Coordinate system Geographical coordinate system

D. Naresh Kumar
Assistant Professor
Civil Engineering Department
St. Martin’s Engineering College

Geographic Coordinate Systems
 A geographic coordinate system is a reference system
for identifying locations on the curved surface of the
earth. Locations on the earth’s surface are measured in
angular units from the center of the earth relative to
two planes: the plane defined by the equator and the
plane defined by the prime meridian (which crosses
Greenwich England). A location is therefore defined
by two values: a latitudinal value and a longitudinal
value.
D. Naresh Kumar St. Martin's Engineering College

 latitudinal lines are shown on the left and examples of
longitudinal lines are shown on the right.

A GCS is defined by an ellipsoid, geoid and datum
 Sphere and Ellipsoid
 Assuming that the earth is a perfect sphere greatly
simplifies mathematical calculations and works well
for small-scale maps (maps that show a large area of
the earth). However, when working at larger scales, an
ellipsoid representation of earth may be desired if
accurate measurements are needed. An ellipsoid is
defined by two radii: the semi-major axis (the
equatorial radius) and the semi-minor axis (the polar
radius).

Geoid
 Representing the earth’s true shape, the geoid, as a
mathematical model is crucial for a GIS environment.
However, the earth’s shape is not a perfectly smooth
surface. It has undulations resulting from changes in
gravitational pull across its surface. These undulations may
not be visible with the naked eye, but they are measurable
and can influence locational measurements. Note that we
are not including mountains and ocean bottoms in our
discussion, instead we are focusing solely on the earth’s
gravitational potential which can be best visualized by
imagining the earth’s surface completely immersed in
water and measuring the distance from the earth’s center to
the water surface over the entire earth surface

Datum
 The alignment can be local where the ellipsoid surface
is closely fit to the geoid at a particular location on the
earth’s surface
 geocentric where the ellipsoid is aligned with the
center of the earth. How one chooses to align the
ellipsoid to the geoid defines a datum.

Local Datum` Geocentric Datum

Projected Coordinate Systems
 The surface of the earth is curved but maps are flat. A
projected coordinate system (PCS) is a reference
system for identifying locations and measuring
features on a flat (map) surface. It consists of lines that
intersect at right angles, forming a grid. Projected
coordinate systems (which are based on Cartesian
coordinates) have an origin, an x axis, a y axis, and a
linear unit of measure. Going from a GCS to a PCS
requires mathematical transformations. The myriad of
projection types can be aggregated into three
groups: planar, cylindrical and conical.

Planar Projections
 A planar projection (aka Azimuthal projection) maps
the earth surface features to a flat surface that touches
the earth’s surface at a point (tangent case),

Cylindrical Projection
 A cylindrical map projection maps the earth surface
onto a map rolled into a cylinder (which can then be
flattened into a plane). The cylinder can touch the
surface of the earth along a single line of tangency
(a tangent case),

 This is a popular projection used in defining the
Universal Transverse Mercator (UTM) and State Plane
coordinate systems. The UTM PCS covers the entire
globe and is a popular coordinate system in the US. It’s
important to note that the UTM PCS is broken down
into zones and therefore limits its extent to these
zones that are 6° wide.

Conical Projection
 A conical map projection maps the earth surface onto
a map rolled into a cone. Like the cylindrical
projection, the cone can touch the surface of the earth
along a single line of tangency (a tangent case),

Geographic Coordinate System
 Longitude specifies positions east and west as the angle between
the prime meridian and a second meridian that intersects the point
of interest. Longitude ranges from +180 (or 180° E) to -180° (or 180° W).
180° East and West longitude together form the International Date
Line.
 Latitude specifies positions north and south in terms of the angle
subtended at the center of the Earth between two imaginary lines, one
that intersects the equator and another that intersects the point of
interest. Latitude ranges from +90° (or 90° N) at the North pole to -90°
(or 90° S) at the South pole. A line of latitude is also known as
a parallel.
 At higher latitudes, the length of parallels decreases to zero at 90°
North and South. Lines of longitude are not parallel but converge
toward the poles. Thus, while a degree of longitude at the equator is
equal to a distance of about 111 kilometers, that distance decreases to
zero at the poles.

THE END

Coordinate system Geographical coordinate system

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