14 Projections for 2021 (Part 8)

Mon Aug 02, 2021 14 Projections for 2021 (Part 8)

If you wonder what this is about at all, you probably didn’t read the intro.

August: Canters W07

Canters W07
Creator	Frank Canters (2002)
Group	Lenticular
Property	Equal-area
Other Names	Optimised version of Hammer-Wagner Wagner VII, Canters Optimization
Remarks	Low Error Optimization of Wagner VII. Please regard Naming Canters’ Projections. Also see my blogpost about the Canters projections, part 1 (W01 - W14) and part 2 (W15 - W34).

Canters W07^[1] is, like last month’s Frančula XIV, an equal-area variant of Wagner VII, optimized for minimum angular distortions. So how come that they look quite different?

First off, they used different metrics: While Frančula optimized using the Airy-Kavrayskiy criterion^[2], Canters used his own mean finite scale factor. But more importantly (I guess) is the fact that Frančula took the entire map between 85° North and 85° South into account, but Canters restricts the optimization to the continental areas excluding Antarctica. The different approaches are reflected in the distributions of the distortions:

I think it is fair to say that both projections achieve their respective goals.
Interestingly, by Canters’ own comparison scheme, the equivalent W07 even beats such advantageous compromise projections like Canters W13, Canters W09 and Winkel Tripel Bartholomew. Nevertheless, I would only use it after careful consideration, because of the strongly curved parallels and the resulting outer shape.

Footnotes

↑ Frank Canters:
Small-scale Map Projection Design.
London & New York 2002.
↑ Nedjeljko Frančula: Die vorteilhaftesten Abbildungen in der Atlaskartographie (German)