Fitting Monotone Surfaces to Scattered Data Using C1 Piecewise Cubics

Authors:
Lu Han;Larry L. Schumaker
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1997

Citing 0
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Abstract

We derive sufficient conditions on the Bézier net of a Bernstein--Bézier polynomial defined on a triangle in the plane to insure that the corresponding surface is monotone. We then apply these conditions to construct a new algorithm for fitting a monotone surface to gridded data. The method uses C1 cubic splines defined on the triangulation obtained by drawing both diagonals of each subrectangle. In addition, we present an algorithm for the monotone scattered data interpolation problem which is based on a method for creating gridded data from the scattered data. Numerical results for several test examples are presented.