologies including finite element analysis, process planning, robotics, and computer controlled manufacturing. Computer simulations save industry both time and money, and computer analyses of geometric models lead to better and cheaper products. Applications of these technologies include the design and manufacture of car bodies, ship hulls, airplane wings, and a large variety of mechanical components and assemblies.

At the core 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.

Members

Research Areas

Led by Professor Goldman and Warren, the group explores the fundamental mathematics associated with shape and application of shape to areas such as those listed above. Their research effort currently focuses on following areas:

Computational mathematics of curves and surfaces

Piecewise polynomials are one of the most popular methods for representing shape. Members of the research group are currently investigating techniques such as NURBS (B-splines) and algebraic surfaces for use in geometric design.

Data visualization

One of the fundamental problems in visualization is creating a shape that interpolates observed data. Members of the group are investigating innovative techniques for creating such interpolating shapes.

Multi-resolution methods for representing shape

Most real-world shapes have a wealth of detail. Algorithms for manipulating such shapes are often overwhelmed by such detail. Researchers in the group are developing hierarchical methods based on wavelets for controlling the level of detail present in such shapes.

Applications of computer graphics and geometric design

Members of the research group are actively involved in collaborations with a wide range of scientists and engineers. Example collaborations include a method for automatic design of a prosthesis for total hip replacement, a visualization package for groundwater flow, and a geological modeling system for exploration and production of petrochemicals.

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