Topics in Computational Geometry:  Curved Objects,          Restricted-Orientation Objects, Grasping, and Arrangements
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{'SignBlockName': 'Krishna M. Kavi', 'PO_EMAI': None, 'PO_PHON': None}
Professor Souvaine will examine results in both rectilinear geometry            and general geometry to determine which of the former can be                    efficiently generalized and which of the latter benefit from a                  restriction to k orientations.  Many robot hands consist of two                 parallel edges that can move closer together or further apart.                  Professor Souvaine conjectures that all polygons admit a stable grip in         this model.  She proved the conjecture and provided linear time                 algorithms for special classes of polygons.  The goal of this research          is to prove the conjecture in full generality and then to study the             corresponding problems for polyhedra and curved objects.  In 2                  dimensions, the least median of squares regression line (LMS) can be            computed efficiently. Replacing the standard vertical line sweep with a         topological line sweep results in a faster algorithm.  The goals are to         discover techniques for computing multidimensional LMS and dynamic LMS          and to determine which problems benefit from topological sweep.
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[{'Code': '286000', 'Text': 'THEORY OF COMPUTING'}, {'Code': '912000', 'Text': 'CROSS-DIRECTORATE PROGRAMS'}]
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