Design of Spatial Information Systems

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DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF
JOENSUU JOENSUU, FINLAND

• Design of Spatial Information Systems
• Lecture 2
• Cartography
• Alexander Kolesnikov

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The Shape of the Earth

• 250 B.C. Eratosthenes measured the Earth using
  basic principles of geometry
• Measuring the angle between Polaris and the
  observers horizon define the astronomic latitude

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Shape of the Earth Sphere
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The Earths Shape Ellipsoid

• Ellipsoid The Earth revolves easterly on its
  axis, generating centrifugal force, causing a
  bulge in the middle and flattening at the poles

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Selected Reference Ellipsoids

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The Earths Shape Geoid

• Geoid Representation of the Earth as an
  equigravitational surface at mean sea level (MSL)
• Variation is about 100 m, that is far less than
  the ellipsoid varies from the sphere

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Difference between geoid and ellipsoid
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Why different ellipsoids?

• Better methods for approximating the surface of
  the Earth
• Developed from different areas of the Earth

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Datum

• The ellipsoid is a mathematical model that
  describes
• the shape of the Earth.
• A datum
• defines the position of the ellipsoid relative
• to the center of the Earth
• provides a frame of reference for measuring
  locations
• on the surface of the Earth
• aligns its spheroid to closely fit the Earths
  surface
• in a particular area

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Datum Ellipsoid(a,b) Shift(dX,dY,dZ)
dY
dX
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Datum Ellipsoid Shift
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Datum Ellipsoid Shift
Datum Ellipsoid dX
dY dZ Area European
1950 International 1924 -87 -98 -121
Finland Pulkovo 1942 Krassovsky 1940 28
-130 -95 Russia WGS 1984 WGS84
0 0 0
Global ...
Find datum for your homeland http//www.colorado.
edu/geography/gcraft/notes/datum/edlist.html
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Geographical coordinates
North Pole
South Pole
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Geocoordinates
Meridians
North pole
Parallels
N
S
E
W
South pole
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Latitude
N
S

• Latitude is the elevation angle of a point on
  the Earth
• above the equator.
• Northern latitude (N) if north of the equator,
• southern (or negative) latitude (S) if south of
  it.
• Parallel is a ring of the intersection with
  Earths
• surface of a plane parallel to the Equatorial
  plane.

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Longitude

• MeridianA great circle on the surface of the
  Earth, passing through the geographical poles and
  some third point on the Earth's surface.
• All points on a given meridian have the same
  longitude.

E
W
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Joensuu in Google Earth
Longitude 632041.64 N Lattitude
284647.62 E
http//www.gorissen.info/Pierre/maps/googleMapLoca
tion.php
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Projection

• A cartographical map projection is a formal
  process
• which converts maps between a spherical or
  ellipsoidal surface and a projection surface,
  often flat.

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Map projections
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Planar Orthographic projection
Normal Transverse Oblique
(Polar) (Equatorial)
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Planar Stereographic projection
Polar Equatorial
Oblique
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Planar Gnomonic projection
Polar Equatorial
Oblique
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Planar polar projections
Orthographic Stereographic
Gnomonic
where (?,?) are Longitude and Latitude, and
(?,?) are polar coordinates on the projected
plane The Earth is a sphere. R is radius of the
Earth.
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Planar polar projections
North Pole
Equator
For simplicity
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Cylindrical projections
Normal (regular) Transverse
Oblique
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Conic projection
Conformal conic map
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View Earth from Sun (1)
19 January at 16.00 UTC
19 January at 08.00 UTC
UTC Coordinated Universal Time is a time
standard based on International Atomic Time (TAI)
with leap seconds added at irregular intervals
to compensate for the Earth's slowing rotation.
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View Earth from Sun (2)
March 22 September 20 / 0700 UTC
June 21 0700 UTC
December 21 0700 UTC
1. View today at 0000 UTC? 2. Which projection?
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View Earth from Sun (2)
March 22 September 20 / 0700 UTC
June 21 0700 UTC
December 21 0700 UTC
Orthographic projection