C1 Positivity Constrained Interpolation By Weighted Rational Cubic Triangles
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Date
2017-02
Authors
Chua, Hua Siong
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
The construction of positivity bivariate 1 C interpolants to scattered data using
rational cubic Bézier triangular patches is considered. The interpolating surface is
formed piecewise as a convex combination of three rational cubic Bézier triangles.
Sufficient 1 C continuity conditions along the common boundary of two adjacent
rational cubic Bézier triangles are shown. The sufficient positivity conditions on
rational cubic Bézier triangle are derived. The initial values of the Bézier ordinates
are determined by the data and the estimated gradient at the data sites while the
weights are given the value one. The boundary Bézier ordinates and the weights are
modified if necessary so that the resulting patch satisfies the 1 C continuity and
positivity conditions. The scheme for constructing 1 C non-negativity preserving
interpolant is local. Several numerical examples are illustrated.
Description
Keywords
C1 positivity constrained interpolation by , weighted rational cubic triangles