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An explicit basis for $$C^ 1$$ quartic bivariate splines. (English) Zbl 0658.65008
If a triangulation of the plane is given, one may define a polynomial over each triangle and then consider the resulting linear space of bivariate polynomials. This paper considers such polynomials of degree four with the stipulation of being $$C^ 2$$ over the whole triangulation. The problem of finding bases for the corresponding linear spaces is solved. The Bernstein-Bézier technique is used as a tool.
Reviewer: G.Farin

MSC:
 65D07 Numerical computation using splines 41A15 Spline approximation 41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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