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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-BĂ©zier technique is used as a tool.
Reviewer: G.Farin

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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