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OUTLINE: scale definition types of scale projection definition projection properties and
classification choosing a map projection
MMAP AP PPROJECTIONSROJECTIONS ANDAND SSCALECALE
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PPROJECTIONSROJECTIONS
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THE GLOBETHE GLOBE
Advantages:
most accurate map
latitude and longitude lines
Disadvantages
expensive to make
cumbersome to handle and store
difficult to measure
not fully visible at one
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PROJECTIONSPROJECTIONS
process of transforming earth’s spherical surface to a flat map while maintaining spatial relationships.
Curved Earth
Flat Map
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projection process involves stretching and distortion
PROJECTIONSPROJECTIONS
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no matter how the earth is divided up, it can not be unrolled or unfolded to lie flat (undevelopable shape).
PROJECTIONSPROJECTIONS
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PROJECTION PROCESSPROJECTION PROCESS
most projections are combinations of the following characteristics:
characteristic of earth features that are maintained
shape of the projection plane (developable shape)
aspect of the projection plane
points or lines of tangency or secancy
location of the false ‘illumination source’
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PROJECTION PROPERTIESPROJECTION PROPERTIES
properties in which distortion is minimized when producing a map
AreaArea
equal area or equivalent
area sizes are correct everywhere on map
shapes greatly distorted
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DistanceDistance
equidistant
distance is correct in all directions from a point
i.e. equidistant projection centered on Winnipeg would show the correct distance to any other location on the map, from Winnipeg only
distorting area and/or direction
PROJECTION PROPERTIESPROJECTION PROPERTIES
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EquidistantEquidistant
PROJECTION PROPERTIESPROJECTION PROPERTIES
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DirectionDirection
azimuthal
compass bearing is maintained in all directions only from a point
shapes, distances and areas are badly distorted
PROJECTION PROPERTIESPROJECTION PROPERTIES
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ShapeShape
conformal
shape maintains its shape across the map distorting area
latitude and longitude cross at right angles
used for navigation
PROJECTION PROPERTIESPROJECTION PROPERTIES
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Area Distance Direction Shape
Equal-Area No Yes No
Equidistant No Yes No
Azimuthal Yes Yes Yes
Conformal No No Yes
PROJECTION PROPERTIESPROJECTION PROPERTIES
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Tissot’s IndicatrixTissot’s Indicatrix
convenient way of showing distortion
size and shape of the indicatrix will vary from one part of the map to another
Mercator projection
Equal-Area projection
PROJECTION PROPERTIESPROJECTION PROPERTIES
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made by projecting a globe onto a surface – developable surface
distortion is least where developable surface touches the earth
accomplished by use of geometry and mathematics
2))sin(1sin(124tanln eeesay
sax
Mercator:
PROJECTIONSPROJECTIONS
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PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
Tangent caseTangent case – shape just touches the earth along a single line or at point.
Secant caseSecant case – shape intersects or cuts through earth as two circles.
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ConicalConical
globe sits under a cone, touching along pre-selected line of latitude
projection developed by cutting cone lengthwise and unrolling
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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normal case:
parallels – concentric circular arcs, meridians – straight equally spaced lines
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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Lambert conformal conic projection
Albers equal-area conic projection
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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Conical Distortion
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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ConicalConical
PolyconicPolyconic – envelopes globe with an infinite number of cones, each with its own standard parallel
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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CylindricalCylindrical
projected onto a cylinder which is also cut lengthwise and unrolled
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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CylindricalCylindrical
evenly spaced network of straight, horizontal parallels and straight vertical meridians (grid like)
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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Cylindrical DistortionCylindrical Distortion
projection of the entire world, significant distortion occurs at the higher latitudes
parallels become
further apart and poles
can not be seen
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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Cylindrical DistortionCylindrical Distortion
sizes of Greenland vs. Africa
Mercator Projection True size
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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CylindricalCylindrical
straight line between any two points follows a single direction called a rhumb line
useful in construction of navigational charts
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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Planar/AzimuthalPlanar/Azimuthal portion of earth’s surface is transformed from a
perspective point to a flat surface
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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Planar/AzimuthalPlanar/Azimuthal perspective point/light source
Light rays
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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Planar/AzimuthalPlanar/Azimuthal
true direction only between center and other locations
most often used to map polar regions
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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NORMAL
OBLIQUE
TRANSVERSE
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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ConicCylindrical
Planar
CANADA PROJECTEDCANADA PROJECTED
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Pseudo map projectionsPseudo map projections
pseudoconic and pseudocylindrical projections - have curved meridians instead of straight ones
Pseudocylindrical
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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Pseudo map projectionsPseudo map projections modified projections - changes have been made to
reduce the pattern of distortion or add more standard parallels
modified to reduce the distortion in the size of areas
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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Pseudo map projectionsPseudo map projections individual or unique projections – can not be easily
related to one of the three developable geometric forms
Goode’s Projection
PROJECTION CLASSIFICATION
PROJECTION CLASSIFICATION
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CHOOSING PROJECTIONCHOOSING PROJECTION
depends on:
purpose for which the data is to be used
property in which distortion is minimized
extent and location of area
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steps:
1. size of area of interest
small area has little distortion, any projection.
2. latitude of area of interest
low-latitudes – cylindrical
mid-latitudes – conical
polar latitudes - planar
CHOOSING PROJECTIONCHOOSING PROJECTION
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3.3. shape of area of interest:shape of area of interest: E-W extent: conic or cylindricalE-W extent: conic or cylindrical N-S extent: cylindricalN-S extent: cylindrical square or circular: planarsquare or circular: planar
4.4. purpose:purpose: navigation – planar or cylindricalnavigation – planar or cylindrical world distributions – cylindricalworld distributions – cylindrical specific locations - planarspecific locations - planar
CHOOSING PROJECTIONCHOOSING PROJECTION
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COMMON PROJECTIONSCOMMON PROJECTIONS
Albers Equal-Area ConicAlbers Equal-Area Conic
equal area, secant conical projection (two standard parallels)
resembles earth graticule
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MercatorMercator
cylindrical, conformal projection
angular relationships are preserved parallels and
meridians appear as straight lines
parallels are farther apart with increased distance from equator
COMMON PROJECTIONSCOMMON PROJECTIONS
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MercatorMercator
change in N-S scale exactly offset change in E-W direction (shapes preserved)
scale is true at equator or at two standard parallels equidistant from equator
all rhumb lines appear as straight lines, while great circle arcs are not (except equator and meridians)
used primarily for navigation and large scale maps
COMMON PROJECTIONSCOMMON PROJECTIONS
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Transverse MercatorTransverse Mercator
cylindrical, conformal projection
similar to Mercator except the axis of projection cylinder is rotated 90o from polar axis
scale is true along central meridian or along two straight lines equidistant from and parallel to central meridian
used to portray areas with larger N-S than E-W extent.
COMMON PROJECTIONSCOMMON PROJECTIONS
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Lambert Conformal ConicLambert Conformal Conic
conformal, secant conical projection with two standard parallels
possesses true shape of small areas with area distortion
concentric parallels (increasing intervals) and equally-spaced straight meridians
COMMON PROJECTIONSCOMMON PROJECTIONS
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COMMON PROJECTIONSCOMMON PROJECTIONS
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COMMON PROJECTIONSCOMMON PROJECTIONS
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MollweideMollweide
pseudocylindrical, equal-area projection
N-S scale is decreased in high latitudes, increased in low latitudes; opposite in E-W direction
parallels are straight, spaced closer together from equator
COMMON PROJECTIONSCOMMON PROJECTIONS
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Polar StereographicPolar Stereographic
directions are true from center point
conformal projection: over a small area, angles in the map are the same as the corresponding angles on Earth's surface
meridians are straight and radiating; parallels are concentric circles
shows only one hemisphere
COMMON PROJECTIONSCOMMON PROJECTIONS
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Polar StereographicPolar Stereographic
preserves circles - all great and small circles are shown as concentric arcs or straight lines
scale true only where the central parallel and meridian cross
used in polar aspect for topographic maps of polar regions, regions that are circular in shape
COMMON PROJECTIONSCOMMON PROJECTIONS
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Eckert IV Equal AreaEckert IV Equal Area
pseudocylindrical and equal-area
scale is true along the parallel at 40:30 North and South
COMMON PROJECTIONSCOMMON PROJECTIONS
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RobinsonRobinson
developed to minimize appearance of angular and area distortion
distorts shape, area, scale and distance in an attempt to balance errors of projection properties
COMMON PROJECTIONSCOMMON PROJECTIONS
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RobinsonRobinson
based on tables of coordinates not mathematical formulae
overall effect – more than 75% of earth is shown with less than 20% departure from true scale size
used for thematic and reference maps
COMMON PROJECTIONSCOMMON PROJECTIONS
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OTHER PROJECTIONSOTHER PROJECTIONS
Berghaus Star
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Sanson-Flamsteed
OTHER PROJECTIONSOTHER PROJECTIONS
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Conoalactic
OTHER PROJECTIONSOTHER PROJECTIONS
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Hammer
OTHER PROJECTIONSOTHER PROJECTIONS
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Eisenlohr
OTHER PROJECTIONSOTHER PROJECTIONS
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Gall Stereographic Cylindrical
OTHER PROJECTIONSOTHER PROJECTIONS
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Cassini
OTHER PROJECTIONSOTHER PROJECTIONS
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SSCALECALE
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SCALE
size of an object on a map compared to the actual object on the ground
distance
distance
ground
mapscalemap
may not be the same in all directions from a point
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SCALE TYPESSCALE TYPES
Verbal scale
describes the scale in words
i.e. “one centimeter represents one kilometer”
commonly found on popular atlases and maps
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Visual scale (bar scale or graphic scale)
graphically illustrates relationship between map distance and ground distance.
one end can be divided
most common
remains correct if reduced or enlarged
SCALE TYPESSCALE TYPES
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Visual scale (bar scale or graphic scale)
SCALE TYPESSCALE TYPES
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Representative Fraction (RF)
ratio (proportion) between map distance to earth distance
i.e. 1:50,000
most versatile; not tied to any specific units
SCALE TYPESSCALE TYPES
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SCALE FACTORSCALE FACTOR
Representative Fraction
Globe distanceEarth distance
=
Map Scale:
(e.g. 1:24,000)
Map Projection:
Scale Factor
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stated scale is correct only at selected points
statement of relation between given scale and actual scale value
scaleprincipalscaleactual
SF
i.e. SF of 2.000 would mean that actual scale is twice the principal scale
SCALE FACTORSCALE FACTOR
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large scale: show a small area with a large amount of detail.
small scale: show a large area with a small amount of detail
all relative
LARGE VS SMALL SCALE
LARGE VS SMALL SCALE
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DETERMING SCALE DETERMING SCALE use map scale to convert map distance to ground
distance.
for verbal and RF scales - multiply by the scale, then convert the ground distance to units suitable for ground measurements.
i.e. we have a map with a scale of 1:50,000. We measure the distance along a property boundary as 1.7 cm. What is the length in the real world?
for graphic scales – mark off a distance on the map and compare it directly to the bar scale.
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Verbal to RF
write verbal scale as a fraction then convert so that both numerator and denominator have the same units and numerator has a 1
i.e. convert verbal scale “1 cm represents 100 km” to RF
RF to Verbal
i.e. convert from RF of 1:25,000 to verbal scale, in metric
TRANSFORMING SCALES
TRANSFORMING SCALES
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Graphic Scales and RF/Verbal
take the measurement from the bar scale to determine the map distance and corresponding ground distance.
i.e. 10 km on ground measures 2.4 cm on map.
use method for verbal scale to RF conversion.
TRANSFORMING SCALES
TRANSFORMING SCALES