Helix splines as an example of affine Tchebycheffian splines (Q1895904)

A brief review of the results on affine Chebyshevian Bézier curves and \(B\)-splines is given. The main part is devoted to the derivation of a new special affine Chebyshevian free-form scheme, so called ``helix scheme'', which provides exact representation of the most important here geometric objects -- straight lines, circles and helix curves in an arc length parametrization. The corresponding tensor product surfaces are studied. Some applications in curve surface design and the construction of planar \(C^2\)-motions interpolating a given set of positions are presented.