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<DT>Some specific ongoing projects include:
<P>
<DT><B>Geometric Modeling:</B>

<DD>Ability to create,  convert between, and to maintain consistency of
distinct  representations  of  mechanical parts is  a major technological
barrier  that undermines  the usefulness  and reliability of commercial
geometric modeling systems.  Current research efforts focus on eliminating
ambiguity in communicating engineering specifications, formal modeling of
parametric families of mechanical parts, and investigating novel methods
and computational techniques in support of design and manufacturing.
<P>
<DT><B>Mechanical Design:</B>

<DD>Today mechanical forms, functions, and fabrication processes cannot be
described combinatorially, in terms of discrete, simple, and  interacting
primitives;  this apparent lack of  combinatorial structure is a
major roadblock for competitive design and manufacturing of mechanical systems.
In collaboration with industry, the present research deals with
theoretical, practical, and computational aspects of  mechanical design
and seeks to establish a formal basis for making mechanical design and
manufacturing of parts more systematic and competitive,  and for smooth
integration of mechanical form modeling with other engineering activities.
<P>
<DT><B>Physical Modeling:</B>

<DD>Geometric models contain only part of the information needed to capture the
desired physical behavior of an artifact, and the processes used to
manufacture it. Recent  study of algebraic topological models (so called
"chain models") of physical behavior suggests that it may be possible to
unify physical and geometric modeling  and thus facilitate development of
new  computer-aided engineering tools.   Current investigations use these
and other models of physical behavior to develop new  engineering languages
and computer algorithms for systematic  specification,  modeling,
simulation, and analysis of physical
objects and systems.
<P>
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