By piecewise Chebyshevian splines we mean splines with pieces taken from different Extended Chebyshev spaces all of the same dimension, and with connection matrices at the knots. Within this very large and crucial class of splines, we are more specifically concerned with those which are good for design , in the sense that they possess blossoms, or, equivalently, refinable B-spline bases. In practice, this subclass is known to be characterised by the existence of (infinitely many) piecewise generalised derivatives with respect to which the continuity between consecutive pieces is controlled by identity matrices. Somehow inherent in the previous characterisation, the construction of all associated rational spline spaces creates an equivalence relation between piecewise Chebyshevian spline spaces good for design, among which the famous classical rational splines. We investigate this equivalence relation along with the natural question: Is it or not worthwhile considering the rational framework since it does not enlarge the set of resulting splines? This explains the parentheses inside the acronym NU(R)BS.

中文翻译：

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几何连续分段切比雪夫 NU(R)BS

分段切比雪夫样条是指样条样条从不同维度的不同扩展切比雪夫空间中取出，并在节点处具有连接矩阵。在这一类非常大且至关重要的样条中，我们更具体地关注那些有利于设计的样条，从某种意义上说，它们具有花朵，或者等效地，可精炼的 B 样条基。在实践中，已知这个子类的特征是存在（无限多个）分段广义导数，关于这些导数，连续片段之间的连续性由单位矩阵控制。不知何故，在先前的特征中，所有相关有理样条空间的构造在有利于设计的分段切比雪夫样条空间之间创建了等价关系，其中著名的经典有理样条。我们研究这种等价关系以及自然问题：是否值得考虑理性框架，因为它不会扩大结果样条的集合？这解释了首字母缩略词 NU(R)BS 内的括号。