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Implementing data-dependent triangulations with higher order Delaunay triangulations

Published: 31 October 2016 Publication History

Abstract

The Delaunay triangulation is the standard choice for building triangulated irregular networks (TINs) to represent terrain surfaces. However, the Delaunay triangulation is based only on the 2D coordinates of the data points, ignoring their elevation. It has long been recognized that sometimes it may be beneficial to use other, non-Delaunay, criteria to build TINs. Data-dependent triangulations were introduced decades ago to address this. However, they are rarely used in practice, mostly because the optimization of data- dependent criteria often results in triangulations with many thin and elongated triangles. Recently, in the field of computational geometry, higher order Delaunay triangulations (HODTs) were introduced, trying to tackle both issues at the same time-data-dependent criteria and good triangle shape. Nevertheless, most previous studies about them have been limited to theoretical aspects. In this work we present the first extensive experimental study on the practical use of HODTs, as a tool to build data-dependent TINs. We present experiments with two USGS terrains that show that HODTs can give significant improvements over the Delaunay triangulation for the criteria identified as most important for data-dependent triangulations. The resulting triangulations have data-dependent values comparable to those obtained with pure data-dependent approaches, without compromising the shape of the triangles, and are faster to compute.

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SIGSPACIAL '16: Proceedings of the 24th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
October 2016
649 pages
ISBN:9781450345897
DOI:10.1145/2996913
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

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Published: 31 October 2016

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  1. Delaunay triangulation
  2. data-dependent triangulations
  3. triangulated irregular networks

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SIGSPATIAL'16

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SIGSPACIAL '16 Paper Acceptance Rate 40 of 216 submissions, 19%;
Overall Acceptance Rate 257 of 1,238 submissions, 21%

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