AbstractWhen regions are represented by their boundary, the number of points ((x, y) coordinate pairs) used to define the boundary can vary. Many more points are required to satisfactorily display a region at a detailed scale than at a broad scale. The area of a region is an important property in geographic and other applications, and it can easily be computed from the sequence of points. However, reducing or increasing the number of points in the sequence will usually alter the area. This paper considers how the region's area could be preserved by approximation algorithms, which reduce the number of points, and by enhancement algorithms, which increase the number of points.