Abstract: This paper aims at adjusting the shape of the quartic triangular Bézier surface without changing the control points. Based on the idea of defining adjustable surfaces by adjustable control points, starting from a geometric perspective, a set of quartic bivariate basis functions with two parameters are constructed and a new triangular patch determined by fifteen control points is defined. The new surface not only inherits the properties of the quartic triangular Bézier surface, but also possesses two parameters which can be used to adjust its shape. Compared with the existing method of constructing triangular Bézier surface whose shape is adjustable, the method provided here defines the new surface from a geometric rather than an algebraic perspective, hence the introduced parameters have definite geometric effect, and the method here does not increase the degree of the basis functions. For convenient application, the G1 smooth join condition of the surface is given. The legends show the correctness and validity of the method.

Key words: surface design, Bézier surface, triangular domain, shape adjustment