Coordinate and Map

Projection Systems

Dr Muhammad Ateeq Qureshi

Assistant Professor

NCRG-IST

From the early civilizations, the effort for determining shape and

size of earth was a major challenge to humans.

Earth Shape?

Earth Shape?

A Greek geographer, gave the notion of spherical earth in

second century B.C.

Isaac Newton first proposed that Earth was not perfectly round

He suggested it was an oblate spheroid — a sphere that is

squashed at its poles and swollen at the equator.

Actually, the Earth is not perfectly spherical.

Earth Shape?

What is the precise shape of the Earth?

Is it a sphere, spheroid, or something else?

Spheres and Spheroids

Spheres

• Sphere is based on a circle.

• The shape of Earth is represented as a sphere through

simplifies many mathematical calculations.

• Depending on the application, the Earth is modeled as a

sphere.

• Possible for small scale maps (1:5,000,000 or less)

Spheroids

• The Earth shape can be mathematically modeled more

accurately as a spheroid.

• Spheroid approximates the shape of the Earth.

The Earth is not a perfect spheroid.

Different spheroids are used in different parts of

the world to create the best possible model of

the Earth’s curvature in each location

Earth Shape?

But now researchers have confirmed that earth’s surface is not

spherical or flat rather it is oblate ellipsoidal, which means all

points on the surface of the earth are not equidistant from the

geometric centre

Latitude - Longitude

Latitude lines are parallel to the Equator and

Longitude lines are perpendicular to the Prime Meridian

Latitude varies from 0o at the equator to 90o North and

South at the poles

Longitude varies from 0o at Greenwich to 180o East and

West

Latitude

• Measured Northward or Southward from the Equator to poles

• Ranging 0 - 900 North or South

• The measuring units are degrees, minutes, and seconds, 10 =

60’ and 1’= 60”

• The length of one degree latitude is similar everywhere, ~69

miles / 111km. The range varies (due to the Earth's slightly

ellipsoid shape) from ~68.703 miles (110.567 km) at the

equator to ~69.407 (111.699 km) at the poles.

• Measured Eastward or Westward from the Prime Meridian at

Greenwich, England to the International Date Line.

• Ranging 0 -1800 East or West, The measuring units are

degrees, minutes, and seconds, 10 = 60’ and 1’=60”

• Length of one degree longitude reduces toward poles.

• A degree of longitude is widest at the equator at ~69.172

miles / 111.321 km and gradually shrinks to zero at the poles.

• At 40° North or South the distance between a degree of

longitude is ~53 miles / 85 km

Longitude

Datum

Datum

• A datum is a mathematical model related to real-world

features.

• The datum consists of a series of numbers that define the

shape and size of the ellipsoid and it's orientation in space.

• A datum is chosen to give the best possible fit to the true

shape of the Earth.

• Most datums are created for use only in specific areas of the

Earth, but the World Geodetic Systems (WGS) can be used

globally.

Major Types

• Geodetic: Aligns the spheroid to fit to a particular area.

• Geocentric: Uses the Earth’s centre of mass as the origin

Coordinate Systems

Coordinate System

• “Location” is the first step towards understanding the spatial

concept.

• The absolute or true location of any point in space can be

defined by its values knows as coordinates.

• A reference system used to measure horizontal and vertical

distance on a flat map.

• Actually, it is used to define a location on the Earth.

• It is created in association with a map projection, datum,

and reference ellipsoid and describes locations in terms of

distances or angles from a fixed reference point.

Coordinate System

• The system may be either a Cartesian system, with

coordinates based on orthogonal or 90-degree angles, or it

may be polar, based on angles measured from a point such

as the center of the Earth.

• For example, in the latitude / longitude system, positions are

described based on angular measurements North or South of

the Equator and East or West of the Prime Meridian, which runs

through Greenwich, England. This is considered a polar

system.

Coordinate System

X’ X

Y’

Y

0,0

Y1

X1

1, 1P (X Y )

180o 0o

270o

90o

P(r1,01)

r

0

Cartesian Polar

Types of Coordinate Systems

The following are two common types of coordinate systems used in a

geographic information system (GIS):

• Geographic Coordinate System (GCS)

• Projected Coordinate System (PCS)

Geographic Coordinate Systems (GCS):

• A coordinate system that enables every location on Earth to

be specified by a set of numbers, letters or symbols.

• The coordinates are often chosen such that one of the

numbers represents a vertical position and two or three of the

numbers represent a horizontal position; alternatively, a

geographic position may be expressed in a combined three-

dimensional Cartesian vector.

• A common choice of coordinates is latitude, longitude and

elevation.

• To specify a location on a plane requires a map projection.

Projected Coordinate System (PCS)

• A PCS is defined on a flat, two-dimensional surface.

• Unlike a GCS, a PCS has constant lengths, angles, and areas

across the two dimensions.

• A PCS is always based on a GCS that is based on a sphere or

spheroid.

• In addition to the GCS, a PCS includes a map projection, a set

of projection parameters that customize the map projection

for a particular location, and a linear unit of measure.

What is Map Projection?

Systematic arrangement of lines of latitudes and longitudes

on a plane is called map projection

Map Projection

• A map projection is a mathematical model for conversion of

locations from a three-dimensional Earth surface to a two-

dimensional map.

• This conversion necessarily distorts some aspect of the Earth's

surface, such as Area, Shape, Distance, or Direction.

• Projection types are based on the geometric form used in the

transfer from the spherical Earth to a flat surface.

Steps in Map Projection

Reduction &

Projection

Reduction Generating

Globe

Projection

Classification of Map Projection

Basis Classes

Method of Construction 1. Perspective

2. Non-perspective

Preservation of qualities 1. Homolographic/equal area

2. Orthomographic/conformal

Developable surface area 1. Cylindrical

2. Conical

3. Azimuthal/zenithal

4. Conventional

Position of tangent surface 1. Polar

2. Equidistant/Normal

3. oblique

Position of viewpoint or light 1. Gnomonic

2. Stereographic

3. Orthographic

4. Others

Construction of Map Projection

Gnomonic

The light source at the centre of the globe

The light source at the antipode of the point of tangency

Stereographic

The light source an infinite distance from the point of tangency,

resulting in parallel light rays.

Orthographic

Types of Map Projections

Cylindrical

• (Transverse Mercator) - good for North-South land areas.

Conical

• (Albers Equal Area, Lambert Conformal Conic) - good

for East-West land areas.

Azimuthal

• (Lambert Azimuthal Equal Area) - good for global views.

Types of Map Projections

Basic of Map Projections

Also called azimuthal or zenithal

Can be any aspect

Planar Projections

Planar Projections - Perspective

Planar Projections - Orthographic

Planar Projections - Sterographic

Planar Projections - Gnomonic

Cylindrical projections

Best for equatorial or low latitudes

Rotate cylinder to reduce distortion along a line

Normal - equatorial / East-West

Transverse - North-South regions

Oblique - other angles

Cylindrical Projections

Cylindrical Projections - Mercator

Cylindrical Projections - Miller

Cylindrical Equal-Area Projection

Mollweide Projection

(equal-area, psuedo-cylindrical)

Cylindrical Projections

Conical Projections

Best for mid-latitudes with an

East-West orientation.

Tangent or secant along 1 or 2 lines of latitude known as

‘standard parallels’.

Conical Projections

Conical Projections

Albers Equal AreaLambert Conformal

Map projection

Projection always introduces distortion of entities

Conformity: when the scale of a map at any point on the map is the same in

any direction, the projection is caller conformal. Meridians (lines of longitude)

intersect at right angles. Shape is preserved locally on conformal maps.

Distance : A map is equidistant when it portrays distance from the

center of the projection to any other place on the map.

Direction: A map preserve direction when azimuths (angles from a point

on a line to another point) are portrayed correctly in all directions.

Map projection

Scale: Scale is the relationship between a distance portrayed on a map

and the same distance on the Earth.

Area: When a map portrays areas over the entire map so that all mapped

areas have the same proportional relationship to the areas on the Earth

that they represent, the map is an equal-area map

Source: Dana,1999

Robinson Projection -- 16,930 Miles

Length of the Arctic Coastline of Russia

Oblique Mercator Projection

-- 10,473 Miles

Mercator Projection

-- 31,216 Miles

Length distortion on World Maps

Montana State Plane Coordinates

-- 13,138.6 Meters

Oblique Mercator Projection --

13,143.5 Meters

Difference = 4.88 Meters One part in 2692 0.0371 Percent

Length distortion on local Maps

Mercator Projection

Lower 48 States --

52,362,000 Sq Miles

Columbia --

4,471,000 SqMiles

Mollweide Projection (equal-area)

Lower 48 States --

30,730,000 Sq Miles

Columbia --

4,456,000 SqMiles

Area distortion on World Maps

Montana State Plane Coordinates

-- 122,314.3 Acres

Albers Equal Area Projection --

122,425.2 Acres

Difference = 110.9 Acres One part in 1104 0.091 Percent

Area distortion on local Maps

ThanksQuestions?