Dataset Open Access

Test data for the transverse Mercator projection

Karney, Charles F. F.

This is a set of 287000 geographic points together with their coordinates in the transverse Mercator projection. The WGS84 ellipsoid (equatorial radius a = 6378137 m, flattening f = 1/298.257223563) is used, with central meridian 0°, central scale factor 0.9996 (the UTM value), false easting = false northing = 0 m.

Each line of the test set gives 6 space delimited numbers

  • latitude, φ (degrees, exact)
  • longitude, λ (degrees, exact — see below)
  • easting (meters, accurate to 0.1 pm)
  • northing (meters, accurate to 0.1 pm)
  • meridian convergence (degrees, accurate to 10−18 deg)
  • scale (accurate to 10−20)

These are computed using high-precision calculations using the exact formulas for the projection, see Lee (1976). The latitude and longitude are all multiples of 10−12 deg and should be regarded as exact, except that λ = 82.63627282416406551° should be interpreted as exactly (1 − e) 90°, where e is the eccentricity given by e2 = f (2 − f ).

The contents of the file are as follows:

  • 250000 entries randomly distributed in φ ∈ [0°, 90°], λ ∈ [0°, 90°]
  • 1000 entries randomly distributed on φ ∈ [0°, 90°], λ = 0°
  • 1000 entries randomly distributed on φ = 0°, λ ∈ [0°, 90°]
  • 1000 entries randomly distributed on φ ∈ [0°, 90°], λ = 90°
  • 1000 entries close to φ = 90° with λ ∈ [0°, 90°]
  • 1000 entries close to φ = 0°, λ = 0° with φ ≥ 0°, λ ≥ 0°
  • 1000 entries close to φ = 0°, λ = 90° with φ ≥ 0°, λ ≤ 90°
  • 2000 entries close to φ = 0°, λ = (1 − e) 90° with φ ≥ 0°
  • 25000 entries randomly distributed in φ ∈ [−89°, 0°], λ ∈ [(1 − e) 90°, 90°]
  • 1000 entries randomly distributed on φ ∈ [−89°, 0°], λ = 90°
  • 1000 entries randomly distributed on φ ∈ [−89°, 0°], λ = (1 − e) 90°
  • 1000 entries close to φ = 0°, λ = 90° (φ < 0°, λ ≤ 90°)
  • 1000 entries close to φ = 0°, λ = (1 − e) 90° (φ < 0°, λ ≤ (1 − e) 90°)

The entries for φ < 0° and λ ∈ [(1 − e) 90°, 90°] use the “extended” domain for the transverse Mercator projection explained in Sec. 5 of Karney (2011). The first 258000 entries have φ ≥ 0° and are suitable for testing implementations following the standard convention.

Files (34.4 MB)
Name Size
TMcoords.dat
md5:91b817eae34aef3cd8d67b5a4e8e798f
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  • C. F. F. Karney, Transverse Mercator with an accuracy of a few nanometers, J. Geodesy 85(8), 475-485 (2011).
  • L. P. Lee, Conformal Projections Based on Elliptic Functions, (B. V. Gutsell, Toronto, 1976).
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