Mathematical Sciences: Multivariate Splines
{'Code': '03040109', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Alvin I. Thaler', 'PO_EMAI': None, 'PO_PHON': None}
This project aims at solving the outstanding problem of the                dimension and basis for the multivariate spline spaces and                      applying the results to the most effective surface interpolation                and computer representation of three dimensional objects via                    computer graphics.  The structure of multivariate spline spaces                 is vastly more complex than in the univariate case and                          fundamental questions are still unanswered.  Among these                        questions are the dimension, the construction of bases, existence               of a local basis, and application to interpolation problems.  The               main tool of this research will be the symbolic manipulation                    language "Reduce", which will enable the investigator to solve                  exactly the large linear systems that arise from the smoothness                 conditions linking polynomials on neighboring triangles.  The                   investigator will blend the Bezier-Bernstein techniques with the                symbolic manipulation and will attempt to apply his results to                  surface representation problems arising in engineering.
{'FirstName': 'Peter', 'LastName': 'Alfeld', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Peter Alfeld', 'EmailAddress': None, 'NSF_ID': '000457047', 'StartDate': '09/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Utah', 'CityName': 'SALT LAKE CITY', 'ZipCode': '841129049', 'PhoneNumber': '8015816903', 'StreetAddress': '201 PRESIDENTS CIR', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Utah', 'StateCode': 'UT', 'CONGRESSDISTRICT': '01', 'CONGRESS_DISTRICT_ORG': 'UT01', 'ORG_UEI_NUM': 'LL8GLEVH6MG3', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF UTAH', 'ORG_PRNT_UEI_NUM': None}
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[{'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}, {'Code': '1463', 'Text': 'INTEGRATION ENGINEERING'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8701121.xml'}