On Simulated Annealing and the Construction of Linear Spline Approximations for Scattered Data

  • Oliver Kreylos
  • Bernd Hamann
Part of the Eurographics book series (EUROGRAPH)


We describe a method to create optimal linear spline approximations to arbitrary functions of one or two variables, given as scattered data without known connectivity. We start with an initial approximation consisting of a fixed number of vertices and improve this approximation by choosing different vertices, governed by a simulated annealing algorithm. In the case of one variable, the approximation is defined by line segments; in the case of two variables, the vertices are connected to define a Delaunay triangulation of the selected subset of sites in the plane. In a second version of this algorithm, specifically designed for the bivariate case, we choose vertex sets and also change the triangulation to achieve both optimal vertex placement and optimal triangulation. We then create a hierarchy of linear spline approximations, each one being a superset of all lower-resolution ones.


Simulated Annealing Delaunay Triangulation Simulated Annealing Algorithm Current Configuration Linear Spline 


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Copyright information

© Springer-Verlag/Wien 1999

Authors and Affiliations

  • Oliver Kreylos
    • 1
    • 2
  • Bernd Hamann
    • 1
  1. 1.Center for Image Processing and Integrated Computing (CIPIC), Department of Computer ScienceUniversity of CaliforniaDavisUSA
  2. 2.Institut für Betriebs- und Dialogsysteme, Fakultät für InformatikUniversität Karlsruhe (TH)KarlsruheGermany

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