Projections 2011

7/28/2019 Projections 2011

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Map Projections andCoordinate Systems

Jan-Van Sickle

Khang-tsung Chang

ESRI Using ArcMap


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Basic Map projection Types Conformal: preserves local shapes and angles

Equivalent/equal area: represents areas in correctrelative size (shapes not preserved)

Equidistant: preserves consistency of scale along

certain lines Azimuthal: preserves accurate directions (e.g.,

angles preserved, but length of lines is not)

Property is often included in name (e.g., Lambertconformal conic projection)

Map can have more than one property, but conformaland equivalent are mutually exclusive


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Conformal projections

Conformal projections preserve local shape.

To preserve individual angles describingthe spatial relationships, a conformal

projection must show the perpendicular

graticule lines intersecting at 90-degree

angles on the map.


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Equal area projections

Equal area projections preserve the area

of displayed features. To do this, the otherpropertiesshape, angle, and scalearedistorted. In equal area projections, the

meridians and parallels may not intersectat right angles.


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Equidistant projections

Scale is not maintained correctly by any

projection throughout an entire map;however, there are, in most cases, one or

more lines on a map along which scale is

maintained correctly. Most equidistant

projections have one or more lines for

which the length of the line on a map is thesame length (at map scale) as the same

line on the globe.


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True-direction or Azimuthal

projections

True-direction,orazimuthal, projections give the

directions or azimuths of all points on the mapcorrectly with respect to the center. Some true-direction projections are also conformal, equalarea, or equidistant.


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Examples

Planer Projections

Polar Map Projections

Secant Map Projections

Simple Conic Projections Lambert Conic Projection

Cylindrical Projections

Universe Transverse Mercator


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Planar Projections


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Plane Polar Map Projections

One tangent plane

A plane touching the globe at a single

point


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Question

Is the Polar Projection an Azimuthal

Projection?


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Answer

YES:

Direction of any line from the central tangent

point on the map to any other point

represents the actual direction of the line.Preserves accurate directions (e.g., angles

preserved, but length of lines is not)


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1 - Stereographic

Imaginary light source

on the opposite pointof tangency


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Question

Is the stereographic projection a Conformal

projection (i.e., preserves shapes)?


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AnswerConformal: preserves

local shapes andangles


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Question

Where is the no distortion (of scale) zone

on the map?


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Answer

Center of map


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Question

Where on the map does distortion increase?


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Answer

Away from the Center


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Rule

The point (standard point) or the line

(standard line) where a map & a globetouch are the only locations on the map

where there are no distortions


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2 - Gnomonic Imaginary light source

at the center of theglobe

Conformal: preserveslocal shapes and

angles


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Modifications to Decrease

Distortions

Basis: Decrease the distance between the

map projection surface and the ellipsoidal

surface


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Surface cuts theellipsoid

The area where

distortion is inacceptable range is

increased

Secant Projection


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Simple Conic Projections

The most simple conic projection is tangent to the

globe along a line of latitude. This line is called the

standard parallel.Straight converging lines (meridians) and concentric

circular arcs (parallels). Central meridian center of

map.


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QuestionFor Simple Conic Projections

Distortion increases as you move

away (E or W) from the Central Meridian

away from the standard parallel (approach pole)

Conic projections are used for mid-latitude

zones that have an EW orientation (True or False)


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Answer Distortion increases as you approach the

poles

Conic projections are used for midlatitudezones that have an EW orientation


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Secant Conic Projections

More complex conic projections that contact the

global surface at two locations.


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Cylindrical Projections


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Universe Transverse Mercator

Projection

Cartesian coordinates

For each zone, the enclosing cylinder is

rotated so that a particular centralmeridian (longitude) is touched.


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Universal Transverse Mercator

(UTM)


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Special Case: State Plane Really a meta-projection

Each state has one or more projections,with one or more zones.


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Data from maps of varying

projections can not be integrated


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Solution: Projection and

Reprojection

Projection: Converts from a geographic

coordinate system to projectedcoordinate system

Re-projection: Projects from one type of

projected coordinates to another type

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Projections 2011

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