Computer-Aided Geometric Design and Computational Geometry  of Geometric Constructs Defined by Line Geometry
{'Code': '07030000', 'Directorate': {'Abbreviation': 'ENG', 'LongName': 'Directorate For Engineering'}, 'Division': {'Abbreviation': 'CMMI', 'LongName': 'Div Of Civil, Mechanical, & Manufact Inn'}}
{'SignBlockName': 'Bruce Kramer', 'PO_EMAI': 'bkramer@nsf.gov', 'PO_PHON': '7032925348'}
Most computer-aided design systems define surfaces as doubly               infinite families of points.  Using point geometry allows only two              geometric constructs: curves and surfaces.  Using lines as the basic            building block of space is more flexible for shape generation and               design since line geometry allows the definition of three types of              geometric constructions.  This research focuses on the development              of the mathematical foundation for computer-aided design of products            based online geometry.  The fundamental idea is to use lines, rather            thanpoints, as the fundamental building block of geometric shapes.              The three geometric constructs defined in a line geometry are ruled             surfaces, line congruences, and line complexes which are one, two,              and three parameter families of lines respectively.  This research              will study the computational geometry of these three geometric                  constructs and,in addition, develop a general framework for                     computer-aided design based on line geometry.
{'FirstName': 'Bahram', 'LastName': 'Ravani', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Bahram Ravani', 'EmailAddress': 'bravani@ucdavis.edu', 'NSF_ID': '000359855', 'StartDate': '06/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Wisconsin-Madison', 'CityName': 'MADISON', 'ZipCode': '537151218', 'PhoneNumber': '6082623822', 'StreetAddress': '21 N PARK ST STE 6301', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Wisconsin', 'StateCode': 'WI', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'WI02', 'ORG_UEI_NUM': 'LCLSJAGTNZQ7', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF WISCONSIN SYSTEM', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1463', 'Text': 'INTEGRATION ENGINEERING'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1986&All=true', 'xml': '8619165.xml'}