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Number of Polygons Generated by Map Overlay: The Case of Convex Polygons
Author(s) -
Sadahiro Yukio
Publication year - 2001
Publication title -
transactions in gis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.721
H-Index - 63
eISSN - 1467-9671
pISSN - 1361-1682
DOI - 10.1111/1467-9671.00087
Subject(s) - polygon (computer graphics) , point in polygon , overlay , regular polygon , perimeter , combinatorics , rectilinear polygon , star shaped polygon , computation , mathematics , polygon mesh , computer science , geometry , algorithm , convex set , convex optimization , telecommunications , frame (networking) , simple polygon , programming language
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.