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Autori: Ágoston Róth, Imre Juhász, Josef Schicho, Miklós Hoffmann
Editorial: Elsevier Science, Elsevier B. V., Computer Aided Geometric Design, 26(5), p.528-546, 2009.
We define a cyclic basis for the vectorspace of truncated Fourier series. The basis has several nice properties, such as positivity, summing to 1, that are often required in computer aided design, and that are used by designers in order to control curves by manipulating control points. Our curves have cyclic symmetry, i.e. the control points can be cyclically arranged and the curve does not change when the control points are cyclically permuted. We provide an explicit formula for the elevation of the degree from n to n+r (r>=1) and prove that the control polygon of the degree elevated curve converges to the curve itself if r tends to infinity. Variation diminishing property of the curve is also verified. The proposed basis functions are suitable for the description of infinitely smooth closed curves and surfaces.
Cuvinte cheie: Closed curve; Closed surface; Trigonometric basis function; Variation diminishing; Degree elevation