Bivariate segment approximation and splines

The problem to determine partitions of a given reet angle which are optimal for segment approximation (e.g. by bivariate pieeewise polynomials) is investigated. We give eriteria for optimal partitions and develop algorithms for eomputing optimal partitions of eertain types. It is shown that there is a surprising relationship between various types of optimal partitions. In this way, we obtain good partitions for interpolation by tensor produet spline spaees. Our numerical examples show that the methods work efficiently.