Delaunay Triangulation Algorithms Useful for Multibeam Echosounding

Abstract

The Delaunay triangulation is a widely appreciated and investigated mathematical model for topographic surface representation. After a brief theoretical description, six possible basic algorithms to construct a Delaunay triangulation are analyzed and properties that can be exploited for multibeam echosounder data processing are investigated. Two concepts will be treated in more depth: the divide-and-conquer construction algorithm and the incremental method. The calculation speed of the divide-and-conquer method makes it an ideal candidate to construct the initial triangulation of multibeam data. Its runtime performance is compared to that of the incremental algorithm to demonstrate this. The algorithm’s merge step appears to be useful also in replacing triangulated areas of existing triangulations by new data. The incremental algorithm does not seem an effective construction method but it can easily be adapted to accommodate insertion of individual vertices into an existing triangulation and as such it is useful for editing purposes.