4 - Map projections Flashcards
Projection def
A mathematical transformation of the earths 3D spheroid
surface into 2D format, so that distances can be measured.
Geographical coordinates -> Cartesian (planar) coordinates
Map projections can be described in terms of their:
- Class (cylindrical, conical or azimuthal),
- Point of secancy (tangent or secant),
- Aspect (normal, transverse or oblique),
- Distortion property (equivalent, equidistant or conformal)
Map projection meaning
surfaces on which we project the shadows of the graticules… (plane, cylinder & cone)
Tangent & secant def
The line of contact between the earth and the projection surface/plane is called a tangent.
If there are two such lines, they are called secants
Tangent cylindrical projection def
Circumference touches globe; one standard parallel
Where do you have 0 distortion?
Tangents or secants; the contact point btwn the spheroidal earth’s surface and the plane of the map projection is the only location where the properties of the projection are true.
Secant cylindrical projection def
Intersects the globe; therefore you have two standard parallels
Where are the 2 standard parallels selected in a secant projection?
Selected at one-sixth below and above the limit of the mapping area
Aspect def
The orientation of the projection plane/surface (normal, transverse or oblique)
Conformal (orthomorphic) projection
Angles btwn lines in the
map are identical to the angles between the original lines on the curved reference surface.
- angles (with short sides)
- shapes (of small areas) are shown correctly on the map.
Equal-area (equivalent) projection
Areas in the map are
identical to the areas on the curved reference surface
Equidistant projection
Length of particular lines in the map are the same as the length of the original lines on the curved reference surface.
Conformal and equivalent are…?
Mutually exclusive (cannot happen at the same time)
Tissot’s Indicatrix
Tissot’s Indicatrix is a method to
visualize the distortions of a map
projection.
Conformal distortions
- Preserves shape
- a=b
-DISTORTS AREA (original size changes) - Parallels and meridians intersect at 90
Conformal examples
- Mercator (cylindrical & conformal)
- Lambert (conic & conformal)
Equal area distortions
- PRESERVES AREA
- correct relative area of infinitesimally small area (Used for theory)
- a X b = 1
- DISTORTS shape
Equal- area examples
- Mollweide (cylindrical, equal area)
- Albers equal area (conic, equal area)
The act involved in South African coordinate reference system
Land Survey Act (Act 8 of 1997)
SA Projection for Orthophoto maps
Gauss Conform (LO system)
1 : 10 000
SA projection for topographical maps
Gauss Conform (LO system)
1 : 50 000
SA projection for aeronautical maps
Lambert Conformal Conic
1 : 1 000 000
SA projection for military maps
Albers Equal area
1 : 250 000
1 : 500 000
Topographical & topo-cadastral maps
South African Projections
- The South African Coordinate Reference System
- Gauss Conform (LO – system)
- Lambert Conformal Conic
- UTM (Universal Transverse Mercator)
- Military maps
Topographical vs topo-cadastral maps
Topographical maps - depict the physical characteristics of the terrain
Topo-cadastral maps -integrate topographical data with data showing property boundaries, subdivision lines, buildings, and related details.
- provide a comprehensive view of both the natural landscape and land ownership boundaries and parcels.
Datum shows us
How the earth’s surface was generalized
Map projection shows us
The nature of distortion on the
map
Coordinate system shows us
How distances are measured
RECAP
Geoid —> Datum —> Map
Geographic coordinate system (GCS)
Defines where the data is located on the earth’s surface.
Projected coordinate system (PCS)
Tells me how to draw on a flat surface, like on a paper map or a
computer screen.
