Journal of Computer Science and Technology

, Volume 6, Issue 4, pp 383–388 | Cite as

The geometric continuity of rational Bézier triangular surfaces

  • Tian Jie 
Regular Papers


The problems of geometric continuity for rational Bézier surfaces are discussed. Concise conditions of first order and second order geometric continuity for rational triangular Bézier surfaces are given. Meanwhile, a geometric condition for smoothness between adjacent rational Bézier surfaces and the transformation formulae between rational triangular patches and rational rectangular patches are obtained.


Geometric Condition Rational Surface Transformation Formula Rectangular Patch Triangular Patch 
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  1. [1]
    Böehm, W., Farin, G. and Kahmann, J., A survey of curve and surface methods in CAGD.Computer Aided Geometric Design,1:1(1984), 1–60.CrossRefGoogle Scholar
  2. [2]
    Farin, G., Triangular Bernstein-Bézier patches.Computer Aided Geometric Design,3: 2(1986), 83–127.CrossRefMathSciNetGoogle Scholar
  3. [3]
    Tiller, W., RationalB-splines for curve and surface representation.IEEE Computer Graphices & Appl.,3: 9 (1983), 61–69.CrossRefGoogle Scholar
  4. [4]
    Tian, J., Geometric properties of rational Bézier surfaces over triangles.Pure and Applied Mathematics,4: 1 (1988), 66–76.MATHGoogle Scholar
  5. [5]
    Herron, G., Techniques for visual continuity. InGeometric modeling algorithms and new trends SIAM, Farin, G., ed., Philadelphia, PA, USA, 1987.Google Scholar
  6. [6]
    kahmann, J., Continuity of curvature between adjacent Bézier patches. InSurfaces in CAGD, Barnhill, G. E. and Böehm, W., eds., North-Holland, Amsterdam, 1983, 65–75.Google Scholar
  7. [7]
    Brueckner, I., Construction of Bézier points of quadrilaterals from those of triangles,Computer Aided Design,12: 1(1980), 21–24.CrossRefGoogle Scholar
  8. [8]
    Goldman, R. N. and Daniel J, Filip., Conversion from Bézier rectangles to Bézier triangles.Computer Aided Design,19: 1 (1987), 25–27.MATHCrossRefGoogle Scholar

Copyright information

© Science Press, Beijing China and Allerton Press Inc. 1991

Authors and Affiliations

  • Tian Jie 
    • 1
  1. 1.National Laboratory of Pattern Recognition, Institute of AutomationAcademia SinicaBeijing

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