GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES

Year 2011, Volume: 4 Issue: 2, 63 - 84, 30.10.2011

Gudrun Albrecht

Abstract

Keywords

rational triangular quadratic Bézier patch, quadric, geometric invariants, quadric’s axes

References

• [1] Albrecht, G., A note on Farin points for rational triangular Bézier patches, Comput. Aided Geom. Design 12, 507–512 (1995).
• [2] Albrecht, G., A geometrical design handle for rational triangular Bézier patches, in The Mathematics of Surfaces VII (T. Goodman, R. Martin, eds.), Information Geometers Ltd., Winchester UK, 161–171 (1997).
• [3] Albrecht, G., Determination and classification of triangular quadric patches, Comput. Aided Geom. Design 15, 675–697 (1998).
• [4] Albrecht, G.,A Practical Classification Method for Rational Quadratic Bézier Triangles with Respect to Quadrics, in Mathematical Methods for Curves and Surfaces II, (M. Dæhlen, T. Lyche, L. L. Schumaker, eds.), VanderbiltUniv. Press, Nashville TN, 1–8 (1998).
• [5] Albrecht, G., Rational Triangular B´ezier Surfaces — Theory and Applications, Shaker Verlag (1999).
• [6] Albrecht, G., An Algorithm for Parametric Quadric Patch Construction, Computing, 72, 1–12, (2004).
• [7] Boehm, W. and Hansford, D., Bézier Patches on Quadrics, in NURBS for Curve and Surface Design (G. Farin, ed.) SIAM, Philadelphia, 1–14, (1991).
• [8] Boehm, W. and Hansford, D., Parametric representation of quadric surfaces, in Math. Modelling and Num. Analysis 26, No. 1, 191–200 (1992).
• [9] Coffman, A., Schwartz, A.J. and Stanton, Ch., The algebra and geometry of Steiner and other quadratically parametrizable surfaces, Comput. Aided Geom. Design 13, 257–286 (1996).
• [10] Degen, W.L.F., The types of triangular Bézier surfaces, in The Mathematics of Surfaces VI (G. Mullineux, ed.), The IMA Conference Series No. 58, Clarendon Press Oxford, 153–170 (1996).
• [11] Farin, G., Curves and Surfaces for Computer Aided Geometric Design, Academic Press Inc., Boston (1990).
• [12] Gregory, J., N –sided surface patches, in The Mathematics of Surfaces, (J. Gregory, ed.), Clarendon Press, Oxford, 217–232 (1986).
• [13] Hagen, H., Nielson, G. and Nakajima, Y., Surface design using triangular patches, Comput. Aided Geom. Design 13, 895–904 (1996).
• [14] Joe, B. and Wang, W.P., Reparametrization of rational triangular Bézier surfaces, Comput. Aided Geom. Design 11, No. 4, 345–361 (1994).
• [15] Karciauskas, K., Quadratic Triangular Bézier Patches on Quadrics, Preprint (1997).
• [16] Kmetová, M., Rational quadratic B´ezier triangles on quadrics, Acta Mathematica 2, Faculty of Natural Sciences, University of Education, Nitra, Slovakia, 97–104 (1995).
• [17] Lü, W., Rational parametrization of quadrics and their offsets, Computing, 57(2), 135–147 (1996).
• [18] Niebuhr, J., Eigenschaften der Darstellung insbesondere degenerierter Quadriken mittels Dreiecks–B´ezier–Fl¨achen, Diss. Universit¨at Braunschweig (1992).
• [19] Pascal, E.,Repertorium der höheren Mathematik, 2. Band (Geometrie), Teubner, Stuttgart (1910/1922).
• [20] Sanchez-Reyes, J. and Paluszny, M., Weighted radial displacement: A geometric look at Bézier conics and quadrics, Comput. Aided Geom. Design , 17(3), 267–289 (2000).
• [21] Sederberg, T. W. and Anderson, D. C., Steiner Surface Patches, IEEE Computer Graphics and Applications, 23–36 (May 1985).
• [22] Theisel, H., Using Farin points for rational Bézier surfaces, Comput. Aided Geom. Design 16, 817–835 (1999).
• [23] Vaisman, I., Analytical Geometry, Series on University Mathematics Volume 8, World Scientific (1997).
• [24] Varady, T., Survey and new results in n–sided patch generation, in The Mathematics of Surfaces II, (R. Martin, ed.), Oxford Univ. Press, Oxford, 203–235 (1987).