An Investigation on Surface-to-Surface Intersection Problems
{'Code': '07030000', 'Directorate': {'Abbreviation': 'ENG', 'LongName': 'Directorate For Engineering'}, 'Division': {'Abbreviation': 'CMMI', 'LongName': 'Div Of Civil, Mechanical, & Manufact Inn'}}
{'SignBlockName': None}
The objective of this work is to investigate a new method to               discover and describe all features of an unknown algebraic curve                resulting in the context of surface to surface intersections.  Our              method involves symbolic derivation of the equation of the curve,               using algebraic geometry techniques, and its representation in the              Bernstein basis within a rectangular window, which allows piecewise             representation and provides geometrical significance to the                     underlying coefficients.  Novel methods to compute the                          characteristic points of the curve, useful in guaranteeing correct              topology, are proposed.  These are based on symbolic computation,               adaptive methods for large scale series summation, to enhance                   accuracy, and minimization techniques.  Interrogation of the curve,             based on non-uniform adaptive subdivision, and derivation of point              and parametric approximations of the implicit curve, with prescribed            distance errors, based on the properties of the Bernstein                       representation, are also proposed for study.  The significance of               the proposed work is that it promises to provide a robust surface to            surface intersection capability, which is necessary in a more                   automated mode of design, analysis and manufacturing of complex                 artifacts.  Many elements of our technique are also parallelizable              which is an important attribute for real time large scale                       applications.
{'FirstName': 'Nicholas', 'LastName': 'Patrikalakis', 'EmailAddress': 'nmp@mit.edu', 'StartDate': '02/01/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Massachusetts Institute of Technology', 'CityName': 'Cambridge', 'ZipCode': '021394301', 'PhoneNumber': '6172531000', 'StreetAddress': '77 MASSACHUSETTS AVE', 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA'}
{'Code': '1463', 'Text': 'INTEGRATION ENGINEERING'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8720720.xml'}