Dynamic Maintenance of Delaunay Triangulations

We describe and analyze the complexity of a procedure for computing and updating a Delaunay triangulation of a set of points in the plane subject to incremental insertions and deletions. Our method is based on a recent algo rithm of Guibas, Knuth, and Sharir for constructing Delaunay triangulations by incremental point insertion only. Our implementation features several meth ods that are not usually present in standard GIS algorithms. Our algorithm involves: Incremental update: During point insertion or deletion only the portion of the triangulation affected by the insertion or deletion is modified. Randomized methods: For triangulation building or updates involving large collections of point, randomized techniques are employed to improve the expected performance of the algorithm, irrespective of the distribution of points. Persistence: Earlier versions of the triangulation can be recovered efficiently.