Projections and Graticules Flashcards
Latitude
The angular distance north or south of the equator
A measure of distance, not a place
Great Circle
A plane that cuts the Earth in half
Equator
Infinite number as long as the go thru the center (all lines of longitude)
Small Circle
A plane through the Earth but not in half
Parallel
Specific small circles parallel to the equator
Parallels are NOT latitudes
A specific “place” not a distance
Infinite number of parallels
Decrease with high latitudes
Longitude
The angular distance east to west of the Prime Miridian
Prime Meridian
Line of longitude setting 0 for east-west
Thru Greenwich
Meridian
A line joining all points that have the same longitude
All great circles
Graticules
The grid formed by parallels and meridians
Converge at right angles
Shortest distance on a sphere
an arc of a great circle
Azimuth
Direction on a globe (sphere)
Angle measured clockwise from true north-south line and great circle path
Loxodrome/Rhumb Line
A line of constant bearing (compass direction)
Eventually leads you to a pole
4 phases to map projection from reality
Geoid
Ellipsoid (reference)
Nominal, reference globe
Map Projection
Projection
Method of representing data from a curved surface onto a flat plane
Systematic and orderly method
General projection errors to graticules
Tearing
Compression
Shearing
4 Projection Distortion Properties (sort of classifications)
Equivalence
Conformal
Equidistant
Azimuthal
Composite
Map Projection Distortion Properties: Equivalence
Area
Preserve area, distort shape
Map Projection Distortion Properties: Conformal
Shape
actually local angle, not exactly shape
True-Shape, scale is the same in all directions about point
Map Projection Distrotion Properties: Equidistance
Distance
Distance is true along standard parallel
Map Projection Distortion Properties: Azimuthal
Distance is correct only from the center
Composite Map Projections
Combines elements of other projection properties to minimize errors
Its a compromise
Distorts everything a little
Map Projection Classes/Geometry
(Developable Surfaces)
Conic
Cylindrical
Azimuthal (Planar?)
Classifications of Projections
Map projections can be defined by their…?
Distortions (equidistant, conformal, etc)
Class/Geometry (Conic, cylindrical, etc)
Point of Secancy
Aspect
Cylindrical projection at equatorial aspect
Parallels and meridians are straight lines
Meridians are orthogonal to parallels and uniformly spaced
Conic projections in the polar aspect
All parallels are concentric arcs of circle
Meridians are straight lines, perpendicular to every parallel and uniformly spaced
Azimuthal in polar aspects
All parallels are circular
Meridians are straight lines, uniformly spaced
Cylindrical projection common use
Entire world
Conic projection common limitation/use
Can only show one hemisphere
3 types of azimuthal projections
Orthographic
Stereographic
Gnomonic
Orthographic projection (azimuthal)
The light source is an infinite distance
Used for perspective view of hemispheres
Distorts area and shape
Stereographic projection (azimuthal)
Light source is antipode
Specific purpose of maintaining shape (conformal)
Useful for areas extending equally in all directions (Asia)
Gnomonic projection (azimuthal)
Light emanates from center of globe
Displays all great circles as straight lines
Pseudo-cylindrical or conic projection
Meridians are arbitrarily curved
Primary accuracy is usually only preserved along standard parallel
Map projections compromise between…
Conformality, equivalence, and equidistance
Developable surfaces
A surfaces that can be flattened out without tearing or distortion
Standard line/parallel/point
The point or line that is correct on a projections
Distortion increases the further you go from these areas
Area of least deformation
Areas of minimum distortion surrounding the standard parallel or point
Map Projection Classification: Secancy vs Tangency
does the developable surface touch the globe as a point secancy or point of tangency
Secant case
the developable surface for projection intersects the globe, there are two standard lines
Distortion decreases both inward and outward from standard lines
Least distortion at points of contact
Transverse Mercator
Tangent case
The developable surface for projection touches the globe, only one standard line
Distortion increases as globe curves, away from tangent point
Map Projection Aspect
The direction of the projection’s plane orientation
Normal
Polar
Equatorial
Transverse
Oblique
Choice of aspect is informed by location and orientation of focus area
Transverse Aspect
Line of tangency oriented along meridian rather than equator
Developable surface on its side (compared to normal)
Great circle formed by a pair of opposing meridians
Oblique Aspect
Developable surface is angled (compared to normal)
Standard point/parallel is not poles or equator
Equatorial Aspect
Developable surface is placed so north-south is up-down
UTM
Universal Transvers Mercator
Secant case
Projected coordinate system
Conformal
UTM x-axis
North Hemisphere @ equator
South Hem @ 10mil meters from equator
US UTM Zones
10 - 19 for lower 48
1 - 10 for Alaska
4 and 5 for HI
State Plane
Projected coordinate system
uses feet
but sometimes meters?
N-S and E-W are perpendicular
120 zones
Small Zones = Higher accuracy
3 Projections used for State Plane
All conformal
Lambert Conformal Conic (E-W)
Transverse Mercator (N-S)
Oblique Mercator (some of Alaska)
State Plane: False Easting
Moves Y axis westward so all X values are positive
Lambert - 600k meters west of CM
Mercator - 200k meters west of CM
Tissot’s Indicatrix
Quantifies and visualizes map distortions
Uses uniform circles to illustrate linear, angular, and areal distortions
3 Primary Factors in Picking a Projection
Shape of the area
Location and Orientation of the area
Purpose of the map
Possible purposes to chose Conformal projection
Maps that preserve shape
Measuring angles
Showing accurate location directions
Representing the shape of an area
Topographic, cadastral, navigation, military
Possible purposes to chose Equivalence projection
Maps that preserve area
Density of an area (Population)
Spatial extent (Land Use)
Quantitative measure by area (GDP by country)
Possible purposes to chose Azimuthal Equidistant projection
Maps that preserve scale*
Airline distances
Seismic maps
Cost based on straight line distance
*Scale only preserved from standard point
Possible purposes to chose Azimuthal projection
Maps that preserve direction
