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I have GIS software that can do this conversion but I need to know the actual formula / math involved. I'm writing code and need to perform a single conversion (WGS to EPSG:3071) so using a library, open source or not, involves too much overhead (20+ MB for one library). I don't need libraries of coordinate systems that will never be used. It would be best if I just write a function to perform the calculation.

How do I convert from WGS84 to EPSG:3071 (Wisconsin Transverse Mercator)?

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    See Snyder's manual, pp 61 - 64. For high accuracy you need series approximations for projection and unprojection. These are expressed as two dozen formulas spread across three pages; it would be inconvenient to reproduce them here (and difficult to read because we do not support mathematical markup). – whuber Feb 7 '15 at 18:15
  • Where did you get vale of 20+ MB? PROJ.4 for example is less than 1MB. – Wernfried Domscheit Feb 7 '15 at 20:11
  • I built a very simple console app with an OSS library. I don't recall the name but the compiled library alone was 20mb. – DenaliHardtail Feb 7 '15 at 20:14
  • Are you using any database in your app? If so, maybe you could use it to do that for you using views. Also dont think that proj4 is that big, you dont need all the EPSG set of data. – Rui Lima Feb 8 '15 at 0:31
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as whuber said, there are several pages of explanations to get the exact formulas. Though you can find some simplified series on wikipedia. For Wisconsin Transverse Mercator, please also note that implementing the projection is not enough, because you also need to code the datum transform between WGS 84 and NAD 83.

My suggestion is to take advantage of open source and pick the transverse Mercator projection in one of the open source libraries (e.g. proj.4).

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