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1
NGA’s Position on “Web-Mercator”
Craig Rollins and Mike Paniccia
NGA Office of Geomatics
(314) 676-9124
ESRI Users Confe...
2
NGA’s Authority
• National Imagery and Mapping Agency, Department of Defense World
Geodetic System 1984 — Its Definition...
3
• Web-Mercator is unacceptable for use in National System of
Geospatial-Intelligence (NSG) products/services
• “NGA does...
4
Agenda
1. What is “web-Mercator”?
2. Why was it invented?
3. What’s wrong with it?
4. What does NGA recommend instead?
A...
5
Short Answers
1. What is “web-Mercator”?
– Ellipsoidal Lat./Lon. used with abbreviated (spherical) Mercator formula
2. W...
6
Agenda
1. What is “web-Mercator”?
2. Why was it invented?
3. What’s wrong with it?
4. What does NGA recommend instead?
A...
7
Symbols Explained
1
tanharctanh 







y
x
e
a


semi-major axis of the ellipsoid (radius of the Equator)
ecc...
8http://www.hpmuseum.org/hp15.htmApproved for Public Release, 15-519
9
The formulas for Mercator (EPSG::3395) are:
The formulas for web-Mercator (EPSG::3857) are:
Mercator v. web-Mercator
)si...
10
1 + 2 = 6
Don’t need a Math degree…
+ 3
Approved for Public Release, 15-434
11
Agenda
1. What is “web-Mercator”?
2. Why was it invented?
3. What’s wrong with it?
4. What does NGA recommend instead?
...
12
The formulas for Mercator (EPSG::3395) are:
The formulas for web-Mercator (EPSG::3857) are:
Mercator v. web-Mercator v....
13
Web-Mercator’s Properties
1. Almost conformal
2. Inverse, i.e. (x, y) to (Lon., Lat.), is accurate
3. Inverse is faster...
14
Mercator web-Mercator
Mercator v. web-Mercator
Approved for Public Release, 15-170
15
Agenda
1. What is “web-Mercator”?
2. Why was it invented?
3. What’s wrong with it?
4. What does NGA recommend instead?
...
16
Commonality
• is the Prime Meridian
• is the Equator
• The Equator is represented at scale 1:1
0x
0y
Approved for Pub...
17
Approved for Public Release, 15-170
Mercator
v.
web-Mercator
18
Web-Mercator
Mercator
v.
web-Mercator
36,700 m at 59°N
33,000 m at 50°N
Visual illustration
of the difference
in map-pr...
19
Mercator v. web-Mercator
Plot of the
difference in
map-projection
Approved for Public Release, 15-519
20
The formulas for Mercator (EPSG::3395) are:
The formulas for web-Mercator (EPSG::3857) are:
Mercator v. web-Mercator
)s...
21
Mercator v. web-Mercator
Error in navigation if mismatch of map-
projection between data and reader
Approved for Public...
22
Navigation
Error:
11′ of Lat.
(13 mi)
(if data and
reader are
mismatched)
2′ graticule
Mercator
projection
I am here us...
23
Almost forgot
to switch from
Mercator to
Web-Mercator
Source: U.S. National Archive
Approved for Public Release, 15-519
24
What’s wrong with web-Mercator?
1. Conflicts with Mercator, e.g. NGA nautical charts
2. Is non-conformal, unlike NGA st...
25
Its defenders say…
1. Almost conformal.
2. Inverse, i.e. (x, y) to (Lon., Lat.), is accurate.
3. Inverse is faster and ...
26
NGA replies …
1. Almost conformal. Mercator actually is
2. Inverse, i.e. (x, y) to (Lon., Lat.), is accurate. (True)
3....
27
Web-Mercator Policy for U.S. DoD
• Web-Mercator is unacceptable for use in DoD products/services
Approved for Public Re...
28
Agenda
1. What is “web-Mercator”?
2. Why was it invented?
3. What’s wrong with it?
4. What does NGA recommend instead?
...
29
• Zoom level n has:
• 2n tiles across
• 2n tiles down
• Each tile is 256 x 256
pixels
• Level-0 Tile extent:
180°W to 1...
30
Innovation or Tradition?
• Tiled Mercator improves all
current systems.
• Science/math are done.
• Changes occur in the...
31
Progress and collaboration…
Various components of
U.S. DoD
Formulate tiled Mercator specification
Write NSG Profile of ...
32
Summary
1. What is “web-Mercator”?
– Ellipsoidal Lat./Lon. used with abbreviated (spherical) Mercator formula
2. Why wa...
33
nga.mil | @nga_geoint | facebook.com/natlgeointagency
Questions?
34
Other topics
5. Sphere
6. WGS 84 compliance
7. Nautical charting
8. Non-conformality of web-Mercator
9. Web-Mercator x,...
35
The formulas for Mercator (EPSG::3395) are:
The formulas for web-Mercator (EPSG::3857) are:
Mercator v. web-Mercator
)s...
36
Sphere vs Ellipsoid
Approved for Public Release, 15-519
37
Sphere vs Ellipsoid
φ = geographic latitude
ψ = geocentric latitude
Approved for Public Release, 15-170
38
Sphere vs Ellipsoid
= geographic latitude
P′


Approved for Public Release, 15-519
39
P′
Sphere vs Ellipsoid
φ = geographic latitude
ψ = geocentric latitude
Approved for Public Release, 15-170
40
Other topics
5. Sphere
6. WGS 84 compliance
7. Nautical charting
8. Non-conformality of web-Mercator
9. Web-Mercator x,...
41
Datum & ellipsoid
Datum Ellipsoid
(historic):
NAD 27 Clarke 1866
Luzon Clarke 1866
European 1950 International 1924
Hon...
42
Web-Mercator confuses things:
• Datum’s ellipsoid ≠ map-projection’s ellipsoid
• Conundrum:
– Spherical Mercator is con...
43
Other topics
5. Sphere
6. WGS 84 compliance
7. Nautical charting
8. Non-conformality of web-Mercator
9. Web-Mercator x,...
44
Chart type Mercator Other TOTAL
Harbor 3856 825 4681
Approach 1218 108 1326
Coastal 2567 327 2894
Bottom Contour 505 22...
45UNCLASIFIED
GeoPackage Technical Meeting
Putting Digital Nautical Charts and other data
in mobile customer’s hands
NGA M...
46
Other topics
5. Sphere
6. WGS 84 compliance
7. Nautical charting
8. Non-conformality of web-Mercator
9. Web-Mercator x,...
47
Approved for Public Release, 15-519
48
n Mercator E-W web-Mercator N-S
Mercator N-S
web-Mercator E-W
0 156448.30995015 155402.25260025
2 39112.07748754 38850....
49
zoom E-W bar N-S bar Scale
level pixels pixels
13 52 53 1:68000
14 105 105 1:34000
15 209 211 1:17000
16 419 422 1:8500...
50
Other topics
5. Sphere
6. WGS 84 compliance
7. Nautical charting
8. Non-conformality of web-Mercator
9. Web-Mercator x,...
51
From: NGA tile server
April 15, 2015
Web-Mercator x, y is never used ?
<BoundingBox SRS=“EPSG:3857” minx=“2.0037508E7”
...
52
Kuiper, James A., Andrew J. Ayers, Michael E. Holm, and Michael J. Nowak. "Python Coding of Geospatial Processing in
We...
53
Other topics
5. Sphere
6. WGS 84 compliance
7. Nautical charting
8. Non-conformality of web-Mercator
9. Web-Mercator x,...
54
Army Program: Raster Graphics
for Mobile/Hand-Held Devices
• GeoPackage
• Allowed map-projections:
• Tiled Mercator
• T...
55
What’s the Difference?
• Scale!
World
Mercator
Transverse
Mercator
Polar
Stereographic
Customary Projections 1.0 0.9996...
56
• Used in nautical products
• Latitude of true scale is:
±31.0606963703645°.
• Scale reduction factor at the Equator is...
57
Tiled Transverse Mercator
• Used in topographic products
• Scale reduction factor at the Central
Meridian (CM) is 0.858...
58
What we have:
Transverse Mercator in ArcGIS
Approved for Public Release, 15-170
What we want:
59
Tiled Polar Stereographic
• Used in products near the pole
• Scale factor at the latitude of true
scale is 0.9286474122...
60
Tiled Polar Stereographic
South North
Approved for Public Release, 15-170
61
How to Display Tiled Mercator in ArcGIS
What we want:What we have:
Approved for Public Release, 15-170
62
Adjust the Scale
Approved for Public Release, 15-170
63
Clip into a Square
Approved for Public Release, 15-170
64
The New Projections in ArcGIS
Tiled Mercator!
Approved for Public Release, 15-170
65
Summary
• No more web-Mercator!
• Replacements are conformal, and thus suitable for navigation and targeting
• The repl...
66
Additional Slides
67
The formulas for Mercator (EPSG::3395) are:
The formulas for web-Mercator (EPSG::3857) are:
Mercator v. web-Mercator

...
68
Plate Carrée 15° x 15° graticule
Approved for Public Release, 15-519
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NGA’s Position on “Web-Mercator”

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Presentation by Craig Rollins and Mike Paniccia from the National Geospatial-Intelligence Agency for the ESRI Users Conference, July 22, 2015

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NGA’s Position on “Web-Mercator”

  1. 1. 1 NGA’s Position on “Web-Mercator” Craig Rollins and Mike Paniccia NGA Office of Geomatics (314) 676-9124 ESRI Users Conference July 22, 2015
  2. 2. 2 NGA’s Authority • National Imagery and Mapping Agency, Department of Defense World Geodetic System 1984 — Its Definition and Relationships with Local Geodetic Systems, NIMA Technical Report 8350.2 Third Edition, 1997. • CJCSI 3900.01C, “Position (Point and Area) Reference Procedures”, 30 June 2007 • Department of Defense Directive 5105.60 (DoDD 5105.60), “Subject: National Geospatial-Intelligence Agency (NGA)”, July 29, 2009 • NGA.SIG.0011_1.0_WEBMERC, “Web Mercator Map Projection”, February 18, 2014 • NGA Advisory Notice on "Web Mercator”, May 22, 2014 http://earth-info.nga.mil/GandG/wgs84/web_mercator/index.html Approved for Public Release, 15-434
  3. 3. 3 • Web-Mercator is unacceptable for use in National System of Geospatial-Intelligence (NSG) products/services • “NGA does not endorse nor does NGA support the spherical based web-Mercator map projection”. – NGA.SIG.0011_1.0.0_WEBMERC, May 2014 • Many commercial GIS packages can convert from web- Mercator into WGS 84 compliant projections. Web-Mercator Policy Approved for Public Release, 15-519
  4. 4. 4 Agenda 1. What is “web-Mercator”? 2. Why was it invented? 3. What’s wrong with it? 4. What does NGA recommend instead? Approved for Public Release, 15-519
  5. 5. 5 Short Answers 1. What is “web-Mercator”? – Ellipsoidal Lat./Lon. used with abbreviated (spherical) Mercator formula 2. Why was it invented? – Better than Plate Carrée; simpler than true (ellipsoidal) Mercator 3. What’s wrong with it? – Conflicts with Mercator; impedes interoperability; duplicates IT effort 4. What does NGA recommend instead? – Mercator; projections like NGA standard products; Tiled Mercator Approved for Public Release, 15-519
  6. 6. 6 Agenda 1. What is “web-Mercator”? 2. Why was it invented? 3. What’s wrong with it? 4. What does NGA recommend instead? Approved for Public Release, 15-519
  7. 7. 7 Symbols Explained 1 tanharctanh         y x e a   semi-major axis of the ellipsoid (radius of the Equator) eccentricity of the ellipsoid (shape of the ellipsoid) longitude (in radians), “lambda” latitude (in radians), “phi” vertical map-projection coordinate horizontal map-projection coordinate (two notations for the inverse hyperbolic tangent) Approved for Public Release, 15-519
  8. 8. 8http://www.hpmuseum.org/hp15.htmApproved for Public Release, 15-519
  9. 9. 9 The formulas for Mercator (EPSG::3395) are: The formulas for web-Mercator (EPSG::3857) are: Mercator v. web-Mercator )sin(arctanh)(sinarctanh   eeaay ax   )(sinarctanh   ay ax   Approved for Public Release, 15-170
  10. 10. 10 1 + 2 = 6 Don’t need a Math degree… + 3 Approved for Public Release, 15-434
  11. 11. 11 Agenda 1. What is “web-Mercator”? 2. Why was it invented? 3. What’s wrong with it? 4. What does NGA recommend instead? Approved for Public Release, 15-170
  12. 12. 12 The formulas for Mercator (EPSG::3395) are: The formulas for web-Mercator (EPSG::3857) are: Mercator v. web-Mercator v. Plate Carrée )sin(arctanh)(sinarctanh   eeaay ax   )(sinarctanh   ay ax   The formulas for Plate Carrée (~EPSG::4326) are:   ay ax   Approved for Public Release, 15-170
  13. 13. 13 Web-Mercator’s Properties 1. Almost conformal 2. Inverse, i.e. (x, y) to (Lon., Lat.), is accurate 3. Inverse is faster and easier to code Approved for Public Release, 15-519
  14. 14. 14 Mercator web-Mercator Mercator v. web-Mercator Approved for Public Release, 15-170
  15. 15. 15 Agenda 1. What is “web-Mercator”? 2. Why was it invented? 3. What’s wrong with it? 4. What does NGA recommend instead? Approved for Public Release, 15-519
  16. 16. 16 Commonality • is the Prime Meridian • is the Equator • The Equator is represented at scale 1:1 0x 0y Approved for Public Release, 15-519
  17. 17. 17 Approved for Public Release, 15-170 Mercator v. web-Mercator
  18. 18. 18 Web-Mercator Mercator v. web-Mercator 36,700 m at 59°N 33,000 m at 50°N Visual illustration of the difference in map-projection Approved for Public Release, 15-170
  19. 19. 19 Mercator v. web-Mercator Plot of the difference in map-projection Approved for Public Release, 15-519
  20. 20. 20 The formulas for Mercator (EPSG::3395) are: The formulas for web-Mercator (EPSG::3857) are: Mercator v. web-Mercator )sin(arctanh)(sinarctanh   eeaay ax   )(sinarctanh   ay ax   Approved for Public Release, 15-170
  21. 21. 21 Mercator v. web-Mercator Error in navigation if mismatch of map- projection between data and reader Approved for Public Release, 15-170
  22. 22. 22 Navigation Error: 11′ of Lat. (13 mi) (if data and reader are mismatched) 2′ graticule Mercator projection I am here using web-Mercator data on a Mercator device. Friendlies arrive here based on bad info 13miles Approved for Public Release, 15-519
  23. 23. 23 Almost forgot to switch from Mercator to Web-Mercator Source: U.S. National Archive Approved for Public Release, 15-519
  24. 24. 24 What’s wrong with web-Mercator? 1. Conflicts with Mercator, e.g. NGA nautical charts 2. Is non-conformal, unlike NGA standard products 3. Contributes no new desirable property 4. Cuts-corners on Mercator implementation Approved for Public Release, 15-519
  25. 25. 25 Its defenders say… 1. Almost conformal. 2. Inverse, i.e. (x, y) to (Lon., Lat.), is accurate. 3. Inverse is faster and easier to code. 4. No one cares about (x, y) anyway. 5. “Visualization only”. 6. “Industry standard”. Approved for Public Release, 15-519
  26. 26. 26 NGA replies … 1. Almost conformal. Mercator actually is 2. Inverse, i.e. (x, y) to (Lon., Lat.), is accurate. (True) 3. Inverse is faster and easier to code. Devices: more power 4. No one cares about (x, y) anyway. Know the future? Pix 5. “Visualization only”. Likely not; analysts will use data 6. “Industry standard”. DoD, IC are to use WGS 84 ellipsoid Approved for Public Release, 15-519
  27. 27. 27 Web-Mercator Policy for U.S. DoD • Web-Mercator is unacceptable for use in DoD products/services Approved for Public Release, 15-519
  28. 28. 28 Agenda 1. What is “web-Mercator”? 2. Why was it invented? 3. What’s wrong with it? 4. What does NGA recommend instead? Approved for Public Release, 15-170
  29. 29. 29 • Zoom level n has: • 2n tiles across • 2n tiles down • Each tile is 256 x 256 pixels • Level-0 Tile extent: 180°W to 180°E (exact), between latitudes: ±85.0840590501104° Tiled Mercator Level 0 Level 1 Level 2 Approved for Public Release, 15-170
  30. 30. 30 Innovation or Tradition? • Tiled Mercator improves all current systems. • Science/math are done. • Changes occur in the background and don’t alter user experience. • Saves money by using consistent projection. • Stick with the 1990s math Approved for Public Release, 15-170
  31. 31. 31 Progress and collaboration… Various components of U.S. DoD Formulate tiled Mercator specification Write NSG Profile of GeoPackage: include Mercator; omit web-Mercator Write NGA.SIG.0014: recommended projections for tiled raster graphics Adopt NSG Profile of GeoPackage Include tiled Mercator in a Web Map Tile Service (WMTS) Develop capability to generate tiled Mercator in GeoPackages Implement GeoPackages into Nett Warrior software baseline Approved for Public Release, 15-519
  32. 32. 32 Summary 1. What is “web-Mercator”? – Ellipsoidal Lat./Lon. used with abbreviated (spherical) Mercator formula 2. Why was it invented? – Better than Plate Carrée; simpler than true (ellipsoidal) Mercator; 3. Why is it wrong for DoD and IC? – Conflicts with Mercator; impedes interoperability; duplicates IT effort 4. What does NGA recommend instead? – Mercator; projections like NGA standard products; Tiled Mercator Approved for Public Release, 15-519
  33. 33. 33 nga.mil | @nga_geoint | facebook.com/natlgeointagency Questions?
  34. 34. 34 Other topics 5. Sphere 6. WGS 84 compliance 7. Nautical charting 8. Non-conformality of web-Mercator 9. Web-Mercator x, y is never used ? 10. NGA’s guidance for tiled raster graphics Approved for Public Release, 15-519
  35. 35. 35 The formulas for Mercator (EPSG::3395) are: The formulas for web-Mercator (EPSG::3857) are: Mercator v. web-Mercator )sin(arctanh)(sinarctanh   eeaay ax   )(sinarctanh   ay ax   Note that e = 0 gives a sphere of radius a. Approved for Public Release, 15-519
  36. 36. 36 Sphere vs Ellipsoid Approved for Public Release, 15-519
  37. 37. 37 Sphere vs Ellipsoid φ = geographic latitude ψ = geocentric latitude Approved for Public Release, 15-170
  38. 38. 38 Sphere vs Ellipsoid = geographic latitude P′   Approved for Public Release, 15-519
  39. 39. 39 P′ Sphere vs Ellipsoid φ = geographic latitude ψ = geocentric latitude Approved for Public Release, 15-170
  40. 40. 40 Other topics 5. Sphere 6. WGS 84 compliance 7. Nautical charting 8. Non-conformality of web-Mercator 9. Web-Mercator x, y is never used ? 10. NGA’s guidance for tiled raster graphics Approved for Public Release, 15-519
  41. 41. 41 Datum & ellipsoid Datum Ellipsoid (historic): NAD 27 Clarke 1866 Luzon Clarke 1866 European 1950 International 1924 Hong Kong 1963 International 1924 (modern): NAD 83 GRS 80 WGS 84 WGS 84 Approved for Public Release, 15-519
  42. 42. 42 Web-Mercator confuses things: • Datum’s ellipsoid ≠ map-projection’s ellipsoid • Conundrum: – Spherical Mercator is conformal – web-Mercator is spherical Mercator (?) – web-Mercator is NOT conformal • Map-projection procedure ≠ map-projection properties Approved for Public Release, 15-519
  43. 43. 43 Other topics 5. Sphere 6. WGS 84 compliance 7. Nautical charting 8. Non-conformality of web-Mercator 9. Web-Mercator x, y is never used ? 10. NGA’s guidance for tiled raster graphics Approved for Public Release, 15-519
  44. 44. 44 Chart type Mercator Other TOTAL Harbor 3856 825 4681 Approach 1218 108 1326 Coastal 2567 327 2894 Bottom Contour 505 22 527 Bathymetric Nav. Planning 586 30 616 TOTAL 8732 1312 10044 Nautical charts • Source: Production Management Alternate Architecture (PMAA, 4/23/2015) • PMAA combines Harbor/Approach. Here, harbor charts are 1:50,000 or larger • “Other”: transverse Mercator, gnomonic, polyconic, polar stereographic, other • BUT there are no instances of web-Mercator (“pseudo-Mercator”) Approved for Public Release, 15-519
  45. 45. 45UNCLASIFIED GeoPackage Technical Meeting Putting Digital Nautical Charts and other data in mobile customer’s hands NGA Maritime Safety Office DNC Mobile Apps 7 April 2015 Approved for Public Release, 15-519
  46. 46. 46 Other topics 5. Sphere 6. WGS 84 compliance 7. Nautical charting 8. Non-conformality of web-Mercator 9. Web-Mercator x, y is never used ? 10. NGA’s guidance for tiled raster graphics Approved for Public Release, 15-519
  47. 47. 47 Approved for Public Release, 15-519
  48. 48. 48 n Mercator E-W web-Mercator N-S Mercator N-S web-Mercator E-W 0 156448.30995015 155402.25260025 2 39112.07748754 38850.56315006 4 9778.01937188 9712.64078752 6 2444.50484297 2428.16019688 8 611.12621074 607.04004922 10 152.78155269 151.76001230 12 38.19538817 37.94000308 14 9.54884704 9.48500077 16 2.38721176 2.37125019 18 0.59680294 0.59281255 20 0.14920074 0.14820314 22 0.03730018 0.03705078 24 0.00932505 0.00926270 Meters/pixel at latitude 2 deg (e.g. Mogadishu) Approved for Public Release, 15-519
  49. 49. 49 zoom E-W bar N-S bar Scale level pixels pixels 13 52 53 1:68000 14 105 105 1:34000 15 209 211 1:17000 16 419 422 1:8500 17 838 843 1:4200 18 1676 1687 1:2100 19 3351 3374 1:1100 20 6702 6747 1:530 1 km scale bars at latitude 2 deg (e.g. Mogadishu) for web-Mercator (Scale is calculated using 0.28 mm as the device pixel size) Approved for Public Release, 15-519
  50. 50. 50 Other topics 5. Sphere 6. WGS 84 compliance 7. Nautical charting 8. Non-conformality of web-Mercator 9. Web-Mercator x, y is never used ? 10. NGA’s guidance for tiled raster graphics Approved for Public Release, 15-519
  51. 51. 51 From: NGA tile server April 15, 2015 Web-Mercator x, y is never used ? <BoundingBox SRS=“EPSG:3857” minx=“2.0037508E7” miny=“2.0037508E7” maxx=“2.0037508E7” maxy=“2.0037508E7”/> Approved for Public Release, 15-519
  52. 52. 52 Kuiper, James A., Andrew J. Ayers, Michael E. Holm, and Michael J. Nowak. "Python Coding of Geospatial Processing in Web-based Mapping Applications." PROC. OF THE 13th PYTHON IN SCIENCE CONF : 40-46. SCIPY 2014. Web. Web-Mercator x, y is never used ? Approved for Public Release, 15-519
  53. 53. 53 Other topics 5. Sphere 6. WGS 84 compliance 7. Nautical charting 8. Non-conformality of web-Mercator 9. Web-Mercator x, y is never used ? 10. NGA’s guidance for tiled raster graphics Approved for Public Release, 15-519
  54. 54. 54 Army Program: Raster Graphics for Mobile/Hand-Held Devices • GeoPackage • Allowed map-projections: • Tiled Mercator • Tiled Transverse Mercator • Tiled Polar Stereographic • Actual meters/pixel depends on … • Common tile pyramid • Map-projection scale parameters • Zoom-level • Location on Earth Zoom Level Meters/pixel 0 134217.728 1 67108.864 2 33554.432 3 16777.216 4 8388.608 5 4194.304 6 2097.152 7 1048.576 8 524.288 9 262.144 10 131.072 11 65.536 12 32.768 13 16.384 14 8.192 15 4.096 16 2.048 17 1.024 18 0.512 19 0.256 20 0.128 21 0.064 22 0.032 23 0.016 24 0.008 Approved for Public Release, 15-170
  55. 55. 55 What’s the Difference? • Scale! World Mercator Transverse Mercator Polar Stereographic Customary Projections 1.0 0.9996 0.994 Tiled Projections 0.857385503731176 0.85882463752355 0.9286474122935 Zoom Level Meters/pixel 0 134217.728 1 67108.864 2 33554.432 … … 22 0.032 23 0.016 24 0.008 Approved for Public Release, 15-170
  56. 56. 56 • Used in nautical products • Latitude of true scale is: ±31.0606963703645°. • Scale reduction factor at the Equator is 0.857385503731176. • Level-0 tile is 180°W to 180°E (exactly) and between latitudes: ±85.0840590501104°. Tiled Mercator Approved for Public Release, 15-170
  57. 57. 57 Tiled Transverse Mercator • Used in topographic products • Scale reduction factor at the Central Meridian (CM) is 0.85882463752355. • Longitude-at-the-Equator of true scale is ±30.700524332812° from the CM. • The vertical extent is the entire central and anti-central meridians. Approved for Public Release, 15-170
  58. 58. 58 What we have: Transverse Mercator in ArcGIS Approved for Public Release, 15-170 What we want:
  59. 59. 59 Tiled Polar Stereographic • Used in products near the pole • Scale factor at the latitude of true scale is 0.9286474122935. • Latitude of true scale is exactly 59°N or 59°S. • North and South have separate tiles. Approved for Public Release, 15-170
  60. 60. 60 Tiled Polar Stereographic South North Approved for Public Release, 15-170
  61. 61. 61 How to Display Tiled Mercator in ArcGIS What we want:What we have: Approved for Public Release, 15-170
  62. 62. 62 Adjust the Scale Approved for Public Release, 15-170
  63. 63. 63 Clip into a Square Approved for Public Release, 15-170
  64. 64. 64 The New Projections in ArcGIS Tiled Mercator! Approved for Public Release, 15-170
  65. 65. 65 Summary • No more web-Mercator! • Replacements are conformal, and thus suitable for navigation and targeting • The replacements are: Tiled Mercator Tiled Transverse Mercator Tiled Polar Stereographic (North and South) Approved for Public Release, 15-170
  66. 66. 66 Additional Slides
  67. 67. 67 The formulas for Mercator (EPSG::3395) are: The formulas for web-Mercator (EPSG::3857) are: Mercator v. web-Mercator               24 tanln   ay ax                         2/ sin1 sin1 24 tanln e e e ay ax    Approved for Public Release, 15-519
  68. 68. 68 Plate Carrée 15° x 15° graticule Approved for Public Release, 15-519

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