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Parametric representation of quadric surfaces. (English) Zbl 0766.65011

This brief well-illustrated paper deals with the parametric representation of quadrics from a geometric point of view. The authors consider several cases where triangular and quadrangular quadratic Bézier patches represent quadrics, which are used in geometric modeling.
A detailed discussion may be found in the first authors’ paper [NURBS for curve and surface design, Collect. Pap. SIAM Conf. Geom. Des., Tempe/AZ(USA) 1990, 1-14 (1991; Zbl 0760.68087)].
Reviewer: G.L.Litvinov

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)

Citations:

Zbl 0760.68087
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References:

[1] W. BOEHM, On Cubics : A Survey. Comput. Graph. Image Process. 19 (1982) pp. 201-226. Zbl0534.65095 · Zbl 0534.65095
[2] W. BOEHM, G. FARIN and J. KAHMANN, A survey of curve and surface methods in CAGD. Comput. Aided Geom. Design, 1 (1984) pp. 1-60. Zbl0604.65005 · Zbl 0604.65005
[3] W. BOEHM and D. HANSFORD, Bézier Patches on Quadrics, in G. Farin, editor, NURBS for Curve and Surface Design, SIAM, Philadelphia (1991) pp. 1-14. Zbl0760.68087 MR1133460 · Zbl 0760.68087
[4] G. FARIN, Curves and Surfaces for Computer Aided Geometric Design. Academic Press, 1988, 2nd Edition 1990. Zbl0694.68004 MR974109 · Zbl 0694.68004
[5] G. FARIN, B. PIPER and A. WORSEY, The octant of a sphere as a non-degenerate triangular Bézier patch. Comput. Aided Geom. Design, 4 (1987) pp. 329-332. Zbl0646.41011 MR937371 · Zbl 0646.41011
[6] G. GEISE and U. LANGBECKER, Finite quadrics segments with four conic boundary curves. Comput. Aided Geom. Design 7 (1990) pp. 141-150. Zbl0716.65012 MR1074604 · Zbl 0716.65012
[7] E. LEE, The rational Bézier representation for conics, in G. Farin, editor, Geometric Modeling : Algorithms and New Trends, SIAM, Philadelphia (1987) pp. 3-19. MR936441
[8] J. NIEBUHR, B-patches on Quadrics. Dissertation TU Braunschweig, to be published in 1991 (in German).
[9] T. SEDERBERG, Implicit curves and surfaces. Ph. D. Thesis, Purdue, 1983.
[10] T. SEDERBERG and D. ANDERSON, Steiner surface patches. IEEE CG&A, May (1985).
[11] D. STRUIK, Lectures on Analytic and Projective Geometry. Addison-Wesley, 1953. Zbl0053.28701 MR57552 · Zbl 0053.28701
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