I/O-Efficient Algorithms for Contour Line Extraction and Planar Graph Blocking

Abstract

For a polyhedral terrain C, the contour at z-coordinate h, denoted Ch, is defined to be the intersection of the plane z = h with C. In this paper, we study the contour-line extraction problem, where we want to preprocess C into a data structure so that given a query z-coordinate h, we can report Ch quickly. This is a central problem that arises in geographic information systems (GIS), where terrains are often stored as Triangular Irregular Networks (TINS). We present an I/O-optimal algorithm for this problem which stores a terrain C with N vertices using O(N/B) blocks, where B is the size of a disk block, so that for any query h, the contour ch can be computed using o(log, N + I&l/B) I/O operations, where l&l denotes the size of Ch. We also present en improved algorithm for a more general problem of blocking bounded-degree planar graphs such as TINS (i.e., storing them on disk so that any graph traversal algorithm can traverse the graph in an I/O-efficient manner), and apply it to two problms that arise in GIS.