Abstract
Many fields in the computational science area need descriptions of complex objects: virtual reality, computational graphics, geometric modeling, computeraided geometric design (CAGD). These descriptions are commonly obtained using basic elements: points, curves, surfaces, and volumes. Elementary tools used to handle these elements are mathematical functions such as polynomials and rational functions, which allow easy graphical representation in many situations: union of objects, intersection, complement.
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Chapter References
P. Bézier, Courbes et Surfaces, Mathématiques et CAO, vol 4, Hermes, Paris, 1986.
P. de Casteljau, Formes à Pôles, Mathématiques et CAO, vol 2, Harmes, Paris, 1985.
S.A. Coons, Surface Patches and B-splines Curves, CAGD, 1974.
G. Farin and D. Hansford, The Essentials of CAGD, AK Peters, 2000.
G. Farin, Curves and Surfaces for CAGD: A Practical Guide, Academic Press 4th ed. New York, 1996.
J. Fèrguson, Multivariable Curve Interpolation, Journal of the Association for Computing Machinery, 1964.
J. Hoschek and D. Lasser, Fundamentals of Computer Aided Geometric Design, Peters, Massachusetts, 1997.
L. Piegl and W. Tiller, The NURBS Book, Springer, Berlin, 1995.
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(2007). Geometrical Design: Bézier Curves and Surfaces. In: Danaila, I., Joly, P., Kaber, S.M., Postel, M. (eds) An Introduction to Scientific Computing. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49159-2_9
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DOI: https://doi.org/10.1007/978-0-387-49159-2_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-30889-0
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