  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 world map projections. We find that the Winkel-Tripel
projection (already adopted for world maps by the National Geographic), has low
distortion on most measures and excellent quality overall.
