A Description and Evaluation of Various 3D Models
Parametric curves and surfaces have been defined for a long time in mathematics, and used extensively in engineering and more recently in computer aided design. In computer graphics outside of CAD, they have been used from simple object models with a few patches to 3-D animation models with several hundred patches.
In spite of all this activity, they still look a little forbidding to most people in computer graphics. This paper attempts to address this problem by describing the motivations, properties and references for the most common types of parametric curves and surfaces.
KeywordsComputer Graphic Bernstein Polynomial Spline Curve Bezier Curve Control Polygon
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- 2.Brian A. Barsky, “A Study of the Parametric Uniform B-spline Curve and Surface Representations.” In preparation.Google Scholar
- 3.Brian A. Barsky, “Algorithms for the Evaluation and Perturbation of Beta-splines.” Submitted for publication.Google Scholar
- 4.Brian A. Barsky, “The Beta-spline: A Curve and Surface Representation for Computer Graphics and Computer Aided Geometric Design.” Submitted for publication.Google Scholar
- 5.Brian A. Barsky, The Beta-spline: A Local Representation Based on Shape Parameters and fundamental Geometric Measures, Ph.D. Thesis, University of Utah, Salt Lake City, Utah (December, 1981).Google Scholar
- 10.Pierre E. Bezier, “Mathematical and Practical Possibilities of UNISURF,” in Computer Aided Geometric Design, ed. Barnhill, Robert E. and Riesenfeld, Richard F., Academic Press, New York (1974).Google Scholar
- 11.Pierre E. Bezier, Essai de definition numerique des courbes et des surfaces experimentales, Ph.D. Thesis, l’Universite Pierre et Marie Curie, Paris (February, 1977).Google Scholar
- 13.Steven A. Coons, Surfaces for Computer Aided Design, Technical Report, Design Division, Mech. Engin. Dept., M.I.T., Cambridge, Massachusetts (1964).Google Scholar
- 14.Steven A. Coons, Surfaces for Computer-Aided Design of Space Forms, Technical Report no. MAC-TR-41, Project MAC, M.I.T., Cambridge, Massachusetts (June, 1967). Available as AD-663 504 from NTIS, Springfield, Virginia.Google Scholar
- 15.Steven A Coons, “Surface Patches and B-spline Curves,” pp. 1–16 in Computer Aided Geometric Design, ed. Barnhill, Robert E. and Riesenfeld, Richard F., Academic Press, New York (1974).Google Scholar
- 16.H. B. Curry and I. J. Schoenberg, “On Spline Distributions and their Limits: The Polya Distribution Functions, Abstract 380t,” Bulletin of the American Mathematical Society 53 p. 1114 (1947).Google Scholar