CE-317 GIS/RS AppIication to CiviI Engineering
Spring 2011
Engr. Faisal ur Rehman
Lecture 03: Coordinate Systems
Datums
Datums: Datums define the reference systems that
describe the size and shape of the earth
It defines the origin and orientation of the
coordinate systems used to map the earth.
Datum
Modern geodetic datums range from flat-earth
models used for plane surveying to complex
models used for international applications
Which completely describe the size shape,
orientation, gravity field, and angular velocity of
the earth.
Datum
Geodetic datums and the coordinate reference
systems based on them were developed to
describe geographic positions for surveying,
mapping, and navigation.
Shape of Earth
Datum Types
1. Horizontal: Datums that define the relationship
between the physical earth and horizontal
coordinates such as latitude and longitude.
Examples include the North American Datum of
1927 (NAD27) and the European Datum 1950
(ED50).
Datum Types
2. Vertical: Datums that define level surfaces.
Examples include the National Geodetic Vertical
Datum of 1929 (NGVD29) and the North
American Vertical Datum of 1988 (NAVD88).
Some are based on sea-level measurements and
levelling networks (NGVD29), others on gravity
measurements (NAVD88).
Datum Types
3. Complete: Datums that describe both vertical and
horizontal systems. Some, such as World
Geodetic System 1984 (WGS-84)
also describe other parameters such as the rotation
rate of the earth
and various physical constants such as the angular
velocity of the earth and the earths gravitational
constant.
Reference Ellipsoids
Reference ellipsoids are defined by either semi-
major (equatorial radius) and semi-minor (polar
radius) axes, or the relationship between the semi-
major axis and the flattening of the ellipsoid
(expressed as its eccentricity).
Many reference ellipsoids are in use by different
nations and agencies.
Reference ellipsoids are identified by a name and
often by a year for example, the Clarke 1866
ellipsoid is different from the Clarke 1858 and the
Clarke 1880 ellipsoids.
Geodetic Datums
Precise positioning must also account for
irregularities in the earths surface due to factors
in addition to polar flattening.
Topographic and sea-level models attempt to model
the physical variations of the surface:
Geodetic Datums
The topographic surface of the earth is the actual
surface of the land and sea at some moment in
time.
Aircraft navigators have a special interest in
maintaining a positive height vector above this
surface.
Geodetic Datums
Sea level can be thought of as the average surface
of the oceans, though its true definition is far
more complex.
Specific methods for determining sea level and the
temporal spans used in these calculations vary
considerably.
Tidal forces and gravity differences from location to
location cause even this smoothed surface to vary
over the globe by hundreds of meters.
GEOlD
Gravity models and geoids are used to represent
local variations in gravity that change the local
definition of a level surface.
Gravity models attempt to describe in detail the
variations in the gravity field.
The importance of this effort is related to the idea
of levelling.
Plane and geodetic surveying uses the idea of a
plane perpendicular to the gravity surface of the
earth
GEOlD
Reference System
Global systems can refer to positions over much of
the Earth.
Regional systems have been defined for many
specific areas, often covering national, state, or
provincial areas.
General Coordinate Systems
Plane
Global
Plane Coordinate System
Plane coordinate system Cartesian coordinates:
Cartesian coordinates are determined by locating
an origin there after setting two axes through
origin in fixed directions, at right angles to each
other.
By convention these are usually identified as x and
y, where x is horizontal and y vertical (x is east, y
is north).
To measure linear displacement from the origin in
directions defined by the two axes produces an
ordered (x, y) pairs.
Storing Coordinates
Integer vs real numbers:
The number is the product (a 10b), e.g., +1234 +2
would indicate 0.1234 102 or 12.34.
Storing Coordinates
Computer precision: In the computer, the number of
digits which can be stored for each value is
limited by the hardware, integers are normally
stored using 16 bits of memory and can have a
range from 32767 to +32767.
Floating point numbers can use single or double
precision.
Single precision commonly allocates 32 bits, or 4
bytes, of memory for each value, equivalent to 7
significant decimal digits
Plane Coordinate System
Plane coordinate system Polar coordinates: Polar
coordinates use distance from origin (r) and angle
from fixed direction (q), usually fixed direction is
north and angle is measured clockwise from it.
Polar coordinates are useful for measuring from
some fixed point such as the center of the city or
when using data from sources such as ground
surveys and radar.
To translate from (r, q) to
(x,y)
???
Earth Coordinate Geometry
The earths spherical shape is more difficult to
describe than a plane surface.
Concepts from Cartesian coordinate geometry have
been incorporated into the earths coordinate
system.
Rotation of the Earth: The spinning of the earth on
its imaginary axis is called rotation.
The spinning has led to the creation of a system to
determine points and directions on the sphere.
Earth Coordinate Geometry
If the North Pole was extended, it would point to a
fixed star, the North Star (Polaris).
Any point on the earths surface moves with the
rotation and traces imaginary curved lines are
Parallel of Latitude.
The Equator: If a plane bisected the earth midway
between the axis of rotation and perpendicular to
it, the intersection with the surface would form a
circle.
Earth Coordinate Geometry
Earth Coordinate Geometry
The Geographic Grid
The Geographic Grid: The spherical coordinate
system with latitudes and longitudes used for
determining the locations of surface features.
Parallels: east-west lines parallel to the equator.
Meridians: north-south lines connecting the poles.
Parallels are constantly parallel, and meridians
converge at the poles.
Meridians and parallels always intersect at right
angles.
The Geographic Grid
The Geographic Grid
Degrees, Minutes, and Seconds: Angular
measurement is used in addition to simple plane
geometry to specify location on the earths
surface.
This is based on a sexagesimal scale
Great and Small Circles
Great and Small Circles
Projections
