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Minkowski geometric algebra of complex sets
PDE & Applied Mathematics| Speaker: | Rida Farouki, UC Davis |
| Location: | 1147 MSB |
| Start time: | Thu, Jan 31 2008, 11:00AM |
Description
Algebraic operations on sets of complex numbers produce
remarkably rich geometrical structures, with diverse applications and
connections to science and engineering. For "simple" operands, such as
circular disks, precise descriptions of their algebraic combinations are
available in terms of the Cartesian and Cassini ovals, and higher-order
generalizations. Algorithms can be formulated to approximate algebraic
operations on complex sets
with general (piecewise-smooth) boundaries to a given precision. This
"Minkowski algebra of complex sets" is the natural extension
of (real) interval arithmetic to sets of complex numbers. It provides a
versatile two-dimensional "shape operator" language,
with connections to mathematical morphology, geometrical optics,
and stability analysis of dynamic systems.