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We consider a blending basis for which we obtain an algorithm for the evaluation of polynomial curves with linear time complexity and we prove that it is a normalized totally positive basis. Therefore, it simultaneously satisfies efficiency and shape preservation. We also provide the corner cutting algorithm for obtaining the Bézier polygon from the control… (More)
All normalized totally positive bases satisfy the progressive iterative approximation property. The normalized B-basis has optimal shape preserving properties and we prove that it satisfies the progressive iterative approximation property with the fastest convergence rates. A similar result for tensor product surfaces is also derived.
The Ball basis was introduced for cubic polynomials by Ball, and two different generalizations for higher degree m polynomials have been called the Said–Ball and the Wang–Ball basis, respectively. In this paper, we analyze some shape preserving and stability properties of these bases. We prove that the Wang–Ball basis is strictly monotonicity preserving for… (More)