Walking algorithms for point location in TIN models

摘要

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 lo cations has to be performed, and so there is a need for fast algorithms having minimal additional memory requirements and resistant to changes in the triangula tion. So-called walking algorithms offer low complexity, easy implementation, and negligible additional mem ory requirements, which makes them suitable for such applications. In this article, we focus on these algo rithms, 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.