Large-Scale Distortions in Map Projections

Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map projection metric, flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce new indicatrices that show not only area and isotropy distortions but flexion and skewness as well. We present a table showing error measures for area, isotropy, flexion, skewness, distances, and boundary cuts allowing us to compare different map projections. The Kavrayskiy VII projection is better than the popular Winkel-Tripel projection in all categories except boundary cuts, where it ties. Following a normalization procedure pioneered by Laskowski(1997a,b) find that the Kavrayskiy VII has the lowest normalized errors of all the projections studied. While this normalization procedure is by no means unique we find that the Kavrayskiy VII performs strongly with a variety of normalizations and (until other contenders appear) is a natural choice for world projections-particularly for atlases that are using the Winkel-Tripel now. The best equal area maps are the Eckert IV and the Breisemeister, and the best conformal projection is the Lagrange. The best 2-Hemisphere map is the Lambert Azimuthal.