Abstract
The paper addresses the problem of how to ensure existence of blossoms in the context of piecewise spaces built from joining different extended Chebyshev spaces by means of connection matrices. The interest of this issue lies in the fact that existence of blossoms is equivalent to existence of B-spline bases in all associated spline spaces. As is now classical, blossoms are defined in a geometric way by means of intersections of osculating flats. In such a piecewise context, intersecting a number of osculating flats is a tough proposition. In the present paper, we show that blossoms exist if an only if Bézier points exist, which significantly simplifies the problem. Existence of blossoms also proves to be equivalent to existence of Bernstein bases. In order to establish the latter results, we start by extending to the piecewise context some results which are classical for extended Chebyshev spaces.
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Communicated by P.J. Laurent
AMS subject classification
65D17, 65D07
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Mazure, ML. Towards existence of piecewise Chebyshevian B-spline bases. Numer Algor 39, 399–414 (2005). https://doi.org/10.1007/s11075-004-7334-2
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DOI: https://doi.org/10.1007/s11075-004-7334-2