Chapter 28

Splines over Triangulations

Frank Zeilfelder and Hans-Peter Seidel

28.1 INTRODUCTION

In the past 35 years, many research papers have been written on bivariate, respectively multivariate splines. This work has been motivated in many cases by the aim to develop powerful tools for fields of application, such as scattered data fitting, the construction and reconstruction of surfaces and the numerical solution of boundary-value problems.

A natural generalization of the classical univariate spline spaces(cf. [16],[87],[112]) which has been widely considered in the literature is defined w.r.t. triangulations (i.e. a finite set of closed triangles in IR2 such that the intersection of any two triangles is empty, a common edge or a common ...

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