## Critical length for design purposes and extended Chebyshev spaces.(English)Zbl 1061.41004

The authors analyze the connection between classes of spaces generated by a basis designed for different purposes. These include spaces generated by an extended Chebyshev basis, designed for Hermite interpolation; B-basis, for shape preserving properties; totally positive-basis; Bernstein basis; normalized basis; bicanonical basis; etc. Attention is paid to uses of the spaces for geometric design and modeling as well as for design purposes. An interesting example is presented of the space with the blended basis $$\{ 1, t, t^2 , \sin t, \cos t \}$$.

### MSC:

 41A10 Approximation by polynomials 42A10 Trigonometric approximation 41A30 Approximation by other special function classes
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