Abstract: Based on the binomial coefficient, a matrix with shape parameters is designed. And then it
is used for constructing a new type of basis function called A-Bernstein basis function. It has the same
degree with the Bernstein basis function and shares several same properties. According to the
A-Bernstein basis function, a corresponding curve named A-Bézier curve is derived. It not only
shares the same properties with a Bézier curve, but also can be adjusted in shape by modifying the
shape parameter without the changing of original control points. Furthermore, the modification of the
matrix is illustrated. It can be used for modifying the A-Bézier curve. Examples show this method is
intuitive and effective.

Key words: curve design, A-Bézier curve, positive coefficient matrix, shape parameter, A-Bernstein
basis function