Results for Modified Stereographic Projection

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)
 6.2
100 world cities
 (85S, 4W)
 5.4
238 world cities
 (83S, 79E)
 7.4
2500 world cities
 (87S, 61W)
 11.2
150 world cities East of the Equator
 (0N, 90W)
 4.9
80 world cities West of the Equator
 (0N, 90E)
 4.7
170 world cites North of the Equator
 (88S, 100W)
 6.2
60 world cites South of the Equator (86N, 95W)
 5.6
200 US cities
 (36S, 120E)
 1.8
15 points near the North Pole
 (90S, 0E)
 4.2
15 points near the South Pole
 (90N, 1W)
 4.7
30 points near both poles
 (0N, 25W)
 6.7
100 grid points
 (3N, 175E)
 4322
400 grid points
 (2N, 175E)
 5481
100 grid points on upper half of sphere
 (90S, 170E)
 17.5
100 grid points on lower half of sphere
 (90N, 172E)
 18.4
100 grid points on right half of sphere
 (0N, 90W)
 21.2
100 grid points on left half of sphere
 (0N, 90E)
 22.4

Distortion values for Modified Stereographic Projection
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.
Analysis of Results
There are no proven theoretical distortion bounds for the Modified Stereographic Projection. It still suffers from the "infinite-poles" problem if there is another point at the antipodal of the "projection point". This was evident in the data sets consisting of grid points. It is more difficult to construct an example that would results in the "infinite-poles" problem since the projection point is dependent on the given input data set. Hence, it performs significantly better than the traditional Stereographic Projection when the data set includes a number of points near the poles.


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