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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 |
Important Terms: B-Spline - A piecewise polynomial function. A spline curve is expressed in terms of B-splines. It is easier to piece curves together using B-splines rather then Bezier curves because they use a set of blending functions that have local support only - the location of the curve depends on only a few control points. Contributors to B-spline development: Ahuja, Catmull and Rom, Clark, Coons, Cox, deBoor, Forest - 1970s. Beta-splines - a generalization of the uniform cubic B-Spline, developed by B. Barsky. at the University of California, Berkeley in 1981. Bezier Curves - polynomial curves expressed in terms of Berstein polynomials. Part of the UNISURF system developed by P. Bezier. Based on a family of functions called Bernstein polynomials. Polynomial Curves - includes Bezier Curves and .NURBs NURBs - Nonuniform rational B-spline curves Computer Aided Geometric Design (CAGD) - pioneered by P. de Casteljau (Citroen) and P. Bezier (Renault), auto designers in the 1960s. control points - a common way of controlling the shape of a curves in a predicable way piecewise - a function describing only a small piece of a curve rational polynomials - defined by the algebraic ratio of two polynomial functions. Developed by Rowin, Roberts, Coons, and Forrest in the 1960s. Surface Patches - the locus of all points of a moving or deforming curve. A surface is often broken down into patches.First developed by Coons. others - quadric surfaces, natural splines, Coons surfaces, etc. |
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