Results

A summary of the results from different data sets using this algorithmic embedding. We also compared the distortion from this embedding verses other commonly used map projections.

Description of Data Set
Calculated Projection Point
Maximum Distortion

10 world cities
(18S, 125W)
4.5
100 world cities
(85S, 4W)
6.1
238 world cities
(83S, 79E)
6.7
2500 world cities
(87S, 61W)
9.7
150 world cities East of the Equator
(0N, 90W)
5.8
80 world cities West of the Equator
(0N, 90E)
4.8
170 world cites North of the Equator
(88S, 100W)
6.8
60 world cites South of the Equator (86N, 95W)
4.2
200 US cities
(36S, 120E)
3.4
15 points near the North Pole
(90S, 0E)
2.3
15 points near the South Pole
(90N, 1W)
2.4
30 points near both poles
(0N, 25W)
7.8
100 grid points
(3N, 175E)
43.2
400 grid points
(2N, 175E)
54.8
100 grid points on upper half of sphere
(90S, 170E)
23.3
100 grid points on lower half of sphere
(90N, 172E)
28.4
100 grid points on right half of sphere
(0N, 90W)
20.1
100 grid points on left half of sphere
(0N, 90E)
19.9

Distortion values for data sets.
The calculated projection point is represented using (latitutde, longitude).
The maximum distortion is the maximum ratio between the distance between any pair of points on the sphere and in the plane.


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