The Centroid? Where would you like it to be be?

The concept of a centroid is useful for many spatial applications, and the determination of the centroid of a plane polygon is standard functionality in most Geographic Information System (GIS) software. A common reason for determining a centroid is to create a convenient point of reference for a polygon, often for positioning a textual label. For such applications, the rigour with which the centroid is determined is not critical, because in the positioning of a label, for example, the main criteria is that it be within the polygon and reasonably central for easy interpretation. However, there may be applications where the determination of a centroid has, at the very least, an impact on civic pride and quite possibly financial repercussions. We refer here to an administrative or natural region where a nominated centroid has a certain curiosity value with the potential to become a tourist attraction. Such centroids provide economic benefit to those in a sub-region, usually in close proximity to the centroid. Various interpretations of a centroid exist and this paper explores these and the methods of calculation. Variation in position resulting from different interpretations is examined in the context of the centroid of the Australian State of Victoria, and GIS software are evaluated to determine the efficacy of their centroid functions.