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I'd like to find a service to convert lat/lon in WGS84 to an arbitrary coordinate system in metric that will be the most accurate for my bounding box. Does something like this exist?

For instance,

lat = {62.0, 61.0} , long = {-149.0, -150.0} 

would perhaps bring up Alaska State Plane 4.

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    What's "accurate" here? Distances, bearings, areas? You could just use an azimuthal projection centred at the centre of your box... – Spacedman Mar 10 '16 at 23:19
  • I guess I don't know enough to create my own projection like that. I am trying to find accurate distances between two points within 1 degree latitude and longitude around the subarctic with at least a meter accuracy. – cylondude Sep 1 '16 at 2:39
  • I'm looking in library(mapproj). Is that the tool that will do what you suggest? – cylondude Sep 1 '16 at 4:04
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Spacedman has the right idea.

Your hypothetical website would need to ask you to choose which of the following attributes to optimize:

  • Those that minimize distortion in shape are called conformal.
  • Those that minimize distortion in distance are known as equidistant.
  • Those that minimize distortion in area are known as equal-area.
  • Those minimizing distortion in direction are called true-direction projections.

(from https://courses.washington.edu/gis250/lessons/projection/index.html)

I don't know of (and couldn't quickly) find any that walk you through the process.

Perhaps https://www.jasondavies.com/maps/transition/ will help you pick a projection. Once you have that, then you can look up which coordinate systems exist for the area of interest using the desired projection.

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