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Literature Review Art894x12 History of Computer Graphics Instructor: Wayne Carlson, Autumn Quarter 2000

     
 

Literature Review: Freeform Curves and Surfaces

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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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[ Literature Review: Free-form curves and surfaces ]