Efficient co-triangulation of large data sets

Presents an efficient algorithm for the reconstruction of a multivariate function from multiple sets of scattered data. Given N sets of scattered data representing N distinct dependent variables that have been sampled independently over a common domain and N error tolerance values, the algorithm constructs a triangulation of the domain of the data and associates multivariate values with the vertices of the triangulation. The resulting linear interpolation of these multivariate values yields a multivariate function, called a co-triangulation, that represents all of the dependent data up to the given error tolerance. A simple iterative algorithm for the construction of a co-triangulation from any number of data sets is presented and analyzed. The main contribution of this paper lies in the description of a highly efficient framework for the realization of this approximation algorithm. While the asymptotic time complexity of the algorithm certainly remains within the theoretical bounds, we demonstrate that it is possible to achieve running times that depend only linearly on the number of data even for very large problems with more than two million samples. This efficient realization of the algorithm uses adapted dynamic data structures and careful caching in an integrated framework.