Sep. 21-22, 2006v FME Worldwide User Conference – Vancouver

Reprojection Problems: Art or Error? Dean Hintz, Safe Software

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ASRP Mixes Cartesian and Polar LL84

All ASRP LL84 coords, But zone 1,8 are polar projections

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Our Fix

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Need for Degrees to Meters conversion Based on Latitude

The Problem: 1 degree can represent radically different distances on the

earths surface depending on where you are. This can become a problem when defining a spatial

reference. Image source resolution usually based on ground distance.

SDE rastermap: first tile in sets the resolution.

For example, at the equator: 1 degree lat = 110574m 1 degree long = 111319m

At 50N: 1 degree lat = 111229 m 1 degree long = 71696 m

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Source ASRP UKH601

Sample source ASRP UKH601

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SDE mosaic: Northern tile is loaded first

UKH601 in SDE mosaic when EUH805 is loaded first

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SDE Mosaic: Southern tile is loaded first

UKH601 in SDE mosaic when UKH601 is loaded first

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Approaches Considered

Solution 1: force most southern tile to load first, or always use equitorial resolution.

Solution 2: Calculate resolution based on minimum latitude

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Step 1: Calculate meters per degree for minimum latitude

rlat = reference latitude in radians = reference latitude * pi/180

At 50 degrees N: rlat = 50* pi/180 = 0.872665 rads

Meters per degree Longitude: = 111132.92 - 559.82 * cos(2* rlat) + 1.175*cos(4*rlat) = 111132.92 - 559.82 * cos(2* 0.872665)+1.175*cos(4*0.872665) = 111132.92 + 97.21 - 1.10 = 111229.0 m/degree latitude

Meters per degree Latitude: = 111412.84 * cos(rlat) - 93.5 * cos(3*rlat) = 111412.84 * cos(0.872665) - 93.5 * cos(3*0.872665) = 71614.79 + 80.97 = 71695.8 m/degree longitude

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Step 2: Calculate degrees per meter for desired resolution

Meters = Degrees * (meters per degree)Degrees = Meters / (meters per degree)

DegreesX = 100m / 71696 m per degree =0.00139 degrees / 100 m per degree

DegreesY = 100m/111229 m per degree =0.000899 degrees / 100 m per degree

Desired resolution at 50N for 100x100m pixel is: X = 0.00139, Y = 0.000899

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Resampler Workspace

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SDE mosaic: tiles resampled to southern most resolution

UKH601 in SDE mosaic when all tiles are resampled to UKH601 resolution.

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Theory & References

Converting UTM to Latitude and Longitude (Or Vice Versa); Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay

http://www.uwgb.edu/dutchs/UsefulData/UTMFormulas.htm

An on-line calculator implemented with Java Script can be seen on the Federation of American Scientists website at:

http://www.fas.org/news/reference/calc/degree.html

An example function implementation from Physical Oceanography, U of California, San Diego

http://www-pord.ucsd.edu/~matlab/coord.htm

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Global Projections

Mercator Demo: Canada as the centre of the Universe

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Mercator - default

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Mercator - Clipped