Numerical Algorithms

, Volume 5, Issue 11, pp 577–587 | Cite as

Scattered data interpolation using minimum energy Powell-Sabin elements and data dependent triangulations

  • Shmuel Rippa
Geometric Modelling


A popular approach for obtaining surfaces interpolating to scattered data is to define the interpolant in a piecewise manner over a triangulation with vertices at the data points. In most cases, the interpolant cannot be uniquely determined from the prescribed function values since it belongs to a space of functions of dimension greater than the number of data points. Thus, additional parameters are needed to define an interpolant and have to be estimated somehow from the available data. It is intuitively clear that the quality of approximation by the interpolant depends on the choice of the triangulation and on the method used to provide the additional parameters. In this paper we suggest basing the selection of the triangulation and the computation of the additional parameters on the idea of minimizing a given cost functional measuring the quality of the interpolant. We present a scheme that iteratively updates the triangulation and computes values of the additional parameters so that the quality of the interpolant, as measured by the cost functional, improves from iteration to iteration. This method is discussed and tested numerically using an energy functional and Powell-Sabin twelve split interpolants.


Minimum Energy Additional Parameter Popular Approach Scattered Data Data Interpolation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© J.C. Baltzer AG, Science Publishers 1993

Authors and Affiliations

  • Shmuel Rippa
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsCambridgeEngland

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