Data structures for optimizing linear spline approximations

We describe the algorithms and data structures used for optimizing linear spline approximations of bivariate functions. Our method creates a random initial triangulation of a given data set and then employs a simulated annealing algorithm to improve this initial approximation. In every iteration step, the current approximation is changed in a random but local way, and the distance measure between it and the data is re-calculated. Depending on the difference between the old and new distance measures, an iteration step is either accepted or rejected. We discuss the basic operations and data structures of our optimization technique. We present a variant of the half-edge data structure and associated algorithms.