Skip to main content

Number of Polygons Generated by Map Overlay: The Case of Convex Polygons

Buy Article:

$51.00 plus tax (Refund Policy)


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.

Document Type: Research Article


Affiliations: University of Tokyo

Publication date: October 1, 2001

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Partial Open Access Content
Partial Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more