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Abstract: Bivariate
3-directional subdivision is a triangulation with least direction. Box
spline built on it is widely applied in the engineering of surface
modeling. The normal algorithm of bivariate 3-directional spline surface
is only for normal control meshes in which every point has valence 6. A
surface algorithm based-on bivariate 3-directional quartic box-spline
for arbitrary triangular control meshes is proposed. Next, the analyses
of its properties, especially continuity, are presented in detail.
Finally, two examples are given. The results show that surfaces got by
this algorithm hold a better smoothness. Two adjacent patches have
continuity of C1 and the inner of any one patch C2. Clearly, the
algorithm can be applied to arbitrary triangular control meshes, so it
is very practically valuable for surface modeling in CAD/CAGD .
Key words: Bivariate 3-directional quartic box-spline Box-spline
surface Arbitrary triangular meshes
CLC No: TP391.72
东南大学优秀青年教师教学科研基金资助项目. Received 20040305, received in revised form
20020040515
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