Warren, JoeWeimer, Henrik2017-08-022017-08-021997-09-03Warren, Joe and Weimer, Henrik. "Fast Approximating Triangulation of Large Scattered Datasets." (1997) https://hdl.handle.net/1911/96472.https://hdl.handle.net/1911/96472This report describes algorithms and data-structures for the fast construction of three-dimensional triangulations from large sets of scattered data-points. The triangulations have a guaranteed error bound, i.e. all the data-points lie within a pre-specified distance from the triangulation. Three different methods for choosing triangulation vertices are presented, based on interpolation, and L2 and L_infinity-optimization of the error over subsets of the data-points. The main focus of this report will be on devising a simple and fast algorithm for constructing an approximating triangulation of a very large set of points. We propose the use of adapted dynamic data structures and excessive caching of information to speed up the computation and show how the method can be extended to approximate multiple dependent datasets in higher-dimensional approximation problems.23 ppengYou are granted permission for the noncommercial reproduction, distribution, display, and performance of this technical report in any format, but this permission is only for a period of forty-five (45) days from the most recent time that you verified that this technical report is still available from the Computer Science Department of Rice University under terms that include this permission. All other rights are reserved by the author(s).Technical reportTR97-288