Azimuthal Projections

 AZIMUTHAL EQUAL-AREA 

The Azimuthal Equal Area projection is an equal-area projection with the azimuthal property showing true directions from the centre of the projection. Its scale at a given distance from the centre varies less from the scale at the centre than the scale of any of the other azimuthal projections.

This projection provides an optional parameter that will rotate the planar coordinates by the specified amount after the projection (or before the inverse). The value should be provided as an angular value east of north. If this parameter is not provided, it will default to 0 (no rotation).

Parameters:

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of the centre of the projection
xy_plane_rotation	XY plane rotation (optional)

Usage:
Hemisphere, continent, regional maps. Not really for a large scale.

Notes:
This projection is also known as Lambert Azimuthal Equal Area.

POLAR AZIMUTHAL AREA

The Azimuthal Equal Area (Polar Aspect) projection is an equal-area projection with the azimuthal property showing true directions from the centre of the projection. Its scale at a given distance from the centre varies less from the scale at the centre than the scale of any of the other azimuthal projections. All meridians in the polar aspect are straight lines.

Parameters:

central_meridian	Longitude of origin
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin

Usage:
Polar maps.

Notes:
This projection is also known as Lambert Azimuthal Equal Area (polar aspect).

AZIMUTHAL EQUIDISTANT

The Azimuthal Equidistant projection is neither an equal-area nor a conformal projection. The outer meridian of a hemisphere on the equatorial aspect is a circle. Distances and directions measured from the centre are true. We recommend using the Azimuthal Equidistant projection for coordinate systems in which distances are measured from an origin.

The Azimuthal Equidistant projection is used in oblique aspect for atlas maps of continents, and in world maps for aviation.

Parameters:

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection

Usage:
Can be used for world maps but usually for hemispheres. Works on large scale maps

Notes:

This projection is also known as Equidistant. ESRI software supports this projection on spheres only so use a spherical geodesic base (e.g. GRS Authalic Sphere) to obtain comparable results.

POLAR AZIMUTHAL EQUIDISTANT

The Azimuthal Equidistant (Polar Aspect) projection is neither an equal-area nor a conformal projection. The outer meridian of a hemisphere on the equatorial aspect is a circle. Parallels on the polar projection are circles spaced at equidistant intervals. All meridians on the polar aspect are straight lines. Distances and directions measured from the centre are true.

Parameters:

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection

Usage:
Polar aspect for world maps and maps of the polar hemispheres.

Notes:

This projection is also known as Equidistant

DOUBLE STEREOGRAPHIC

The Double Stereographic projection consists of two mappings. First, the ellipsoidal data is mapped conformally to a conformal sphere. Then a second conformal mapping transforms the spherical data to the plane.

Parameters:

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection
scale_factor	Scale reduction factor at the centre of the projection

Usage:
Large scale maps - New Brunswick, Canada and the Netherlands.

Notes:
This projection is also known as Oblique Stereographic

EUROPEAN STEREOGRAPHIC

The European Stereographic projection is a derivation of the Stereographic projection for use in the Netherlands

Parameters:

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection
scale_factor	Scale reduction factor at the centre of the projection

Usage:
Large scale maps of the Netherlands.

GNOMIC

The Gnomic projection is used for plotting great circle arcs as straight lines on a map. Scale, shape and area are badly distorted along these paths, but the great circle routes are precise in relation to the sphere.

Parameters: 

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of the centre of the projection
spherical_radius	Radius of the sphere (e.g. 6378137m)

Usage:
Navigational maps.

Notes:

Should not be used for areas extending more than 60° from the centre. Only a spherical form of this projection is supported.

GUAM

This is a specially modified version of the azimuthal equidistant projection used in Guam.

Parameters:

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection
xy_plane_rotation	XY plane rotation.

Usage:
Maps of Guam island.

ORTHOGRAPHIC

The Orthographic projection closely resembles a globe in appearance, since it is a perspective projection from infinite distance. Only one hemisphere can be shown at a time. This projection is used chiefly for pictorial views and is used only in spherical form.

Parameters:

central_meridian	Longitude of the central meridian
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection
spherical_radius	Radius of the sphere (e.g. 6378137)

Usage:
Aesthetic hemispherical maps.

Notes:

The Orthographic projection is an hemispheric projection (valid for half the globe). Therefore, the map or image should be cropped to an extent centered on the central meridian with -90°/+90° range prior to transforming to a coordinate system using this projection.

Only a spherical form of this projection is used. The Radius of the Sphere parameter is only used for legacy support. When set to 0, the semi-major axis of the ellipsoid specified in the coordinate system datum definition is used.

POLAR STEREOGRAPHIC

The Polar Stereographic projection somewhat resembles other polar azimuthal projections, with straight radiating meridians and concentric circles for parallels. This projection is used for polar mapping within the Universal Polar Stereographic (UPS) coordinate system.

Three variants of the Polar Stereographic projection are recognized and differentiated by their defining parameters. This projection definition applies for the variant A and B:

• In the basic variant (variant A) the latitude of origin is either the north or the south pole, at which is defined a scale factor at the natural origin, the meridian along which the northing axis increments and along which intersecting parallels increment towards the north pole (the longitude of origin), and false grid coordinates.
• In variant B instead of the scale factor at the pole being defined, the (non-polar) latitude at which the scale is unity – the standard parallel – is defined.
• In variant C the latitude of a standard parallel along which the scale is unity is defined; the intersection of this parallel with the longitude of origin is the false origin, at which grid coordinate values are defined. See next projection.

Parameters:

		Variant A	Variant B
central_meridian	Longitude of natural origin of the projection
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of natural origin of the projection	± 90°
scale_factor	Scale reduction factor at the centre of the projection	≠ 1	=1

Usage:
Polar maps (UPS system).

Notes:

Variant A: the Scale Factor must be a value other than 1. In this variation, the Latitude of Origin is used only to identify the hemisphere the projection, and thus the only valid values are ±90° or the equivalent in an alternate angle unit.

Variant B: the Scale Factor must be equal to 1, and will thus be ignored. The actual scaling factor will be calculated by using the value of the Latitude of Origin parameter which in this case actually represents the latitude of the standard parallel (i.e. the latitude of true scale). In this case, the sign of the latitude (+ or -) is likewise used to determine the hemisphere of the projection.

POLAR STEREOGRAPHIC VARIANT C

The Polar Stereographic Variant C projection corresponds to the third variant of the Polar Stereographic projection described earlier.

Parameters:

central_meridian	Longitude of natural origin of the projection
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of origin of the projection

Usage:
Polar maps (UPS system).

STEREOGRAPHIC

The Stereographic projection is the only known true perspective projection of any kind that is also conformal. The central meridian and a particular parallel (if shown) are straight lines. All other meridians and parallels are shown as arcs of circles.

This projection provides an optional parameter that will rotate the planar coordinates by the specified amount after the projection (or before the inverse). The value should be provided as an angular value east of north. If this parameter is not provided, it will default to 0 (no rotation).

Parameters:

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of the centre of the projection
scale_factor	Scale reduction factor at the centre of the projection
xy_plane_rotation	XY plane rotation (optional).

Usage:
Hemispherical maps.

STEREOGRAPHIC 70

Stereographic 70 is a derivation of the Stereographic projection for use in Romania.

Parameters: 

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of the centre of the projection
scale_factor	Scale reduction factor at the centre of the projection

Usage:
Maps of Romania

VERTICAL PERSPECTIVE

The Vertical Perspective projection represents a view of the Earth from space in which the view is from a point precisely facing the centre of the Earth. This projection is therefore used to generate pictorial views of the Earth resembling those seen from space. It is an azimuthal projection that is neither conformal nor equal area. The central meridian and a particular parallel (if shown) are straight lines.

Other meridians and parallels are usually arcs of circles or ellipses, but some may be parabolas or hyperbolas. If the point of perspective is above the sphere, less than one hemisphere may be shown.

Parameters:

central_meridian	Longitude of the centre of the projection
false_easting	False easting
false_northing	False northing
latitude_of_origin	Latitude of the centre of the projection
height	Height of the view.

Usage:
Aesthetical view of Earth from space.

Notes:
The Height should be set to 10000km or so to get an interesting view from space.

Only a spherical form of this projection is used. The semi-major axis of the ellipsoid specified in the coordinate system datum definition is used as sphere radius.