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Issue No.06 - June (1986 vol.6)
pp: 52-59
Thomas Sederberg , Brigham Young University
Ronald Goldman , Control Data Corporation
ABSTRACT
Classical algebraic geometry has been virtually ignored in computer-aided geometric design. However, because it deals strictly with algorithms, it is really more suited to this field than is modern algebraic geometry, which introduces abstractions far removed from the algorithmic nature of computer-aided design. This tutorial examines resultants, curve implicitization, curve inversion, and curve intersection. Discussion follows a series of examples simple enough for those with only a modest algebra background to follow.
INDEX TERMS
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CITATION
Thomas Sederberg, Ronald Goldman, "Algebraic Geometry for Computer-Aided Geometric Design", IEEE Computer Graphics and Applications, vol.6, no. 6, pp. 52-59, June 1986, doi:10.1109/MCG.1986.276742
REFERENCES
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10. T.W.Sederberg, "Implicit and Parametric Curves and Surfaces for Computer-Aided Geometric Design," 1983
11. T.W.Sederberg, D.C.Anderson, and R.N.Goldman, "Implicit Representation of Parametric Curves and Surfaces," Computer Vision, Graphics and Image Processing Vol. 28, pp. 72-84 1984
12. J.Kajiya, "Ray Tracing Parametric Patches," Computer Graphics Vol. 16, No. 3, pp. 245-254 Mar. 1982
13. Y. deMontaudouin and W.Tiller, "The Cayley Method in Computer-Aided Geometric Design," Computer Aided Geometric Design Vol. 1, No. 4, pp. 309-326 Dec. 1984
14. R.N.Goldman, T.W.Sederberg, and D.C.Anderson, "Vector Elimination: A Technique for the Implicitization, Inversion, and Intersection of Planar Parametric Rational Polynomial Curves," Computer Aided Geometric Design Vol. 1, No. 4, pp. 327-356 Dec. 1984
15. T.W.Sederberg, R.N.Goldman, and D.C.Anderson, Implicitization, Inversion and Intersection of Rational Cubic Curves," Computer Vision, Graphics and Image Processing Vol. 31, pp. 89-102 1985
16. T.W.Sederberg and S.Parry, Computer Aided Design , (to appear)
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