Approximate Algebraic Methods in Computer Aided Geometric   Design
{'Code': '07030000', 'Directorate': {'Abbreviation': 'ENG', 'LongName': 'Directorate For Engineering'}, 'Division': {'Abbreviation': 'CMMI', 'LongName': 'Div Of Civil, Mechanical, & Manufact Inn'}}
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This research is to investigate fundamental algorithms for                 computer aided geometric design based on algebraic methods                      operating in a finite precision computing environment.  This                    proposal is motivated by the basic intersection problems in                     computer aided geometric design: curve-curve intersection,                      curve-surface intersection, and surface-surface intersection.                   The investigators plan to explore efficient and robust methods for              computing the points of intersection between two nonplanar rational             curves, the points of intersection between a rational curve and a               rational surface, and the curve of intersection between two rational            surface patches.  Several other basic and supporting problems will              also be addressed.  These problems include: finding a tight upper               bound on the number of intersection points between two non-planar               rational curves of known degrees, determining if a rational surface             patch is improperly parametrized, deciding how base points affect the           degree of a parametric patch in floating point arithmetic, and                  developing exact global and approximate local implicitization                   algorithms for rational surface patches.  The research will also                investigate numerically stable alternatives to Euclid's Greatest                Common Division algorithm for floating point arithmetic.                             This will also involve a combination of theoretical,                       empirical, and practical work.  The investigators plan first to                 develop the mathematical theory, then to test this theory on curves             and surfaces used in industrial applications, and finally to code the           algorithms into practical software.
{'FirstName': 'Thomas', 'LastName': 'Sederberg', 'PI_MID_INIT': 'W', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Thomas W Sederberg', 'EmailAddress': 'tom@cs.byu.edu', 'NSF_ID': '000381388', 'StartDate': '12/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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[{'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}, {'Code': '1463', 'Text': 'INTEGRATION ENGINEERING'}, {'Code': '4715', 'Text': 'COMPUTER SYSTEMS ARCHITECTURE'}]
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