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A totally positive basis for circle approximations. (English) Zbl 1480.65029

Summary: We construct a six-dimensional space of polynomials containing approximations of trigonometric functions. In this way, an approximation of a circle can be represented as a parametric curve in this space. We show that the space has shape preserving representations and we construct the basis with optimal shape preserving properties.

MSC:

65D05 Numerical interpolation
41A05 Interpolation in approximation theory
65D17 Computer-aided design (modeling of curves and surfaces)
41A10 Approximation by polynomials
42A10 Trigonometric approximation
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