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Two Talks given at Vanderbilt University, May 1, 1997

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1. Bivariate Splines and the Four Color Map Problem

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Abstract

Bivariate Splines are smooth piecewise polynomial functions
defined on triangulations. Some open spline problems resemble
the four color map problem in that they concern a *map*
(i.e., the triangulation) and that they are global in the sense
that action in any part of the map affects the spline everywhere
else. The problems may be solvable using the same techniques
that were employed in the proof of the four color map theorem.
That connection is explored in this talk.
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2. Effects of Non-generic Triangulations on Bivariate
Spline Interpolants.

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Abstract

Bivariate Splines are smooth piecewise polynomial functions
defined on triangulations. The dimension of spline spaces
depends on the precise location of the vertices and may change
under an arbitrarily small change of some vertex locations. In
this talk we examine the effects of such changes on the
solutions of certain interpolation problems.
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The Bernstein Bézier Form of a Bivariate Polynomial

Both talks use the Bernstein Bézier form of a
bivariate polynomial which will be defined in the first
talk. However, you can see a separate
summary of multivariate splines and the Bernstein B
ézier form.

**[28-Apr-1997]**

Go to Peter Alfeld's Home Page.