The storage and reconstruction of polygon boundaries using circles

Abstract

This paper investigates the accuracy of using circles to store polygon boundaries. Can a series of xy points be accurately replaced by a smaller array of variably-sized circles used in a non space filling sense to approximate to the edge of the polygon? Two measures were used to ascertain this, areal error and visual error. A vector dataset representing the island of Rarotonga was converted from boundary coordinates to circle storage using a Voronoi-based medial axis approach. Three parameters were altered to derive as many as 150 circle-based realisations – minimum allowed circle radius, degree of overlap allowed between circles and Douglas-Peucker algorithm threshold (the latter algorithm of line reduction was used to extract “important” points from the polygon and add them to the circle list as “zero-radius circles”). This presentation presents and analyses the areal error and visual error results for all realisations.