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TitleOn Simulated Annealing and the Construction of Linear Spline Approximations for Scattered Data (In Proceedings)
inProceedings of the Joint EUROGRAPHICS-IEEE TVCG Symposium on Visualization
Author(s) Oliver Kreylos, Bernd Hamann
Year 1999
LocationVienna, Austria
DateMay 1999
Pages189--198
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Abstract 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.