Level Line Trees on 2D Voronoi Diagrams

Abstract We present a topdown algorithm to compute the level line tree of a 2D point set with a Voronoi diagram and scalar values. A level line is a boundary of a component of an upper/lower level set. All level lines are nested to form a tree, called the level line tree. The running time of the algorithm is O (n + L), where n is the size of the input data, L is the total length of all level lines, and the length of a level line is measured by the number of Voronoi edges in it. The efficiency of the algorithm is illustrated by experiments.