It is about conformal mapping and projection types along with process of projection

1. Distortion Preservation on on
Conformal Mapping
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2. Horizontal Positioning
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Undulating
Surface
Earth Mathematical Surface
Reference Ellipsoid
Reference Frame &
Datum
Best fit surface of Earth
Coordinate System
Horizontal Position

3. Process of Projection
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2. Project undulating geoid
to regular oblate spheroid
1. Defining Surface
topography wrt geoid
3. Projecting spherical into
map coordinate syetem

4. Projection System
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Physical model
Cylindrical Projection (Cylinder)
Tangent case
 Secant case
 Conic Projection (Cone)
Tangent case
 Secant case
 Azimuthal Projection (Plane)
Tangent case
 Secant case
Distortion Properties
Conformal Projection (preserve
local angles and shape)
 Equal Area or Equivalent (Area)
 Equidistant (Scale along center
line)
 Azimuthal (Directions)

5. July 16, 2015
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Cylindrical Transverse Cylindrical Oblique Cylindrical Secant Cylindrical
Conical
Secant Conical Planar Secant Planar

6. Mapping Plane
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 Plane in which the surface of earth
is projected.
 Distortion is minimum at the point
of contact
 Mapping involves transformation
of geographic coordinates
(∅, 𝛌) 𝐢𝐧𝐭𝐨 (𝐱, 𝐲) in terms of
easting and northing.

7. Conformal Projection
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Properties
Preserve Shape
(only for small areas)
Preserve Angles
Used for Large Scale Mapping
Distortion increases outwards from the
central meridian and standard parallel
Fig. Lambert conformal conic
projection

8. Distortion
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Conformal projection best suits for large scale map or
small area also scale remains moreover constant.
For small scale map, scale gets distorted.
Meridians and Parallels intersect at right angle.
Area and Length are affected due to conformal projection.

9. Lambert Conformal Conic Projection
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North Standard
Parallel
South Standard
Parallel
Parallel of
Grid Origin
(Base Parallel)
Central Meridian
Polar Axis
On development
Type: Conic & Secant
Property: Conformal

10. Transformation
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 The coordinates from spherical datum can
be transformed to Lambert Conformal
Conic Projection by the following formulas,
where
 λis longitude λ0 is reference longitude
 ϕ1 and ϕ2 are reference parallels
 ϕ0 is reference latitude.
 ϕ is latitude.

11. Features
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 Distances are true only along the standard parallels.
 Other regions have reasonable accurate length.
 Directions are reasonably accurate.
 Distortions of shape is minimal at standard parallels
 eg. Used for maps of North America with standard parallel 33N
and 45N with scale error of 2.5% for topographic maps.

12. Scale Error
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 Map projection without distortions
would correctly represent shape, angle,
area, distance, direction anywhere on
the map.
Hence a map projection is associated
with scale distortions.
 It depends on the size of area being
mapped and type of map projection
selected.
Fig. Scale distortion after
flattening

13. Singularity
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 It is error encountered in
conformal map (at least one
point)
 Green circle on map
represents 254 ° 33´.
 The opposite pole is second
singularity which is absent on
map.
It can be mapped at infinity.
Fig. conic conformal map
Fig. Earth

14. Application
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Navigation Charts
(pilots)
Weather Maps
(Weather forecasting)
Topographic
Mapping
(North America)
Large Scale
Surveying
(USA)

15. Country using Lambert
Conformal Conic Projection
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 USA
 Belgium
 France
 Ireland
Fig. Map projection of International Map series
Source: Map projections for Europe (European Commission Joint
Research Center) Edited by A. Annoni, C. Luzet, E. Gubler, J. Ihde 2001

16. Advantage
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 Angles and small shapes are preserved.
 Minimum area distortion around standard parallel.
 Accurate distance over standard parallel.
 Best suited over middle latitudes and those having east-west
extent.
Limitation
 Increase in distortions (shape, size and area) away form
standard parallels.
 It cannot be used for thematic and statistical mapping.
 Error due to Singularity.

17. References
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http://kartoweb.itc.nl/geometrics/map%20projections/mappro.html
http://geokov.com/education/map-projection.aspx
https://en.wikipedia.org/wiki/Lambert_conformal_conic_projection
http://geospatial.referata.com/wiki/Lambert_conformal_conic_projection
http://www.progonos.com/furuti/MapProj/Normal/ProjConf/projConf.html
 Map projections for Europe (European Commission Joint Research Center)
Edited by A. Annoni, C. Luzet, E. Gubler, J. Ihde 2001.
 Map Projections – A Working Manual by John P. Snyder
(US Geological Survey Professional Paper 1395)

18. THANK YOU
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