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On convex Bézier triangles

H. Prautzsch

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1992)

  • Volume: 26, Issue: 1, page 23-36
  • ISSN: 0764-583X

How to cite

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Prautzsch, H.. "On convex Bézier triangles." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 26.1 (1992): 23-36. <http://eudml.org/doc/193657>.

@article{Prautzsch1992,
author = {Prautzsch, H.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {convexity; triangular Bézier nets},
language = {eng},
number = {1},
pages = {23-36},
publisher = {Dunod},
title = {On convex Bézier triangles},
url = {http://eudml.org/doc/193657},
volume = {26},
year = {1992},
}

TY - JOUR
AU - Prautzsch, H.
TI - On convex Bézier triangles
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1992
PB - Dunod
VL - 26
IS - 1
SP - 23
EP - 36
LA - eng
KW - convexity; triangular Bézier nets
UR - http://eudml.org/doc/193657
ER -

References

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  1. [1] G. CHANG and P. DAVIS, The convexity of Bernstein polynomials over triangles, J. Approx. Theory 40, (1984), 11-28. Zbl0528.41005MR728296
  2. [2] G. CHANG and Y. FENG, A new proof for the convexity of the Bernstein - Bézier surfaces over triangles, Chinese Ann. Math, Ser., B6 (2), (1985), 172-176. Zbl0575.41010MR841865
  3. [3] G. CHANG and J. HOSCHEK, Convergence of Bézier triangular nets and a theorem by Pólya, J. Approx. Theory, Vol. 58, N°. 3, (1989), 247-258. Zbl0724.41005MR1012674
  4. [4] W. BOEHM, G. FARIN and J. KAHMANN, A survey of curve and surface methods in CAGD, Comput. Aided Geom. Design 1, (1984), 1-60. Zbl0604.65005
  5. [5] W. DAHMEN and C. A. MICCHELLI, Subdivision algoritmus for the génération of box simple surfaces, Compt. Aided Geom. Desing 1, (1984), 115-129. Zbl0581.65011MR1230249
  6. [6] W. DAHMEN and C. A. MICCHELLI, Convexity of multivariate Bernstein polynomials and box spline surfaces, Studia Sci. Math. Hungar. 23, (1988), 265-287. Zbl0689.41013MR962457
  7. [7] G. FARIN, Triangular Bernstein-Bézier patches, Comput. Aided Geom. Design, Vol. 3, Number 2, (1986), 83-127. MR867116
  8. [8] T. N. T. GOODMAN, Convexity of Bézier nets on triangulations, to appear in Comput. Aided Geom. Design. Zbl0731.41009MR1107853
  9. [9] T. A. GRANDINE, On convexity of piecewise polynomial functions on triangulations, Comput. Aided Geom. Design 6, (1989), 181-187. Zbl0675.41029MR1019422
  10. [10] J. A. GREGORY and J. ZHOU, Convexity of Bézier nets on sub-triangles, Technical Report 04/90, Brunel University, Dept. of Math. and Statistics, March (1990). Zbl0756.41026MR1122914
  11. [11] S. L. LEE and G. M. PHILLIPS, Convexity of Bernstein Polynomials on the standard triangle, preprint. 
  12. [12] C. A. MICCHELLI, H. PRAUTZSCH, Computing surfaces invariant under subdivision, Comput. Aided Geom. Design 4, (1987), 321-328. Zbl0646.65013MR937370
  13. [13] H. PRAUTZSCH, Unterteilungsalgorithmen für multivariate Splines - Ein geometrischer Zugang, Diss., TU Braunschweig (1983/84). Zbl0647.41015

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