The document discusses various projection systems used in cartography to transform spherical coordinates into planar coordinates, emphasizing their importance for accurately depicting distances, areas, and directions on maps. It categorizes projection systems into conical, cylindrical, and planar (zenithal), detailing specific types such as the Albers equal area conic and Mercator projections, along with their properties and distortions. Additionally, it explains coordinate systems, distinguishing between geographic coordinate systems (GCS) and projected coordinate systems (PCS) used for mapping geographic features.

1. PROJECTIONS
&COORDINATE SYSTEMS
BY,
K.SAI TARUN,
4/4 GEO-INFORMATICS.

2. PROJECTION SYSTEMS :
 Projections are a mathematical transformations that take spherical
coordinates (latitude and longitude) and transform them to an XY
(planar) coordinate system. This enables you to create a map that
accurately shows distances, areas, or directions.
 Projections are chosen based on the needs of the map or data analysis and
on the area of the world. The method used to portray a part of the spherical
Earth on a flat surface, whether a paper map or a computer screen, is called
a map projection.
 A flat map can show one or more--but never all--of the following:
• True directions
• True distances
• True areas
• True shapes

3. PROJECTION SYSTEMS :
 Each & every country , continent on the surface of the
earth/globe is uniquely located & earth is not a perfect
spheroid.
 “A particular projection is not suitable for all the countries
as they are located at different places from the equator.
 Maps are the representations of reality.
 Construction of a map : 1)select projection
2)Select a model for the shape of the earth (sphere or
ellipsoid).
3) Transform the Geographic coordinates to planar coordinate
system

4. DIFFERENT TYPES OF PROJECTION
SYSTEMS :
Projection systems are mainly classified into three
types, they are
*conical projections
*cylindrical projections
*Planar or Zenithal projections.

5. TYPES OF CONICAL PROJECTIONS :
 Albers Equal Area Conic Projection :- The Albers Equal Area Conic
projection is commonly used for displaying large countries that require equal-
area representation. For example, the USGS uses this conic projection for
maps showing the conterminous United States (48 states).
 H. C. Albers introduced this map projection in 1805 with two standard parallels
(secant). As the name states, the purpose was to project all areas on the map
proportionally to all areas on Earth.
 Albers Equal Area Conic Projection Distortion :Albers Equal Area Conic
Projection has map distortion. Distances and scale are true only on both standard parallels
with directions being reasonably accurate. Areas are equal to the same areas on Earth

6. TYPES OF CONICAL PROJECTIONS :
 Lambert Conformal Conic Projection : It looks like the Albers
Equal Area Conic, but graticule spacings differ so that it’s
conformal rather than equal area.
 It uses a conic developable surface secant at two standard
parallels, usually at 33° and 45° to minimize distortion. However,
standard parallels vary depending on location. For example,
Canada’s standard parallels are usually 49ºN. and 77ºN.
 Lambert Conformal Conic Projection Map Properties : The
major advantage of the Lambert Conformal Conic map projection is how it
retains conformality.
 Despite how distances are reasonably accurate and retained along
standard parallels, it isn’t equal area as distortion increases away from
standard parallels.

7. TYPES OF CONICAL
PROJECTIONS :
 Polyconic Projection : This map projection uses an infinite number of cones
tangent to an infinite number of parallels. This type of projection is generally used for
countries that span along a longitudinal extent.
 In a polyconic projection, all meridians except the central one have
curved lines. Only along the central meridian, distances, direction,
shape, and areas are true. However, distortion increases away from its
central meridian.

8. TYPES OF CYLINDRICAL PROJECTIONS :
 Mercator Projection : Gerardus Mercator created the Mercator
projection by mathematically projecting a vertically oriented cylinder tangent to
the Equator.
 Navigators used this type of map because any straight line on a Mercator map
is a rhumb line (line of constant direction). However, navigators often
combined this type of map with the Gnomonic projection because of how
straight lines are great circles showing the shortest path between points.
 Mercator Map Projection Properties : Directions along a Rhumb line
are true between any two points on a map. Distances are true only along the
Equator. Although it has a conformal property, areas are greatly distorted
increasing size at poles.

9. TYPES OF CYLINDRICAL PROJECTIONS
:
 Transverse Mercator Projection : Lambert introduced the Transverse
Mercator in 1772. It uses a horizontally oriented cylinder tangent to a Meridian.
This is particularly useful for mapping large areas that are mainly north-south
in extent.
 The whole UTM grid system uses 60 horizontally oriented
cylinders secant to the globe.
 Transverse Mercator Map Properties : Distances are true only
along the central meridian but all distances, directions, shapes, and

10. TYPES OF CYLINDRICAL PROJECTIONS :
 Outside of 15°central meridian, distortion increases significantly
for size, distance and direction.
 The Transverse Mercator projection is conformal with shapes
being true in small areas. While the equator is a straight line, other
parallels are complex curves concave toward nearest pole.

11. UTM PROJECTION :
 UTM is the acronym for Universal Transverse Mercator, a plane
coordinate grid system named for the map projection on which it
is based (Transverse Mercator).
 The Universal Transverse Mercator (UTM) is a map
projection system for assigning coordinates to locations on the surface
of the Earth. It is a horizontal position representation, which means it
ignores altitude and treats the earth as a perfect ellipsoid.
 The Universal Transverse Mercator is a system of map projections divided into
sixty zones across the globe, with each zone corresponding to 6 degrees of
longitude.

12. UTM PROJECTION :
 A UTM zone is a 6° segment of the Earth. Because a circle has
360°, this means that there are 60 UTM zones on Earth. (360 ÷ 6
= 60).

13. UTM PROJECTION :
The transverse Mercator map projection is an adaptation
of the standard Mercator projection which flips the
cylinder 90 degrees (transverse).
The UTM projection flattens the sphere 60 times by
shifting the cylinder central meridian 6° for each zone.
This gives cartographers a map to work with always in
meters.
 The Universal Transverse Mercator is horrible for small-scale
(less-detailed) maps like world atlases and perfect for
mapping narrow regions.

14. UTM PROJECTION :
 UTM applies a secant cylinder that intersects the ellipsoid along
two small circles parallel to the central Meridian. This means that
scale is constant north-south along the Meridians. But scale varies
east-west along parallels.
 The two small circles are 180 kilometers east and west of the
central Meridian at the Equator. The small circles have a scale
factor of 1, meaning a distance of 100 meters in the ellipsoid
would be the same on the map projection.
 The centerline of a UTM grid zone has a scale factor of 0.9996. This means
that a distance of 100 meters on an ellipsoid would be 99.96 meters on a
map.

15. TYPES OF CYLINDRICAL PROJECTIONS :
 Miller Projection : The Miller Projection was developed by O. M. Miller in
1942 using a cylinder projection developable surface tangent at the Equator.
 The Miller map projection is very similar to Mercator, but straight lines are not
Rhumb Lines. This means that it’s not particularly useful for navigation, but
more so for wall
 Miller Projection Map Distortion :Area and shapes are still
distorted, but not as extreme as the Mercator projection. The
Miller projection it isn’t equal in area, equidistant, or conformal,
and doesn’t sacrifice either one at extremes. Directions distortion
increases further away from the Equator at higher latitudes.

16. TYPES OF CYLINDRICAL PROJECTIONS :
■ Pseudocylindrical Projections : The cylindrical family of map
projections typically has equally spaced meridians to horizontal latitude lines.
■ While the pseudocylindrical such as the Sinusoidal and Robinson projections
have a central Meridian and horizontal parallels as straight line segments but
not other Meridian lines.

17. TYPES OF CYLINDRICAL PROJECTIONS :
 Sinusoidal projection : The sinusoidal projection is a
pseudocylindrical equal-area map projection, sometimes called the Sanson–
Flamsteed or the Mercator equal-area projection.
 The projection has also been used for maps of continents near the
equator, like South America and Africa, centered on their own central
meridians.
 The projection represents the poles as points, as they are on the sphere, but
the meridians and continents are distorted. The equator and the prime
meridian are the most accurate parts of the map, having no distortion at all,
and the further away from those that one examines, the greater the distortion.

18. The projection is defined by,
X = 𝜆 − 𝜆0 cos 𝛹 .
Y = 𝛹.
Where phi is latitude, lambda is longitude & lamda not
is longitude of the central meridian.
 Scale is constant along the central meridian, and east–west scale
is constant throughout the map. Therefore, the length of each
parallel on the map is proportional to the cosine of the latitude, as
it is on the globe. This makes the left and right bounding meridians
of the map into half of a sine wave, each mirroring the other.
 Each meridian is half of a sine wave with only the amplitude
differing, giving the projection its name.
SINUSOIDAL PROJECTION :

19. ROBINSON PROJECTION :
 The Robinson projection is a map projection of a world map which
shows the entire world at once. It shows the whole globe as a flat image.
 Robinson's map is best within 45° of the equator. Distances along
the equator and the lines parallel to it are true.
 Advantage: The Robinson map projection shows most distances, sizes
and shapes accurately. Disadvantage: The Robinson map does have
some distortion around the poles and edges.

20. MOLLWEIDE PROJECTION :
 The Mollweide projection is an equal-area, pseudocylindrical
map projection generally used for maps of the world or celestial
sphere. It is also known as the Babinet
projection, homolographic projection, and elliptical projection.
 The projection trades accuracy of angle and shape for accuracy of
proportions in area.

21. PLANAR PROJECTIONS :
 Planar projections project map data onto a flat surface
touching the globe. A planar projection is also known as an
azimuthal projection or a zenithal projection.
 This type of projection is usually tangent to the globe at one
point but may be secant also. The point of contact may be
the North Pole, the South Pole, a point on the equator, or any
point in between(INCLINED OBLIQUELY).

22. COORDINATE SYSTEMS :
 A coordinate system is used to determine each point uniquely in a
plane.
 A coordinate system is a system that uses numbers or
coordinates to determine the position of a point .
 A coordinate system is also used as a reference system to
represent locations of geographic features, observation points,
GPS (Global Positioning System) points.

23. GCS & PCS :
A GCS defines where the data is located on the earth's
surface. It’s shaped like a globe—spherical. Its units
are angular, usually degrees. A GCS is often incorrectly
called a datum, but a datum is only one part of a GCS. A GCS
includes an angular unit of measure, a prime meridian, and a
datum (based on a spheroid). EX :- WGS1984.
 A PCS tells the data how to draw on a flat surface, like on a
paper map or a computer screen. Its units are linear, most
commonly in meters. EX :- UTM.