MAP PROJECTIONS LECTURE_removed.pdf

❑ A map projection is a method for
mapping spatial patterns on a
curved surface (the Earth’s
surface) to a flat surface.
❑A map projection is a systematic
rendering of locations from the
curved Earth surface onto a flat
map
MAP PROJECTION

▪GLOBE
▪The earth is a spheroid
The best model of the earth is a globe
•not easy to carry
•not good for making
planimetric measurement
(distance, area, angle)
▪2D-FLAT
▪MEDIUM
Maps are flat
easy to carry
good for measurement
scaleable

Cutting the
earth’s
sherical
shape
into several
parts
some Parts
Will give
way

o Most map projections are based on a
developable surfaces-
•Cones (conic)
•Cylinders (cylindrical)
•Planes (azimuthal)
• Some projections are not based on developable
surfaces-Mathematical calculations
TYPES OF MAP PROJECTION

o On the basis of drawing techniques, map Projections
maybe classified perspective, non-perspective and
conventional or mathematical.
o Perspective projections can be drawn taking the help of
a source of light by projecting the image of a network of
parallels and meridians of a globe on developable
surface.
o Non¬perspective projections are developed without the
help of a source of light or casting shadow on surfaces,
which can be flattened.
o Mathematical or conventional projections are those,
which are derived by mathematical computation and
formulae and have little relations with the projected
image.
CLASSIFICATIONMAP PROJECTION

o On the basis of drawing techniques, map Projections
maybe classified perspective, non-perspective and
conventional or mathematical.
o Perspective projections can be drawn taking the help of
a source of light by projecting the image of a network of
parallels and meridians of a globe on developable
surface.
o Non¬perspective projections are developed without the
help of a source of light or casting shadow on surfaces,
which can be flattened.
o Mathematical or conventional projections are those,
which are derived by mathematical computation and
formulae and have little relations with the projected
image.
ON THE BASIS OF DRAWING TECHNIQUES

o 2. On the basis of developable surface, it can be
developable surface and non developable surface.
o
o A developable surface is one, which can be flattened,
and on which, a network of latitude and longitude can
be projected.
o A globe or spherical surface has the property of non-
developable surface whereas a cylinder, a cone and a
plane have the property of developable surface.
o On the basis of nature of developable surface, the
projections are classified as cylindrical, conical and
zenithal projections.
ON THE BASIS OF DEVELOPABLE SURFACE

o 3. On the basis of global properties, projections are
classified into equal area, orthomorphic, azimuthal and
equidistant projections.
o 4. On the basis of location of source of light, projections
maybe classified as gnomonic, stereographic and
orthographic.
o The correctness of area, shape, direction and distances
are the four major global properties to be preserved in a
map. But none of the projections can maintain all these
properties simultaneously. Therefore, according to
specific need, a projection can be drawn so that the
desired quality may be retained.
ON THE BASIS OF GLOBAL PROPERTIES & SOURCE OF LIGHT

o Reduced Earth: A model of the earth is represented
by the help of a reduced scale on a flat sheet of
paper. This model is called the “reduced earth”.
o Parallels of Latitude: These are the circles running
round the globe parallel to the equator and
maintaining uniform distance from the poles.
o Meridians of Longitude: These are semi-circles drawn
in north-south direction from one pole to the other,
and the two opposite meridians make a complete
circle, i.e. circumference of the globe.
ELEMENTS OF MAP PROJECTION

o Global Property: In preparing a map projection the
following basic properties of the global surface are to be
preserved by using one or the other methods:
o Distance between any given points of a region;
o Shape of the region;
o Size or area of the region in accuracy;
o Direction of any one point of the region bearing to
another point image.
ELEMENTS OF MAP PROJECTION

◼an imaginary light is “projected” onto a “developable surface”
◼a variety of different projection models exist

secant cone
tangent cone
Cone as developable surface

tangent cylinders
cylinder as developable surface

EXAMPLES OF CYLINDRICAL PROJECTION
Cylindrical Equal Area Equirectangular
Transverse Mercator
Mercator
Miller Cylindrical

MAP PROJECTION CHARACTERISTICS

o On cylindrical projection, lines of longitudes are
typically appears as straight, equally spaced,
parallel lines
o Where as, lattitude lines appears straight parallel
lines that increase the lines of longitude at right
angles.
o The spacing of parallel distinguishes one
cylindrical projection from another.
CYLINDRICAL MAP PROJECTION

o Through the manipulation of mathematical
equations, numerous projctions are possible with
each having specific characteristics.
o Based on them, THREE major characteristics exist:
o A CLASS- This Concpt is a constructive way to
describe the overall shape and appearance of
th graticule after the projection process is
complete.
o Three common map projection CLASSES are:
o 1. Cylindrical 2. Conic and 3. Panar/Azimuthal
MAP PROJECTION CHARACTERISTICS

o On conic class of projection result from wrapping the
developable surface of a cone around the referenced
globe, projecting the landmass and graticule on the
cone, and then unrolling the cone.
o Lines of longitude on this projection typically appears
straight lines of equal length radiating from a centre
point (usually one of the poles)
o Where as, lines of latitude appears as concentric circular
arcs centred about one of the poles.
o The overall shape of most conic projection can be
described as a pie wedge, where a pie would be a full
circle.
o The angular extent of the pie wedge and the spacing of
the parallels distinguishe one conic projection from
CONIC MAP PROJECTION

o The planar projection result from positioning the
developable surface of a plane next to the ref. globe
and protecting the landmasses and graticlules on the
plane.
o On planar projection, lines of longitude typically appears
as straight, equally spaced, parallel lines that radiate
from the centre ( where he cntre appear as equally
spaced concentric circles centred about a point).
o The spaces of the parallels distinguishes one planar
projection from the other.
PLANAR/AZIMUTHAL PROJECTION

o The CASE of aprojection relates to how the developable
surface is positioned with respect to the ref. globe and is
either TAGENT or SECANT
o TAGENT:- Conceptually speaking, consider a ball rolling
across he floor.
o At any given time, there is exactly one point in common
between the ball and the floor.
o The point of contact is called – THE POINT OF TAGNECY
o If all points were connected together( in either on the
point o on the floor), a line of tagency would result.
o In tagent case, the ref. globe touches the dev. Surface
along only one line or at one point.
Map Projection based on CASE

o
o SECANT:-The secant case of a projection occurs when
the dev. Surface pass through the ref. globe of cylindrical
and conic projection.
o In the Secant case, there are two secant lines where as
in the case of planar projection there is one secant line.
o With conic class, any line of latitde can be selected as
the tangent line.
o In secant case, of the conic class, any two lines of
latitude can be selected.
o The secant lines and point of tangency each has the
same scale as the principal scale of the ref. globe.
o The choice of the tangency or secant case as well as
their placement with respect to ref. Globe impacts the
shape of the landmasses and the arrangement of the
graticule.
Map Projection based on CASE

o
o The aspect of a Map projection concerns the placement
of the projection’s centre with respect to the Earth’s
surface.
o In general terms, a projection can have one of the three
aspects: 1. Equatorial, 2. Oblique and 3. Polar.
o EQUATORIAL:- An equatorial aspect is centred
somewhere along the equator.
o POLAR: -A polar aspect is centred about one of the
poles.
o OBLIQUE:- An oblique aspect is centred somewhere
between a pole snd the equator.
o The aspect of the projection can be defined more
precisely in terms of the central meridian and the latitude
of origin.
Map Projection based on ASPECT

EXAMPLE:-
A central Meridian of -96ºW and Origin of 0º= Equatorial Aspect
A central Meridian of -96ºW and Origin of 30ºN= Oblique Aspect
A central Meridian of -96ºW and Origin of 60ºN= Oblique Aspect
A central Meridian of -96ºW and Origin of 60ºN = Polar Aspect
o All of these on a cylindrical projection.
Map Projection based on ASPECT

o A Map projection is said to possesse a specific
property when it preserves one of the spatial
relationships i.e.
o Areas, Angles, Distances and Direction found on
the earth’s surface.
o PRESERVING AREAS:- Projection that preserve
areas throughout the projection area called
Equivalent projection (Equal Areas).
o Equivalent projection preserves landmasses in
their true proportions as found on the Earth’s
surface.
o To be sure that areas are preserved in equivalent
proj., the SF’s must be controlled so that each
indicatrix contains the same area.
MAP PROJECTION PROPERTIES

o PRESERVING ANGLES- Projection that preserve angles
throughout the proj. is called CONFORMAL Projection.
o Conformal projections preserve angular relationships
around a point by uniformly preserving scale relations
about that point in all directions.
o NOTE: Conformal projection does not preserve shapes of
landmasses per se/entirely (with large & small) rather,
it’s preservation of the shape is found only at infinitely
small points.
o Largely conformal projection preserve angular relation
by ensuring that its SF’s change along ‘a’ & ‘b’ at the
same time. E.g Lambert conformal conic projection.

o PRESERVING DISTANCES- When ALL distances from a
particular location are correct, then the projection is said
to be Equidistant.
o In simpler terms, equidistant projection maintains the
principal scale from two (2) points on the map to any
other point on the map. EG. Plate Carree Projection.
o PRESERVING DIRECTIONS:- When direcctions or azimuths
is preserved from one central point to all others, it is
called Planar/azimuthal projection.
o When measuring azimuths from the cente of the
projection, all straight lines drawn or measued to distant
points also represent great circle routes.
o It has been used extensively for navigaion and pin
pointing locations e.g Lambert equidistant, Lambert
orthographic and Gnomonic.

o COMPOMISE PROJECTIONS:- In both conformal &
equivalent projection, the size & shape of landmasses are
often visually distorted to the point of being unrecognizable.
o A solution to this problem is the compromise projection which
manipulates the SF’s so that the extreme angular and areal
distortion found on equidistant & conformal projection is not
present.
o A compromise projection strikes a balance between the
distortion in area that is present on conformal projection and
the angular distortion that is common on a purely equivalent
projection.
o The combined areal & angular distortion is usually less than if a
single property was preserved and the resulting map
generally gives a better visual representation of landmasses.
o A most notable compromise projection is the Robinson
Projection (1988) & until 1998 when it was replaced with Winkle
Tripel Projection.

o Mercator’s Projection is very useful for navigational purposes.
A Dutch cartographer Mercator Gerardus Karmer developed
this projection in 1569. The projection is based on
mathematical formulae.
o Properties:
o It is an orthomorphic projection in which the correct shape is
maintained.
o The distance between parallels increases towards the pole.
o Like cylindrical projection, the parallels and meridians
intersect each other at right angle. It has the characteristics of
showing correct directions.
o A straight line joining any two points on this projection gives a
constant bearing, which is called a Laxodrome or Rhumb line.
o All parallels and meridians are straight lines and they intersect
each other at right angles.
MERCATOR PROJECTION & ITS PROPERTIES

o Properties:
o All parallels have the same length which is equal to the length
of equator.
o All meridians have the same length and equal spacing. But
they are longer than the corresponding meridian on the globe.
o Spacing between parallels increases towards the pole.
o Scale along the equator is correct as it is equal to the length of
the equator on the globe; but other parallels are longer than
the corresponding parallel on the globe; hence the scale is not
correct along them.
o Shape of the area is maintained, but at the higher latitudes
distortion takes place.
o The shape of small countries near the equator is truly preserved
while it increases towards poles.
o It is an azimuthal projection.

o Properties:
o This is an orthomorphic projection as scale along the meridian
is equal to the scale along the parallel.
o Limitations
o There is greater exaggeration of scale along the parallels and
meridians in high latitudes.
o As a result, size of the countries near the pole is highly
exaggerated.
o Poles in this projection cannot be shown as 90° parallel and
meridian touching them are infinite.
o https://www.youtube.com/watch?v=nJ5r4HJMrfo

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