Chief Directorate Surveys and Mapping Map Projections Map

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Chief Directorate: Surveys and Mapping

Chief Directorate: Surveys and Mapping

Map Projections

Map Projections

Map Projections • Attempts to portray the surface of the earth or a portion

Map Projections • Attempts to portray the surface of the earth or a portion of the earth on a flat surface. • Some distortions of conformality, distance, direction, and area always result from this process. • Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. • Some projection are attempts to only moderately distort all of these properties

Projection Properties (1) Conformality (major property) • Shape is preserved locally on conformal maps.

Projection Properties (1) Conformality (major property) • Shape is preserved locally on conformal maps. • When the scale of a map at any point on the map is the same in any direction, the projection is conformal. • Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles.

Projection Properties (2) Equivalence(major property) • Area is preserved. • When a map portrays

Projection Properties (2) Equivalence(major property) • Area is preserved. • When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area map.

Projection Properties (3) Equidistance (minor property) A map is equidistant when it portrays distances

Projection Properties (3) Equidistance (minor property) A map is equidistant when it portrays distances from the center of the projection to any other place on the map. Azimuthal / Direction (minor property) A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions.

Projection Properties (4) • Most maps don’t preserve ANY of the properties mentioned! •

Projection Properties (4) • Most maps don’t preserve ANY of the properties mentioned! • This is because accuracy in one property causes distortion in the others • Consequently, many maps are compromise projections, which don’t preserve any of the properties but which don’t make extreme distortion in any of the globe’s properties either

Map Projections Classes Map projections fall into four general classes. These are: • Conic

Map Projections Classes Map projections fall into four general classes. These are: • Conic projections • Cylindrical projections • Azimuthal projections • Miscellaneous projections

Cylindrical Projection (1) Cylindrical: Screen is a cylindrical surface. Examples: Mercator, Transverse Mercator. Good

Cylindrical Projection (1) Cylindrical: Screen is a cylindrical surface. Examples: Mercator, Transverse Mercator. Good for North-South land areas.

Cylindrical Projection (2)

Cylindrical Projection (2)

Cylindrical Projection (3) Good for equatorial regions but greatly distorted at high latitudes. This

Cylindrical Projection (3) Good for equatorial regions but greatly distorted at high latitudes. This one of the oldest and most common projections.

Aspect of a projection surface Normal aspect of a cylindrical projection: a cylinder is

Aspect of a projection surface Normal aspect of a cylindrical projection: a cylinder is orientated tangent along the equator. When you change the projection surface 90º from normal, the result is a transverse projection An oblique projection results if the projection surface is at an angle between the normal and transverse position

Conic Projection (1) Screen is a conic surface. Lamp at the center of the

Conic Projection (1) Screen is a conic surface. Lamp at the center of the earth. Examples: Albers Equal Area, Lambert Conformal Conic. Good for East-West land areas.

Conic Projection (2)

Conic Projection (2)

Azimuthal / Planer Projections (1) Screen is a flat surface (a plane) tangent to

Azimuthal / Planer Projections (1) Screen is a flat surface (a plane) tangent to the earth. Lamp at the center of the earth (gnomonic), at the other side of the earth (stereographic), or far from the earth (orthographic). Examples: Lambert Azimuthal Equal Area. Good for global views.

Azimuthal / Planer Projections (2)

Azimuthal / Planer Projections (2)

Types of Projections § Lambert’s Conformal Conic § Mercator • Transverse Mercator ü Universal

Types of Projections § Lambert’s Conformal Conic § Mercator • Transverse Mercator ü Universal Transverse Mercator (UTM) ü Gauss Conform

Lambert’s Conformal Conic (1)

Lambert’s Conformal Conic (1)

Lambert’s Conformal Conic (2) • A projection is conformal if the angles in the

Lambert’s Conformal Conic (2) • A projection is conformal if the angles in the original features are preserved • The transformation is made to the surface of a cone tangent at a small circle (tangent case) or intersecting at two small circles (secant case) on a globe

Mercator Projection (1)

Mercator Projection (1)

Transverse Mercator Projection (UTM) (1) Based on a cylinder tangent to the globe along

Transverse Mercator Projection (UTM) (1) Based on a cylinder tangent to the globe along a chosen pair of opposite meridians. The scale of the map is constant only along the central meridian.

UTM (2) • Special case of the Transverse Mercator projection. • 6° bands with

UTM (2) • Special case of the Transverse Mercator projection. • 6° bands with a Central Meridian • 60 zones cover the earth from East to West starting at 180° West. • Reference Latitude (fo) is the equator. • Units are meters • In South Africa (CM = 15°E-zone 33, 21 ° - zone 34; 27 °E – zone 35). • Most satellite imagery referenced to UTM • Military uses UTM

UTM Zones

UTM Zones

UTM Zones – South Africa 16 E 17 E 18 E 19 E 20

UTM Zones – South Africa 16 E 17 E 18 E 19 E 20 E 21 E 22 E 23 E 24 E 25 E 26 E 27 E 28 E 29 E 30 E 31 E 32 E

Gauss Conform Projection (1) • Special case of the Transverse Mercator • Transverse aspect

Gauss Conform Projection (1) • Special case of the Transverse Mercator • Transverse aspect of the Mercator projection (which is a cylindrical projection, turned about 90 so that the projection is based on meridians and not the parallels). • This projection is used for the computation of the plane y. Lo and x. Lo coordinates, commonly known as the “Lo coordinate system".

Gauss Conform Projection (2) 16 E 17 E 18 E 19 E 20 E

Gauss Conform Projection (2) 16 E 17 E 18 E 19 E 20 E 21 E 22 E 23 E 24 E 25 E 26 E 27 E 28 E 29 E 30 E 31 E 32 E

Chief Directorate: Surveys and Mapping Private Bag X 10 Mowbray 7705 (Van der Sterr

Chief Directorate: Surveys and Mapping Private Bag X 10 Mowbray 7705 (Van der Sterr Building, Rhodes Avenue) Tel: 021 658 4300 Fax: 021 6891351 http: //w 3 sli. wcape. gov. za