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Homogeneous polynomial splines

Published online by Cambridge University Press:  14 November 2011

T. N. T. Goodman  and
S. L. Lee
T. N. T. Goodman
Affiliation:
Department of Mathematics and Computer Science, The University, Dundee DD1 4HN, Scotland, U.K
S. L. Lee
Affiliation:
Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511
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Synopsis

We construct functions which are piecewise homogeneous polynomials in the positive octant in three dimensions. These give a rich and elegant theory which combines properties of polynomial box splines see [6] and the references therein) with the explicit representation of simple exponential box splines [11], while enjoying complete symmetry in the three variables. By a linear transformation followed by a projection on suitable planes, one obtains piecewise polynomial functions of two variables on a mesh formed by three pencils of lines. The vertices of these pencils may be finite or one or two may be infinite, i.e. the corresponding pencils may comprise parallel lines. As a limiting case, all three vertices become infinite and one recovers polynomial box splines on a three-direction mesh.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 117 , Issue 1-2 , 1991 , pp. 89 - 102
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

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