1. Walking algorithms for point location in TIN models
- Author
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Roman Soukal, Ivana Kolingerová, and Martina Málková
- Subjects
Theoretical computer science ,Triangulation (social science) ,Minimum-weight triangulation ,Computer Science Applications ,Triangulated irregular network ,Computational Mathematics ,Computational Theory and Mathematics ,Search algorithm ,Triangle mesh ,Point location ,Point (geometry) ,Computers in Earth Sciences ,Focus (optics) ,Algorithm ,Mathematics - Abstract
Finding which triangle in a planar or 2.5D triangle mesh contains a query point (so-called point location problem) is a frequent task in geosciences, especially when working with triangulated irregular network models. Usually, a large number of point locations has to be performed, and so there is a need for fast algorithms having minimal additional memory requirements and resistant to changes in the triangulation. So-called walking algorithms offer low complexity, easy implementation, and negligible additional memory requirements, which makes them suitable for such applications. In this article, we focus on these algorithms, summarize, and compare them with regard to their use in geosciences. Since such a summary has not been done yet, our article should serve those who are dealing with this problem in their application to decide which algorithm would be the best for their solution. Moreover, the influence of the triangulation type on the number of the visited triangles is discussed.
- Published
- 2012
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