Q-Baskakov Bases and q-Baskakov Curves and Surfaces

In this paper, we discuss q-Baskakov bases and study some important geometric and analytic properties of these bases, such as non-negative, partition of unity, linear independence, degree elevation, degree reduction and end-point properties. Furthermore, we propose q-Baskakov-Bernstein bases, which are a new class of mix tensor product bases. By means of these bases, we construct a new class of curves and a new class of surfaces. We obtain some important geometric properties and geometric characterization, such as geometric and affine invariance, convexity preserving, end-point interpolation, degree elevation and De Casteljau algorithm, for these curves and surfaces.