Presidential Young Investigator Award: 2-D and 3-D Interactive Computer Modeling Systems

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A research program in interactive computer modeling is being initiated. This research concentrates on mathematical techniques for curve and surface representation and their implementation in geometric modeling systems. Many theoretical and practical issues are explored, including allowing local shape parameters, generalizing in higher degree, determining divided-difference formulas, deriving recurrence relations, developing subdivision techniques, and designing rendering algorithms. Research in all these topics uses symbolic computation tools such as Vaxima to handle the formal calculations. This work is pursued both for its intrinsic mathematical interest and its potential use in computer graphics and computer-aided geometric design. It is hoped that studying the mathematical theory in response to the needs of the application area will engender a better fundamental understanding and provide useful techniques in the fields of computer graphics and computer-aided geometric design.