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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.
A nonsingular matrix is called almost strictly totally positive when all its minors are nonnegative and, furthermore, these minors are strictly positive if and only if their diagonal entries are strictly positive. Almost strictly totally positive matrices are useful in Approximation Theory and Computer Aided Geometric Design to generate bases of functions(More)