Map projections

Question 1

What is a map projection?

Answer 1

a mathematical transformation of the earths 3D spheroid
surface into 2D format. So that distances can be measured.

Geographical coordinates are transformed to
Cartesian coordinates.

Question 2

Difficulty with choosing map projections

Answer 2

Various projections therefore:
* Different projections distort different properties.
* Different projections preserve different properties.

Question 3

How can map projections be described
or classified?

Answer 3

1. Class (cylindrical, conical or azimuthal).
2. Point of secancy (tangent or secant).
3. Aspect (normal, transverse or oblique).
4. Distortion property (equivalent, equidistant or conformal).

Question 4

What does class refer to?

Answer 4

the projection surface/plane.

1. Planar
2. Cylindrical
3. Conical

Projection planes are:
plane, cylinder and cone.

Question 5

What does secancy refer to?

Answer 5

The line of contact between the earth and the projection surface/plane is called a tangent.

The contact point (or points) between the spheroidal earth’s surface
and the plane of the map projection is the only location where the properties of the projection are true.

tangents are the points of contact between the earth’s surface and the projection plane. As you move further away from the tangent distortion increases.

Question 6

What are the projections of secancy?

Answer 6

• A cylindrical projection:
• Tangent projection: circumference touches globe; one standard
  parallel
• Secant projection: Intersects the globe and therefore you have two
  standard parallels (are selected at one-sixth below and above the
  limit of the mapping area)

Question 7

What does aspect refer to?

Answer 7

The orientation of the projection plane/surface.
Can be oblique, transverse or normal.

Question 8

What is the distortion property?

Answer 8

How a projection is done determines which kind of distortion properties the map will have compared to the original curved reference surface. The distortion properties of map are typically classified according to what is not distorted on the map.

Question 9

What is a conformal projection?

orthomorphic

Answer 9

Map projection the angles between lines in the
map are indentical to the angles between the original lines on the curved reference surface.

[ angles and shapes are preserved ]

Question 10

What is an equal-area map?

Equivalent

Answer 10

Map projection the areas in the map are identical to the areas on the curved reference surface. Which means that areas are represented correctly on the map.

[ preserve directions, only from centre of map to any other point along a great circle. ]

Question 11

What is an equidistant map?

Answer 11

Map projection the length of particular lines in the map are the same as the length of the original lines on the curved reference surface

[ Preserving the principle scale between 2 points on a map. Distance can only be preserved in one direction]

Question 12

Map projections can have more than one preserved property BUT ->

Answer 12

Conformal and equivalent properties are mutually exclusive!

Question 13

What is Tissot’s Indicatrix?

Answer 13

Uses a graphic device (infinitely small circle of radius 1.0) to illustrate
the angular and areas distortions that occur at points as a result of a
transformation.

After a transformation the circle will change in size and/or in shape (become an ellipse) depending on the type of projection that is used.

[ Provides a visual means of showing how distortion varies at point locations across a projection.
A quantitative analysis of distortion that describes the amount and type of distortion that occurs at points across the map ]

Question 14

How can we use Tissots indicatrix to analyse distortion?

Answer 14

based on a unit circle
r-1.0, where all spatial relationships are preserved.

a=b=1
when a=b there is no distortion

when a=/b but a=1 then there is angular distortion

when a=b but a=/ 1 then aerial distortion takes place

when a=/b and a=/1 angular and aerial distortion occurs

Question 15

What are south africa’s projections?

Answer 15

• The South African Coordinate Reference System
• Land Survey Act (Act 8 of 1997).

Gauss Conform (LO – system)
- 1:10 000 Orthophoto and
- 1:50 000 Topographical maps

Lambert Conformal Conic
- 1:1 000 000 Aeronautical maps

UTM (Universal Transverse Mercator)

• Military maps
• Albers Equal Area
• 1:250 000, 1:500 000 Topographical and topo-cadastral maps

Question 16

South African map projections

Answer 16

Gauss Conformal (Transverse Mercator), Lambert Conformal, Albers Equal Area
and UTM are the most commonly used map projections in South Africa