Algebraic Splines for Molecular Modeling

Saturday, June 2, 2007 - 9:00am - 9:50am
EE/CS 3-180
Chandrajit Bajaj (The University of Texas at Austin)
This talk shall describe a survey of algebraic spline
(A-spline and A-patch)
construction techniques for capturing molecular surfaces and implicit solvation
shells (models for molecules in their watery environment). These molecular
surfaces are obtained from either atomic 3D coordinates (scattered data) of the
molecule, or segmented 3D electron microscopy maps (dense data). For 3D maps at
5- 20 Angstrom resolution, I shall also present algebraic spline algorithms to
detect and represent secondary (helices, sheets) and/or tertiary (sandwiches,
barrels, etc.) structural molecular models. For these latter algorithms, we
employ techniques from computational algebraic geometry and differential
topology, especially the computation of stable/unstable manifolds of certain
critical points of distance functions of molecular surface boundaries.