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Tissot indicatrices have provided visual measures of local area and isotropydistortions. Here we show how large scale distortions of flexion (bending) andskewness (lopsidedness) can be measured. Area and isotropy distortions dependon the map projection metric, flexion and skewness, which manifest themselveson continental scales, depend on the first derivatives of the metric. Weintroduce new indicatrices that show not only area and isotropy distortions butflexion and skewness as well. We present a table showing error measures forarea, isotropy, flexion, skewness, distances, and boundary cuts allowing us tocompare different world map projections. We find that the Winkel-Tripelprojection (already adopted for world maps by the National Geographic), has lowdistortion on most measures and excellent quality overall.

Flexion and Skewness in Map Projections of the Earth