Tensor-product monotonicity preservation (Q1272512)

The authors study conditions concerning monotonicity of bivariate functions defined as tensor products. Monotonicity-preserving spline schemes are important in the context of the approximation and interpolation (of tensor product data) when it is known that the discrete data originate from an originally monotonically increasing function. Bernstein-Bézier and \(B\)-spline methods involve the use of a so-called ``control net'', given by the set of Bernstein-Bézier/\(B\)-spline control points, and it is highly desirable to know conditions for the control net such that the implied analytical function is monotonic. The authors study and derive conditions for control nets relating monotonic behavior of the nets to the resulting functions. In particular, conditions are provided for general-monotonicity preservation, i.e., for preservative of monotonicity in arbitrary directions, not just axial directions.