Geometric modeling with quasi-Hermite curves and surfaces

A class of quasi-Hermite base function is established in space Gamma = {1, t, sin t, cos t, cos 2t}. The corresponding quasi-Hermite curves with a shape parameter alpha are defined by the introduced base function. The curves can easily be adjusted by using the shape parameter alpha. With the parameter chosen properly, the defined curves can precisely be used to represent straight line segment, circular arcs, elliptic arcs, cycloid, sine and cosine curves. And quasi-Coons surface is defined by quasi-Hermite base function in stand of Hermite base function. At last, the quasi-bicubic Coons surfaces is discussed especially, and the surfaces can represent spherical surfaces, ellipsoid, cylinder, anchor ring and circular conical surface exactly.