Download Faculty of Transportation Sciences

Czech Technical University
in Prague
Faculty of Transportation
Sciences
Department of Transport Telematics
Geographical Information Systems
Doc. Ing. Pavel Hrubeš, Ph.D.
Rehearsal

Vector data models
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Spaghetti model
Topological model
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Model of the Earth
 Sphere

Big scales
 Elipsoid/Spheroid

Closer to reality
 Geoid

The closest to reality
 Model of elevation
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
České
vysoké
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technick
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Praze Fakulta
dopravní
Katedra
řídící
techniky
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telematik
y
Parameters for Mapping
 A mathematical model of the earth
must be selected. Spheroid

The mathematical model must be related
to real-world features. Datum
 Real-world features must be
projected with minimum distortion
from a round earth to a flat map; and
given a grid system of coordinates.
Projection
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Spheroid

A mathematical model of the earth must
be selected.
 Simplistic - A round ball having a radius
big enough to approximate the size of the
earth.
 Reality - Spinning planets bulge at the
equator with reciprocal flattening at the
poles. e.g.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Different Spheroids
•
GRS80 (North America)
•
Clark 1866 (North America)
•
WGS84 (GPS World-wide)
•
International 1924 (Europe)
•
Bessel 1841 (Europe)
Name
Equatorial axis
(m)
Airy 1830
6 377 563.4
Clarke 1866
6 378 206.4
Bessel 1841
6 377 397.155
International 1924 6 378 388
Krasovsky 1940 6 378 245
GRS 1980
6 378 137
WGS 1984
6 378 137
Sphere (6371 km) 6 371 000
Polar axis (m)
6 356 256.9
6 356 583.8
6 356 078.965
6 356 911.9
6 356 863
6 356 752.3141
6 356 752.3142
6 371 000
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Inverse
flattening,
299.324 975 3
294.978 698 2
299.152 843 4
296.999 362 1
298.299 738 1
298.257 222 101
298.257 223 563
Why use different spheroids?

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The earth's surface is not perfectly symmetrical, so the
semi-major and semi-minor axes that fit one geographical
region do not necessarily fit another.
Satellite technology has revealed several elliptical
deviations. For one thing, the most southerly point on the
minor axis (the South Pole) is closer to the major axis (the
equator) than is the most northerly point on the minor axis
(the North Pole).
The earth's spheroid deviates slightly for different regions of
the earth.
Ignoring deviations and using the same spheroid for all
locations on the earth could lead to errors of several
meters, or in extreme cases hundreds of meters, in
measurements on a regional scale.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Datum

A mathematical model must be related to real-world
features.

A smooth mathematical surface that fits closely to
the mean sea level surface throughout the area of
interest. The surface to which the ground control
measurements are referred.
Provides a frame of reference for measuring
locations on the surface of the earth.
Changes to the values of any datum parameters
can result in changes to coordinate values of points.
If you have two different datums, in practice you
have two different geographic coordinate systems.
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Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
How do I get a Datum?


To determine latitude and longitude, surveyors
level their measurements down to a surface
called a geoid. The geoid is the shape that the
earth would have if all its topography were
removed.
Or more accurately, the shape the earth would
have if every point on the earth's surface had the
value of mean sea level.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Model of the Earth
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Graticules
Latitude/Longitude


Lines of latitude
N or S of Equator
Longitude lines
E or W of Prime
Meridian
Also called parallels and meridians.
Latitude lines are parallel, run east and west around the
earth's surface, and measure distances north and south of
the equator.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Location on the Earth


Longitude lines run north and south around the earth's surface,
intersect at the poles, and measure distances east and west of the
prime meridian.
Based on 360 degrees. Each degree is divided into 60 minutes
and each minute into 60 seconds.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Projection

Real-world features must be projected
with minimum distortion from a round
earth to a flat map; and given a grid
system of coordinates.

A map projection transforms latitude and
longitude locations to x,y coordinates.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Projection
 Sphere
 Elipsoid

 Plane
 Cylinder
 Cone
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
What is a Projection?


If you could project light from a source through
the earth's surface onto a two-dimensional
surface, you could then trace the shapes of the
surface features onto the two-dimensional
surface.
This two-dimensional surface would be the basis
for your map.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Why use a Projection?
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Can only see half the earth’s surface at a time.
Unless a globe is very large it will lack detail and
accuracy.
Harder to represent features on a flat computer
screen.
Doesn’t fold, roll or transport easily.
Converting a sphere to a flat surface results in
distortion.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Map Projection & Distortion
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
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Shape (conformal) - If a map preserves shape,
then feature outlines (like county boundaries) look
the same on the map as they do on the earth.
Area (equal-area) - If a map preserves area, then
the size of a feature on a map is the same relative
to its size on the earth. On an equal-area map
each county would take up the same percentage
of map space that actual county takes up on the
earth.
Distance (equidistant) - An equidistant map is
one that preserves true scale for all straight lines
passing through a single, specified point. If a line
from a to b on a map is the same distance that it
is on the earth, then the map line has true scale.
No map has true scale everywhere.
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Map projection
- Azimuthal (projections onto a plane)
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Map projection - Azimuthal
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Map projection - Cylindrical
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Map projection – Conical
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Map projections
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Křovak’s projection
Czech Technical University in Prague - Faculty of Transportation Sciences
Department of Transport Telematics
Planar Coordinate Systems
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Coordinate systems identify locations by making
measurements on a framework of intersecting
lines that resemble a net.
On a map, the lines are straight and the
measurements are made in terms of distance.
On a round surface (like the earth) the lines
become circles and the measurements are made
in terms of angle.
Cartesian Coordinate System
Planar coordinate systems are based on
Cartesian coordinates.
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The origin of the coordinate
system is made to coincide with
the intersection of the central
meridian and central parallel of the
map.
But this conflicts with the desire to
keep all their map coordinates
positive (within the first quadrant)
and unique numbers.
This conflict can be resolved with
false easting and false northing.
Adding a number to the Y axis
origin (false easting) and another
number to the X axis origin (false
northing) is equivalent to moving
the origin of the system.

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The projected coordinate system is a Cartesian
coordinate system with an origin, a unit of
measure (map unit), and usually a false easting
or false northing.
The main value of Cartesian coordinates is for
making measurements on maps. Before the age
of computers formulas for converting latitude and
longitude were too cumbersome to be done
quickly, but Cartesian coordinates offered a
satisfactory solution.