<div dir="ltr"><div>Ken,</div><div><br></div>lat_ts is a setup parameter used in a few of the projections supported by proj (cea, merc, stere, wag3 and wink1) - it is not a magic incantation you can slap on any projection definition string to force it to be "exact" along any given latitude.<div><br></div><div>But the proj program has functionality to provide a large amount of projection distortion information: Try running</div><div><br></div><div>echo 12 55 | proj -VS +proj=merc +ellps=GRS80 +lat_ts=55</div><div><br></div><div>Which will give you information about the distortion of a point at 12 E, 55 N (near Copenhagen, Denmark), for a mercator projection with a latitude of true scale of 55. Not surprising, the scale is 1:</div><div><br></div><div><br></div><div><div>#Mercator</div><div>#<span style="white-space:pre"> </span>Cyl, Sph&Ell</div><div>#<span style="white-space:pre"> </span>lat_ts=</div><div># +proj=merc +ellps=GRS80 +lat_ts=55</div><div>#--- following specified but NOT used</div><div># +ellps=WGS84</div><div>#Final Earth figure: ellipsoid</div><div># Major axis (a): 6378137.000</div><div># 1/flattening: 298.257222</div><div># squared eccentricity: 0.006694380023</div><div>Longitude: 12dE [ 12 ]</div><div>Latitude: 55dN [ 55 ]</div><div>Easting (x): 767929.55</div><div>Northing (y): 4211972.20</div><div>Meridian scale (h) : 1.00000000 ( 8.866e-009 % error )</div><div>Parallel scale (k) : 1.00000000 ( -1.066e-010 % error )</div><div>Areal scale (s): 1.00000000 ( 8.759e-009 % error )</div><div>Angular distortion (w): 0.000</div><div>Meridian/Parallel angle: 90.00000</div><div>Convergence : 0d [ -0.00000000 ]</div><div>Max-min (Tissot axis a-b) scale error: 1.00000 1.00000</div><div><br></div></div><div><br></div><div>Then try changing +lat_ts=55 to +lat_ts=54:</div><div><br></div><div><div>#Mercator</div><div>#<span style="white-space:pre"> </span>Cyl, Sph&Ell</div><div>#<span style="white-space:pre"> </span>lat_ts=</div><div># +proj=merc +ellps=GRS80 +lat_ts=54</div><div>#--- following specified but NOT used</div><div># +ellps=WGS84</div><div>#Final Earth figure: ellipsoid</div><div># Major axis (a): 6378137.000</div><div># 1/flattening: 298.257222</div><div># squared eccentricity: 0.006694380023</div><div>Longitude: 12dE [ 12 ]</div><div>Latitude: 55dN [ 55 ]</div><div>Easting (x): 786909.29</div><div>Northing (y): 4316073.03</div><div>Meridian scale (h) : 1.02471546 ( 2.472 % error )</div><div>Parallel scale (k) : 1.02471546 ( 2.472 % error )</div><div>Areal scale (s): 1.05004178 ( 5.004 % error )</div><div>Angular distortion (w): 0.000</div><div>Meridian/Parallel angle: 90.00000</div><div>Convergence : 0d [ -0.00000000 ]</div><div>Max-min (Tissot axis a-b) scale error: 1.02472 1.02472</div><div><br></div></div><div>Indeed a quite useful feature of proj! That said, you will probably also need some basic literature about projections to make real use of this feature.</div><div><br></div><div>/thomas</div><div><br></div></div><div class="gmail_extra"><br><div class="gmail_quote">2017-11-20 20:28 GMT+01:00 Micah Cochran <span dir="ltr"><<a href="mailto:mcochran@athensal.us" target="_blank">mcochran@athensal.us</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Hello Ken,<div><br></div><div>Just for completeness a projection is a flat representation of earth. The earth is usually represented as an oblate spheroid. Any projection has some level of approximation between distance, area, direction, and form (does the landmass look like what it should look like). Some projections are good used for surveying application, others are better for representing a really large area.</div><div><br></div><div>For basic information about projections:</div><div><a href="http://axismaps.github.io/thematic-cartography/articles/projections.html" target="_blank">http://axismaps.github.io/<wbr>thematic-cartography/articles/<wbr>projections.html</a><br></div><div><br></div><div>If you limit the scope of area, you can very accurate measurements.</div><div><br></div><div>It depends upon what projection that you are using to what kinds of errors you will get. Mercator projection is very accurate at the 0 deg latitude. Transverse Mercator project is very accurate at along a line of longitude.</div><div><br></div><div>Errors can be both latitude and longitude, depending on the projection. For example, a polar projection will have distortion anywhere but the center (the pole).</div><div><br></div><div>Tissot's indicatrix is used as a graphic illustration of a projection's distortion.</div><div><a href="https://en.wikipedia.org/wiki/Tissot%27s_indicatrix" target="_blank">https://en.wikipedia.org/wiki/<wbr>Tissot%27s_indicatrix</a><br></div><div><br></div><div>You can calculate a grid distance, which can be very close or not close at all based on the projection. Geodetic/geodesic distance algorithms from the GeographicLib::Geodesic libary (included with PROJ.4) has very accurate distance calculations.</div><div><a href="http://proj4.org/geodesic.html" target="_blank">http://proj4.org/geodesic.html</a><br></div><div><br></div><div>I'm not to sure about keeping track of the errors of a particular projection or how to exactly answer your specific questions. I hope that gives you some pointers.</div><div><br></div><div>In a slightly different tangent about using US Customary units for area and exactitude, I was looking at the difference between calculating acres using international feet (0.3048 m) and US Survey feet (0.3048006 m). The size of this City is about 1000 sq km. When converting to acres (area) using the two different feet as the basis of acres, I got a difference of 100 acres (40 hectares or 0.4 sq km) between the asnwers. US Customary units make me crazy.</div><span class="HOEnZb"><font color="#888888"><div class="gmail_extra"><br></div><div class="gmail_extra">Micah Cochran</div></font></span><div><div class="h5"><div class="gmail_extra"><br><div class="gmail_quote">On Mon, Nov 20, 2017 at 11:13 AM, Ken Mankoff <span dir="ltr"><<a href="mailto:mankoff@gmail.com" target="_blank">mankoff@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Dear List,<br>
<br>
I've just learned that GRASS has a function to provide the true scale for a given cell. From this, I can determine the map projection error.<br>
<br>
My understanding is that for a given projection, the "lat_ts" term of the proj4 string describing the projection is where 1 m in GRASS is actually 1 m. Elsewhere, errors grow. I'd like to track these.<br>
<br>
I asked the following on the GRASS list and was advised that this list might be a better place to ask:<br>
<br>
Is the scale error only in longitude and never in latitude? Or can it be in both? Is there a way to find the error for a length error rather than an area error? Specifically, for a vector line with an arbitrary heading?<br>
<br>
Thank you,<br>
<br>
-k.<br>
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