On the convergence of approximating tensor-product rational Bézier surfaces using tensor-product Bézier surfaces

In this paper, we derive the uniform convergence of approximating tensor-product rational Bézier surfaces using tensor-product Bézier surfaces. Our main result is that arbitrary given order derivative vectors of approximating tensor-product Bézier surface sequence converge uniformly to those of the original tensor-product rational Bézier surface as the elevated degree tends to infinity, with inequality skills and infinitesimal analysis techniques. The approximating tensor-product Bézier surface sequence has the same degree and new control points of the degree-elevated tensor-product rational Bézier surfaces.