Abstract

This paper introduces the arc tree, a hierarchical data structure to represent arbitrary curved shapes. The arc tree is a balanced binary tree that represents a curve of length l such that any subtree whose root is on the k-th tree level is representing a subcurve of length l/2k-1. Each tree level is associated with an approximation of the curve; lower levels correspond to approximations of higher resolution. Based on this hierarchy of detail, queries such as point search or intersection detection and computation can be solved in a hierarchical manner. We present the results of a practical performance analysis for various kinds of set and search operators. Several related schemes are also discussed.

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