Abstract
We prove some new relations between functions defined as shadows of cones (cone splines) and simplices (simplex splines). We use them to show how ans-variate simplex spline of some orderk can be written as a sum ofk+1 (s-l)-variate simplex splines of orderk-1. A recurrence relation on the spatial dimension of the simplex spline,s, is proposed as an interesting alternative to the recurrence relation in [17], where one uses the orderk for recursion, but not the spatial dimensions.
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Communicated by Klaus Höllig.
On leave from the Department of Computer Science, University of Utah, Salt Lake City, Utah, U.S.A.
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Cohen, E., Lyche, T. & Riesenfeld, R.F. Cones and recurrence relations for simplex splines. Constr. Approx 3, 131–141 (1987). https://doi.org/10.1007/BF01890559
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DOI: https://doi.org/10.1007/BF01890559