Technical Note Number of Polygons Generated by Map Overlay: The Case of Convex Polygons Yukio Sadahiro Center for Spatial Information Science University of Tokyo Abstract This paper analyzes the number of polygons generated by map overlay. Overlay of maps yields a number of small polygons, and often causes problems in computation, handling, and storage of derived polygons. One method to deal with these problems is to estimate the number of derived polygons before executing overlay operation. To this end, a stochastic model is proposed by which the expected number of derived polygons is calculated. The results are summarized as follows: (1) the number of polygons generated by map overlay depends on the number of original polygons and their perimeters; (2) the number of derived polygons increases with the perimeters of original polygons; (3) McAlpine and Cook's (1971) earlier method underestimated the number of derived polygons; and (4) the number of polygons generated by the overlay of maps having the same lattice system is proportional to the square of the number of overlaid maps and the number of polygons on the map, and inversely proportional to the area-perimeter ratio of the unit cell. 1 Introduction Map overlay is one of the fundamental operations of GIS. Overlay of vector maps creates a new map on which generated polygons inherit attributes from the original maps, and enables us to perform spatial analysis on the integrated data. Consider two maps, for instance, a census map reporting socioeconomic data and a land cover map based on a square lattice. Each polygon generated by overlay of these maps has at least two attributes, say, population count and land cover type. Therefore, the new map may reveal an interesting relationship between these variables. Transactions in GIS, 2001, 5(4): 345±353 ß 2001 Blackwell Publishers, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA. Address for correspondence: Yukio Sadahiro, Center for Spatial Information Science, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan. E-mail: sada@okabe.t.u- tokyo.ac.jp