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Goal:

I want to run various algorithms in Shapely on some geographic data that I have. It is acceptable to have some measure of error, as long as it is "reasonable". e.g. find closest pair.

Method:

I would like to project the points from latitude-longitude to cartesian space such that

euclidan_distance(P(p0), P(p1)) ~= geodesic_distance(p0, p1)

I was thinking of using PyProj but it may be overkill, and it doesn't seem the easiest thing to do.

Naive approach:

y = latitude * 110574
x = longitude * 11320 * cos(radians(latitude))

(numbers from https://en.wikipedia.org/wiki/Latitude#Length_of_a_degree_of_latitude )

Results of naive approach:

I put in a set of coordinates nearby, and got relative errors of 0.5%-15.3%. 15% seems excessive.

1 Answer 1

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You could use one of the "AUTO" projections described by Appendix E of the WMS specification

  1. AUTO:42001 - Universal Transverse Mercator
  2. AUTO:42002 - Transverse Mercator
  3. AUTO:42003 - Orthographic
  4. AUTO:42004 - Equirectangular

The specification gives WKT projection strings for them all (all you have to do is add the coordinates of your centre point). They are supported in MapServer so I would expect them to be available in all Proj4+ based systems.

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  • Since I am not very knowledgeable in this, and quickly reading up on wikipedia does not provide this information, which of these four projections does the best job at preserving distances (for short distances of <10km)?
    – lorg
    Mar 5, 2020 at 17:48

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