Positivity-preserving scattered data interpolation

Authors:
Abd. Rahni Mt. Piah;Tim N. T. Goodman;Keith Unsworth
Affiliations:
School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia;Department of Mathematics, University of Dundee, Dundee, Scotland;Applied Computing Group, Lincoln University, Canterbury, New Zealand
Venue:
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Year:
2005

Citing 5
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Abstract

The construction of a C1 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bézier points in order to ensure that surfaces comprising cubic Bézier triangular patches are always positive. In the current work, simpler and more relaxed conditions are derived on the Bézier points. The gradients at the data sites are then calculated to ensure that these conditions are satisfied. Each triangular patch of the interpolating surface is formed as a convex combination of three cubic Bézier triangular patches. Its construction is local. A number of examples are presented.