Generalized tensor product Bézier surfaces

In order to adjust effectively the shape of the tensor product Bézier surfaces and to connect conveniently the surface patches, generalized tensor product Bézier surfaces with local directional control derivative vectors are given in this paper. The given surface expression is a modification based on a kind of higher approximate polynomials of a function. Taking the tensor Bézier surfaces as a special case, the given surface is an effective modification for the Bézier surface of higher degree by adjusting the directional target derivative vectors. A method for connecting surface patches on rectangle domain is presented; it can be used to realize C¹ continuous connection of two surface patches without any constraint conditions for the control grid points.