Post on 15-Apr-2020
Web Mercator Projection & Raster Tile Maps
Two cornerstones of Online Map Service Providers
Emmanuel Stefanakis Dept. of Geodesy & Geomatics Engineering
University of New Brunswick
estef@unb.ca
Annual Conference – 2017 – Ottawa May 31- June 2, 2017
Online Map Service Providers
O Available for ~12 years
O Well established (difficult to remember how
life was without them)
2
Online Map Service Providers
3
4
Online Map Service Providers
Challenges ?
• Technological
• Cartographical
Online Map Service Providers Framework
CLIENT
HTTP
Request (where/what/resolution)
Map Product
SERVER
End-users
Map Repository (Data+Images)
Map Service
5
Technological Challenges
O High and steadily increasing demand
O Voluminous data (vectors and images)
O Bandwidth limitations
O Concurrent access
O Security issues
O Data protection
6
Cartographical Challenges
O Visualize the map on Web browser
O flat/rectangular monitor
O Multi-resolution representation
O various zoom levels
O Multi-theme mapping
O various themes (layers)
O Multi-language mapping
O various languages
7
8
Online Map Service Providers
Web Mercator
Projection
Raster Tile
Maps
Map Product Flat Monitor
CLIENT
HTTP
Request (where/what/resolution)
Map Product
SERVER
Map Repository (Data+Images)
Map Service
9
Map Projection
X
Y
φ
λ(Χ,Υ) ƒ(φ, λ)
X
Y
X
Y
φ
λ
φ
λ(Χ,Υ) ƒ(φ, λ)
O A function f ...
10
Choose a Map Projection
11
Choose a Cylindrical
O Best fit
O Rectangular grid
12
Conical Projection ?
13
Conical Projection ?
14
Cylindrical Projection ?
15
Cylindrical Projection
O Simulation of a cylindrical projection
16
Cylindrical Projection
O Simulation of a cylindrical projection
17
Which Cylindrical?
Miller’s
Plate Carree
Mercator
18
Mercator Projection
O Most popular
O Conformal
O Easy math (low complexity)
O …to serve high demand
19
Mercator Projection
X
Y
X
Y
X
Y
φ
λ
2πR
2πRcos(φ) < 2πR
2πR
2πR
20
1512-1594
O Conformal
O Support navigation in Seas
Mercator Projection
2πR
2πR
21
Mercator Projection
Scale factor on horizontal (along parallels at φ): 2πRcos(φ) 2πR
Mercator’s goal preserve
shapes/directions
22
Mercator Projection
Scale factor on horizontal (along parallels at φ): 2πRcos(φ) 2πR
Mercator applied… Scale factor on vertical (along meridians at φ): 2πRcos(φ) 2πR
23
Mercator Projection
All parallels have the same length = equator (2πR)
At latitude φ the scale factor on the parallel is equal to:
secφRcosφ2π
R2π
φ
24
Mercator Projection
Mercator applied the same factor on the parallels… The actual distance between two parallels at latitude φ is equal to: He made it equal to:
dN = R secφ dφ
dN = R dφ
φ2
φ1
dN
25
Mercator Projection
By integrating the last formula we get: (sphere)
2
φ45RlntandφsecφRN o
φ
0
equator
North pole
South pole
φ
N
2π R
φ
2π R
26
Mercator Projection O Spherical Formulas
Easting
Northing
Sphere
P(φs , λs)
Spherical Formulas
P(Es , Ns)
27
Mercator Projection O Ellipsoidal Formulas
Easting
Northing
P(φe , λe)
WGS’84
Ellipsoidal Formulas
P(Ee , Ne)
28
Mercator Projection O Spherical Formulas
O Ellipsoidal Formulas
Easting
Northing
Easting
Northing
29
Adopt Mercator Projection
CLIENT
HTTP
Request (where/what/resolution)
Map Product
SERVER
Map Repository (Data+Images)
Map Service
30
O Ellipsoid Coordinates
O Mercator Projection
Web Mercator O Make it even less computational expensive
O Ellipsoid Coordinates – Spherical Formulas
P(φe , λe)
WGS’84
Sphere
P(φs , λs)
Web Mercator
Spherical Formulas
P(E, N)
31
32
Online Map Service Providers
Web Mercator
Projection
Web Mercator (vs) Mercator
O Mercator basic properties are lost
O Non-Conformal
O Loxodromes Not straight lines
O Rationale (Google)
O Simpler calculations
O Map to be projected on a computer monitor
O No body can notice the differences
33
34
Criticism
O Geodesy Subcommittee of the Oil and Gas
Producers (aka EPSG) rejected it in 2008 as
“technically flawed” & “an inappropriate geodesy
and cartography”
O National Geospatial-Intelligence Agency of the
US Department of Defense declared it as
“unacceptable for any official use, because a
general lack of understanding of its properties
has caused considerable confusion and misuse”
35
A Code for Web Mercator
O An unofficial code “900913” (GOOGLE
spelled with numbers) was initially assigned
O Later, EPSG introduced an official identifier:
EPSG:3857 -- WGS84 Web Mercator
(Auxiliary Sphere)
36
Web Mercator Map of the World
O Absolute square…
O Very convenient in
panning, tiling, and
indexing
37
40,075,017.25
40,0
75,0
17.2
5
85.051129 South
85.051129 North
38
Online Map Service Providers
Challenges ?
• Technological
• Cartographical
How to deliver the map product?
CLIENT
HTTP
Request (where/what/resolution)
Map Product
SERVER
Map Repository (Data+Images)
Map Service
39
How to deliver the map product?
40
SERVER
Map Repository(Data+Images)
Map Service
Web Mercator
One map?
How to deliver the map product?
41
SERVER
Map Repository(Data+Images)
Map Service
Web Mercator
One map?
Map product:
Various areas
How to deliver the map product?
42
SERVER
Map Repository(Data+Images)
Map Service
Web Mercator
One map?
Map product:
Various resolution
How to deliver the map product?
43
SERVER
Map Repository(Data+Images)
Map Service
Web Mercator
One map?
Map product:
Various theme
Various language
44
One map ?
Multiple themes
Multiple Languages
SERVER
Map Repository(Data+Images)
Map Service
On-the-fly rendering ?
45
On-the-fly generalization ?
Use of Map Tiles
CLIENT
HTTP
Request (where/what/resolution)
Map Product
SERVER
Map Repository (Data+Images)
Map Service
46
Preprocessing generation of map tiles
One map not an option
47
Online Map Service Providers
Raster Tile
Maps
Use of Map Tiles
CLIENT
HTTP
Request (where/what/resolution)
Map Product
SERVER
Map Repository (Data+Images)
Map Service
48
Preprocessing generation of tiles
Tiled maps
O A series of precompiled maps…
O for… various areas
O in… various resolutions
49
Map Repository (Data+Images)
Tiled maps – An old practice
O Old practice…
O Sheet Division and Organization of
Topographic maps
50
Map Repository (Data+Images)
Sheet Division & Organization
O Topographic Maps
51
Sheet Division & Organization
O NRCan: National Topographic Map Index
52
Web Mapping Tiled Maps
O Web mapping
O rapid growth of map data availability
O rapid growth of demand
O Use of map tiles (slippy maps)
O pre-computation and caching of map image tiles
O map servers use far fewer resources than maps rendered on demand
O delivery only limited by the bandwidth of the connection with the map server
53
Tiled Maps
O Google…
O was the first major mapping provider to adopt
the tiled web maps
O Others followed…
O Bing and OpenStreetMap, Esri and Oracle
O provide functionality for map tiling and caching
of vector layers and/or raster images
54
Google Maps
O Conventions…
O All map tiles
O Square-shaped and equal-sized
O 256x256 pixels
O World rendered in a single tile at the outer
most zoom level: 0
O Projection: Web Mercator
O latitude values [-85.0511, +85.0511] degrees
55
Google Maps
56
x
y0,0
0,0 1,0
0,1 1,1
0,0 1,0
0,1 1,1
0,2 1,2
0,3 1,3
2,0 3,0
2,1 3,1
2,2 3,2
2,3 3,3
Zoom Level: 0Number of Tiles: 1
Zoom Level: 1Number of Tiles: 4
Zoom Level: 2Number of Tiles: 16
column
row
Bing Maps
O Quadtree encoding: Quadkeys
57
Google Maps – Zoom Level [0-24]
58
59
60
http://www.maptiler.org/google-maps-coordinates-tile-bounds-projection/
to Zoom Level 23…
#Tiles & Pixel size / Zoom Level
61
Each tile: 256x256 pixels
LEVEL TILES/LEVEL Pixel Size (m)0 1 156,543.034
1 4 78,271.517
2 16 39,135.758
3 64 19,567.879
4 256 9,783.940
5 1,024 4,891.970
6 4,096 2,445.985
7 16,384 1,222.992
8 65,536 611.496
9 262,144 305.748
10 1,048,576 152.874
11 4,194,304 76.437
12 16,777,216 38.219
13 67,108,864 19.109
14 268,435,456 9.555
15 1,073,741,824 4.777
16 4,294,967,296 2.389
17 17,179,869,184 1.194
18 68,719,476,736 0.597
19 274,877,906,944 0.299
20 1,099,511,627,776 0.149
21 4,398,046,511,104 0.075
22 17,592,186,044,416 0.037
23 70,368,744,177,664 0.019
24 281,474,976,710,656 0.009
4 ^ LEVEL 2πR/(256*2^LEVEL)
GRS80 (eq) 6,378,137.00 m
Circumference (2πR) 40,075,016.69 m
62
Kotsollaris, M., 2017. A Scalable Web Tiled Map Management System. MScE Thesis. University of New Brunswick.
Map Tile Management
Interoperability across multiple Map Providers
63
http://docs.opengeospatial.org/wp/16-019r4/16-019r4.html
64
Online Map Service Providers
Web Mercator
Projection
Raster Tile
Maps
References
O Stefanakis, E., 2015. Web Mercator: the de facto standard, the
controversy, and the opportunity. GoGeomatics. Magazine of
GoGeomatics Canada. October 2015.
O Stefanakis, E., 2015. Map Tiles and Cached Map Services.
GoGeomatics. Magazine of GoGeomatics Canada. December
2015.
O MapTiler. Tiles à la Google Maps: Coordinates, Tile Bounds and
Projection. http://www.maptiler.org/google-maps-coordinates-tile-
bounds-projection/
O Tilesets: Google Maps Structure – MicroImages.
http://www.microimages.com/documentation/TechGuides/78goo
gleMapsStruc.pdf
65