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This
project describes an algorithm for maintaining an approximating triangulation
of a deforming surface in three-dimensional space. The surface is the
envelope of an infinite family of spheres defined and controlled by a
finite collection of weighted points. The triangulation adapts dynamically
to changing shape, curvature, and topology of the surface. We plan to
take the results of this work into various directions: - incorporation
into the Alpha Shapes molecular geometry library as a standard molecular
surface representation, - exploiting the high quality meshing produced
by the algorithm for numerical computations on the surface, - simulating
proteins in motion and track their motion by monitoring basic topological
and geometric properties.
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