Abstract: In order to endow the cubic triangular Bézier surface the ability of shape adjustment, this
paper constructs a set of cubic bivariate basis functions with a parameter and defines a new triangular
surface determined by ten control points. The new surface has corner interpolation property. The tangent
planes at the corner points are determined by the corner points and the two adjacent points which lie on
the same edges. Changing the parameter value can adjust the shape of the surface. For convenient
application, the G1 smooth join condition and the geometric iterative algorithm of the surface are given.
The convergence as well as the relationship of the convergent rate and the parameter selection of the
algorithm is analyzed. The legends show the correctness and validity of the method.

Key words: triangular Bézier patch, shape adjustment, geometric iteration, interpolation, surface joining