Total Positivity and Convexity Preservation
نویسنده
چکیده
It is well established that systems of totally positive blending functions, such as the Bernstein and B-spline bases, preserve monotonicity and convexity and are generally ‘shape preserving’ [9 ]. In this paper we show that total positivity is equivalent to the preservation of all orders of convexity. By a system we understand a sequence of functions (u0, . . . , un) defined on an interval [a, b]. Given points P0, . . . , Pn ∈ IR , called control points, the system generates a curve
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تاریخ انتشار 1997