Normalized trivariate B-splines on Worsey-Piper split and quasi-interpolants

In this work, we give an algorithm for constructing a normalized B-spline basis over a Worsey-Piper split of a bounded domain of ℝ 3 . These B-splines are all positive, have local support and form a partition of unity. Therefore, they can be used for constructing local approximants and for many other applications in CAGD. We also introduce the Worsey-Piper B-spline representation of C 1 quadratic polynomials or splines in terms of their polar forms. Then, we use this B-representation for constructing several quasi-interpolants which have an optimal approximation order.