Convexity preserving splines over triangulations

A general method is given for constructing sets of sufficient linear conditions that ensure convexity of a polynomial in Bernstein–Bézier form on a triangle. Using the linear conditions, computational methods based on macro-element spline spaces are developed to construct convexity preserving splines over triangulations that interpolate or approximate given scattered data.

► We give conditions for the convexity of a polynomial in terms of its B-coefficients.
► The derivation is based on blossoming.
► Our conditions include all previously known ones as special cases.
► We illustrate the use of the conditions to construct convex spline interpolants.