Research Article
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Year 2011, Volume 4, Issue 2, 63 - 84, 30.10.2011

Abstract

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).

GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES

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

Abstract



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).

Details

Primary Language English
Journal Section Research Article
Authors

Gudrun ALBRECHT This is me

Publication Date October 30, 2011
Published in Issue Year 2011, Volume 4, Issue 2

Cite

Bibtex @research article { iejg599490, journal = {International Electronic Journal of Geometry}, eissn = {1307-5624}, address = {}, publisher = {Kazım İLARSLAN}, year = {2011}, volume = {4}, number = {2}, pages = {63 - 84}, title = {GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES}, key = {cite}, author = {Albrecht, Gudrun} }
APA Albrecht, G. (2011). GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES . International Electronic Journal of Geometry , 4 (2) , 63-84 . Retrieved from https://dergipark.org.tr/en/pub/iejg/issue/47488/599490
MLA Albrecht, G. "GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES" . International Electronic Journal of Geometry 4 (2011 ): 63-84 <https://dergipark.org.tr/en/pub/iejg/issue/47488/599490>
Chicago Albrecht, G. "GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES". International Electronic Journal of Geometry 4 (2011 ): 63-84
RIS TY - JOUR T1 - GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES AU - GudrunAlbrecht Y1 - 2011 PY - 2011 N1 - DO - T2 - International Electronic Journal of Geometry JF - Journal JO - JOR SP - 63 EP - 84 VL - 4 IS - 2 SN - -1307-5624 M3 - UR - Y2 - 2022 ER -
EndNote %0 International Electronic Journal of Geometry GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES %A Gudrun Albrecht %T GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES %D 2011 %J International Electronic Journal of Geometry %P -1307-5624 %V 4 %N 2 %R %U
ISNAD Albrecht, Gudrun . "GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES". International Electronic Journal of Geometry 4 / 2 (October 2011): 63-84 .
AMA Albrecht G. GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES. Int. Electron. J. Geom.. 2011; 4(2): 63-84.
Vancouver Albrecht G. GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES. International Electronic Journal of Geometry. 2011; 4(2): 63-84.
IEEE G. Albrecht , "GEOMETRIC INVARIANTS OF PARAMETRIC TRIANGULAR QUADRIC PATCHES", International Electronic Journal of Geometry, vol. 4, no. 2, pp. 63-84, Oct. 2011