Computer Graphics/Geometric Design Group
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.
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:
Feel free to browse the individual home pages listed above
for selected references to these and other topics.
- 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
- 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