ISAAC 2008: Algorithms and Computation pp 544-555

# Preprocessing Imprecise Points and Splitting Triangulations

• Marc van Kreveld
• Maarten Löffler
• Joseph S. B. Mitchell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)

## Abstract

Given a triangulation of a set of n points in the plane, each colored red or blue, we show how to compute a triangulation of just the blue points in time O(n). We apply this result to show that one can preprocess a set of disjoint regions (representing “imprecise points”) in the plane having total complexity n in O(n logn) time so that if one point per region is specified with precise coordinates, a triangulation of the n points can be computed in O(n) time.

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## Authors and Affiliations

• Marc van Kreveld
• 1
• Maarten Löffler
• 1
• Joseph S. B. Mitchell
• 2
1. 1.Department of Information and Computing SciencesUtrecht UniversityThe Netherlands
2. 2.Department of Applied Mathematics and StatisticsState University of New York at Stony BrookUSA