Design of Spatial Information Systems

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DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF
JOENSUU JOENSUU, FINLAND

• Design of Spatial Information Systems
• Lecture 3
• Map Projections
• Alexander Kolesnikov

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Cartesian coordinates in 2-D space
Euclidean distance L between points P1 and P2
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Polar coordinates in 2-D space
y
r
?
x
Distance L between two points (r,?1) and (r,?2)
on a circle
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Cartesian coordinates in 3-D space
Euclidean distance L between points P1 and P2 in
Cartesian coordinates
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Spheric coordinates in 3-D space
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Distance between two points on a sphere

• Distance L between two points P1 (R,?1,?1) and
• P2(R,?2,?2) on a sphere in spherical
  coordinates

Problems with this formula...
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Haversine formula for the distance

• Distance L between two points P1 (R,?1,?1) and
• P2(R,?2,?2) on a sphere in spherical
  coordinates

We know the distance L, then how to define the
shortest path from the point (?1,?1) to point
(?1,?1)?
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Arc of the Great Circle
http//216.147.18.102/dist/index
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Transverse Cylindrical Projections
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Transverse Cylindrical Projections

• Mercator projection
• Tranverse Mercator projection (TM)
• Gauss-Krueger (GK) projection
• Universal Tranverse Mercator (UTM) projection
• KKJ
• YKJ
• EUROREF-FIN (after 2003)

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Mercator (after Gerardus Mercator) Map

Gerhard Kramer
1569 year
Mostly used for naval ocean navigation
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How to do?
Mercator
Read more
http//www.math.ubc.ca/israel/m103/mercator/
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Keep constant angle with the meridians
y
x
Coordinates x and y of a point on a Mercator map
from its longitude ? and latutude ?.
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Formula for the Mercator projection
?
90
y
-90
Coordinates x and y of a point on a Mercator map
from its longitude ? and latutude ?.
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The main property of Mercator map
Vancouver
Ruhmb line
Hawaii
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Problem with Mercator projection

• Greenland is presented as large as Africa.
• In fact Africa's area is 13 times that of
  Greenland.

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Transverse Mercator (TM)

• A conformal cylindrical projection
• The accuracy of TM projections quickly decreases
  from the
• central meridian.
• Therefore the longitudinal extent of the
  projected region is
• restricted to 3? from the central meridian.

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Transverse Mercator (TM)
TM for one zone
TM for 2 zones
Each TM Zone is in fact a different
projection using a different system of
coordinates. Area, size, and angle distortions
are very small.
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Gauss-Krueger (GK)

• GK system using TM projections to map the world
  into numerous standard zones that are 3? wide.
• X-coordinate Northing
• Y-ccordinate Easting
• False Easting 500 000 m
• False Northing 0 m for Northern
  hemisphere
• 10 000 000 m for
  Southern hemisphere
• Scale factor 1.0
• Germany, Finland, USSR, Eastern Europe, South
  America.
• The European alternative to UTM

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Universal Transverse Mercator (UTM)

• The UTM system applies the TM projection to
  mapping the
• world, using 60 pre-defined standard zones.
• UTM zones are 6? wide.
• Each zone exists in a North and South variant.
• X-coordinate Northing
• Y-coordinate Easting
• False Easting 500 000 m
• False Northing 0 m for Northern
  hemisphere
• 10 000 000 m for
  Southern hemisphere
• Scale factor 0.9996
• The UTM is defined for areas between latitudes
  80?S and 84?N.

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UTM Zone parameters
Zone width 6? Zone numbers 1..60 Central
meridians n?6?-183? Northern hemisphere
0?-84?N False Easting 500 000 m False
Northing 0 m Southern hemisphere
80?-0?S False Easting 500 000 m False
Northing 10 000 000 m Scale factor 0.9996 Two
undistorted meridians ?1?37
Why?
.
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UTM Zones
West Lon Zones 1..30 East Lon
Zones 31..60
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Irregularities in the UTM grid in Europe
UTM zones for Finland 34, 35 and 36.
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http//cs.joensuu.fi/koles/utm/
Geocoordinates 68?35.59 N
29?45.45 E UTM Zone 35 (Central meridian
27?) Easting 612 294.5 m Northing 7 611
714.9 m
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http//cs.joensuu.fi/koles/utm/
Geocoordinates 68?35.59 N
29?45.45 E UTM Zone 35 (Central meridian
27?) Easting 612 287.7 m Northing 7 611
515.8 m
Easting 612 294.5 m Northing 7 611 714.9 m
ED50
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Arc of the Great Circle or Rhumb Line?
http//216.147.18.102/dist/index
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Finnish national projection grids

• VVJ Vanha Valtion koordinaattijärjestelmä
• (Old Finnish National System), until 1970.
• KKJ Kartaskoordinaattijärjestelmä
• (Map Coordinate System)
• Peruskoordinaattisto
• or Basic Coordinate System
• YKJ Yhtenäiskoordinaattisto
• (Uniform Coordinate System)
• EURO-FIN (from 2003)
• EUROREF89

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VVJ Vanha Valtion koordinaattijärjestelmä

• Projection Transverse Mercator
• Grid Gauss-Krueger
• Reference ellipsoid Hayford 1909International
  1924
• Scale factor 1
• In use from 1919 till 1970

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KKJ Basic coordinate system
Finland is divided into 4 projection zones of 3?
wide 21?E, 24?E, 27?E, and 30?E. Zones
1,2,3, and 4
Extended zones 18, 21, 24, 27, 30 ja
33 numbered from 0 to 5.
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KKJ Basic coordinate system

• Zones 1,2,3, and 4
• False Easting 500 000 m 500 km
• The ordinal number of Zone is added before the
  actual
• value of easting 1 500, 2 500, 3 500, and 4
  500 km.
• False Northing 0 m (Northern Hemisphere).
• Projection Transversal Mercator (Gauss-Krueger)
• Reference ellipsoid International 1924 (Hayford
  1909)
• 
  (a6378388, 1/f297.0)
• Datum European 1950 (ED50)
• Scale factor 1.0

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YKJ Uniform coordinate system

• Finland is represented in one projecton zone.
• The central meridian is 27?E
• Projection Transverse Mercator (Gauss-Krueger)
• Reference ellipsoid International 1924
• (a6378388,
  1/f297.0)
• Datum European 1950 (ED50)
• Scale factor 1.0

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EUROREF-FIN

• Since 2003 year
• 3D geocentric
• Finland is represented in one projecton zone.
• The central meridian is 27?E
• Projection Universal Transverse Mercator
• Reference ellipsoid GRS1980
• (a6378137, 1/f298.257222101)
• Scale factor 0.9996
• Accuracy of realization few centimeters

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EUROREF89

• For GPS applications
• 3D geocentric
• Finland is represented in one projecton zone.
• The central meridian is 27?E
• Projection Universal Transverse Mercator
• Reference ellipsoid WGS84
• Scale factor 0.9996

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Projected coordinates conversion
Scheme of conversion for projected coordinates
from projection system S1 to projection system
S2 1) (X,Y)S1 ? (Latitude, Longitude) 2)
(Latitude, Longitude) ? (X,Y)S2
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Example KKJ ? YKJ
1) (Zone, N,E)KKJ ? (Latitude, Longitude) 2)
(Latitude, Longitude) ? (N,E)YKJ
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1st step (N,E)KKJ ? (L,L)
Press
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2nd step (L,L) ? (N,E)YKJ
Press
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Result (Zone,N,E)KKJ ? (N,E)YKJ
KKJ
YKJ
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Example KKJ (ED50) ? UTM (WGS84)
1) (Zone, N,E)KKJ ? (Latitude, Longitude) 2)
(Latitude, Longitude) ? (Zone,N,E)UTM
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Conversion (N,E)KKJ ?(L,L) ? (N,E)UTM
1
1
4
2
2
4
3
3
KKJ
UTM