[Proj] "Reverse" graticule for the transverse Mercator projection

[Noel Zinn (cc)]

Charles,

This is too cool!  It is particularly interesting at the intersection of the 
Equator and the Y-axis (the "meta poles"?), where the TM scale factor 
decreases the size on the Earth of the 1000 grid km spacing.

Is this the Karney-Kruger TM algorithm ... or Lee?

Noel

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)

-----Original Message----- 
From: Charles Karney
Sent: Tuesday, July 26, 2011 10:14 AM
To: PROJ.4 and general Projections Discussions
Subject: [Proj] "Reverse" graticule for the transverse Mercator projection

Projections are often visualized by plotting graticules, lines of
constant latitude or longitude, in the projected space.  With tools such
as Google Earth that allow you to see the world in 3d, it makes sense to
display the *reverse* graticule for the projection, that is lines of
constant easting and northing on the 3d world.

For your amusement, download

   http://geographiclib.sourceforge.net/tm-graticule.kml

and load into Google Earth.  This shows the reverse graticule for
transverse Mercator for the WGS84 ellipsoid with a 1000 km spacing.  I
adjusted the scale so that the distance from the equator to the pole is
10000 km and chose the prime meridian for the central meridian.  The
projection is well behaved at the north and south poles.  The projection
has a branch cut on the equator near the "meta poles", namely for
longitude in [-97.36373, -82.63627] and in [82.63627, 97.36373].

-- 
Charles Karney <charles.karney at sri.com>
SRI International, Princeton, NJ 08543-5300
Tel: +1 609 734 2312
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