Abstract: In order to improve the shape control capability of the cubic triangular Bézier surface, the Bernstein basis function of the cubic triangular with two parameters is constructed from the point of view of the local and global shape parameters. The cubic triangular  λα-Bézier surface is defined by the basis function, and different control effects are achieved by changing the values of the two parameters. The condition of  C1,G1,  continuity between cubic triangular λα-Bézier surface patches and its proof is given. Related examples also confirm that: the cubic triangular λα-Bézier surface not only inherits the good properties of the cubic triangular Bézier surface, but also improves the shape control ability of the surface by changing the values of the parameters. In surface stitching, the parameter is also changed to construct multiple joining styles.  

Key words: triangular Bézier surface, base function, shape parameter, surface joining, continuity