Oscar Palacios-Velez
Abstract
A new, dynamic, hierarchical subdivision and recursive algorithm for computing Delaunay triangulations is presented. The algorithm has four main steps: (1) location of the already formed triangle that contains the point (2) identification of other adjoining triangles whose circumcircle contains the point (3) formation of the new triangles, and (4) database update. Different search procedures are analyzed. It is shown that the “oriented walk” search, when the total number of points is less than 417 or when the points are presorted by distance or coordinates. The algorithm has point-deletion capabilities which are discussed in detail.
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Index Terms
- A dynamic hierarchical subdivision algorithm for computing Delaunay triangulations and other closest-point problems
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Reviews
Ian Gladwell
The new algorithm for building Delauney triangulations by recursive addition of points given in this paper consists of four steps: location of the existing triangle containing the point to be isolated, identification of adjoining triangles whose circumcircle contains the points to be inserted, formation of new triangles (which includes deleting sides of some adjoining triangles), and updating the data structure of triangles and their relative positions. The author demonstrates that for a large enough number of points, a hierarchical subdivision approach with an oriented walk search is the most effective. Problems of realistic size are used to demonstrate this. The paper shows under what circumstances the algorithm used lends itself to deletion and replacement of points. Here the hierarchical subdivision approach's efficiency depends on the order of insertion of the points. The author has written FORTRAN programs implementing the methods described.
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