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| Jonathan Gladden Literature Review Art894x12 History of Computer Graphics Instructor: Wayne Carlson Autumn Quarter 2000 | ||||
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Literature Review: Freeform Curves and Surfaces page 1 - Introduction page 2 - B-Splines and Beta Splines page 3 - Important Terms page 4 - Bibliography page 5 - types of curves page 6 - patches of different resolutions page 7 - merging two patches page 8 - timeline Link to lists of works by the contributors to Curve and Suface Research > |
Introduction: Free-form curves and surfaces where developed to describe curved 3-D objects without using polyhedral representations which are bulky and intractable. To get a precise curve with polygons might require thousands of faces, whereas a curved surface requires much less calculations. The development of Free-form curves and surfaces for computer graphics begins late 60s with, P. de Casteljau (Citroen) and P. Bezier (Renault), engineers in the french auto industry. Bezier created the UNISURF CAD system for designing cars which utilized his curve theories. P. de CasteljauŐs research was earlier than Bezier, but was never published so Bezier get most of the credit. These men were pioneers in Computer Aided Geometric Design (CAGD) for the auto industry, which replaced the use of hand drawn french-curve templates in design of auto bodies. Bezier curves were based on Berstein Polynomials which had been developed by the mathematician Berstein much earlier. Another kind of basic curve predating the Bezier was the Hermite Curve developed by the mathematician C. Hermite. Also in the same era as Bezier, Schonenberg, a mathematician at the University of Wisconsin was working on Mathematical Splines, which would influence the work of S. Coons at MIT in Splines, Bicubic Surface Patches, Rational Polynomials around 1968. A surface patch is freeform curved surface defined by two or more curves. A. Forrest at MIT and Riesenfeld at Syracuse in 1973 based their research into Parametric B-Splines on CoonŐs work. The main difference between B-Splines and Bezier curves is the former allows for local control of key control points and the later has more of a global control system. B-Splines are also faster to calculate for a computer than cubic polynomial based curves like the Hermite and Bezier. RiesenfeldŐs pioneering development of B-Splines later influenced the E. CatmullŐs research at Utah. |
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