Abstract
A relation between univariate trigonometric and polynomial B-splines is extended to higher dimensions and used to construct a class of multivariate trigonometric B-splines from the multivariate polynomial ones. These new functions are trigonometric splines in each variable, but they are not tensor product splines. They are smooth and have local non-polygonal support. They possess a recurrence relation similar to that of the multivariate polynomial B-splines.
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