My research is in the area of computer graphics.  More specifically, I
work on Computer Aided Geometric Design (CAGD), which is the study of
issues related to curves and surfaces, including both mathematical and
modeling problems.  My research contributions have been primarily in
three areas of CAGD.

Recently, I have begun investigating surface pasting, an approximation
technique for adding details to a base surface.  This is joint work
with Richard Bartels.  Together with our students, we are investigating
topics such as using quasi-interpolation to improving the
approximation; pasting cylinders on surfaces; direct manipulation of
pasted surfaces; and issues related to the animation of pasted
surfaces.

My second area of research is surface fitting.  My goal here is to find
local parametric schemes that create surfaces with good shape.  I began
this work as part of my doctoral studies, when I surveyed a large
number of previously published tangent-plane-continuous surface
interpolation techniques and found them all to be inadequate.  My
research showed that tangent plane continuity (the common definition
for surface patches to appear visually to meet ``smoothly'') was
neither necessary nor sufficient, and for my dissertation, I devised a
scheme that was not tangent plane continuous but resulted in smoother
looking surfaces.  Since completing my Ph.D., I have used local
optimization techniques to improve surface quality.  More recently, I
found a local method that gives substantial improvement without using
optimization.

My third area of contribution is in devising efficient CAGD
algorithms.  While the mathematics of many CAGD problems is clear,
devising efficient algorithms to work with the representations commonly
used in CAGD is more problematic.  Again, I began this work while I was
a graduate student.  I developed an efficient algorithm for polynomial
composition.  Since graduation, I have continued my work on algorithm
development, devising a fast method for evaluating a surface for both
position and normal, and finding an optimal polynomial composition
algorithm.  While Wayne Liu was my student, he developed an efficient
algorithm for degree raising B-splines.

In addition, I have done research in other areas
of computer graphics, including radiosity, 3D user interfaces, and cone
tracing, and have published two papers and one technical report on this
work.