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: Arbitrary triangular meshes, Bivariate 3-directional quartic box-spline, Box-spline surface