Azimuthal Projection

azimuthal projection
[map projections] A map projection that transforms points from a spheroid or sphere onto a tangent or secant plane. The azimuthal projection is also known as a planar or zenithal projection.

Azimuthal Projection
A map projection on which the azimuths of all points are shown correctly with respect to the center (Snyder 1987, p. 4). A plane tangent to one of the Earth's poles is the basis for polar azimuthal projection.

Azimuthal Projections
Introduction
Given a reference point A and two other points B and C on a surface, the azimuth from B to C is the angle formed by the minimum-distance lines AB and AC (which, on a sphere, ...

It is a cylindrical projection preserving the direction from any place to another, predetermined place while avoiding some of the bizarre distortion of the Hammer retroazimuthal projection.

Azimuthal projections
An azimuthal projection is obtained by projecting the earth, either literally or figuratively, onto a plane that touches the earth at a single point, called the center of the map..

Azimuthal Projection - Stereographic
The oldest known record of this projection is from Ptolemy in about 150 AD. However it is believed that this projection was well known long before that time - probably as far back as the 2nd century BC.

Azimuthal projections result from projecting a spherical surface onto a plane.
When the plane is tangent to the sphere contact is at a single point on the surface of the Earth.
Projection of a Sphere onto a Plane (Tangent Case) ...

3 Azimuthal projections
The five common azimuthal (also known as Zenithal) projections are the Stereographic projection, the Orthographic projection, the Lambert azimuthal equal-area projection, ...

Planar or Azimuthal Projection
With the planar projection, a portion of the Earth's surface is transformed from a perspective point to a flat surface.

References: Azimuthal projections (Strahler and Strahler 1987, p. 13, Robinson et al 1984, p. 102)
stereographic projection
gnomic projection
Lambert's azimuthal equal-area projection
orthographic projection ...

Tables, formulas and explanations for several cylindrical, conic, psuedocylindrical and azimuthal projections are provided. The second appendix shows the proof of Tissot's Indicatrix.

Normally though, the azimuthal projection is used for polar charts due to distortion at other latitudes.
A cylindrical projection usually places the earth inside a cylinder with the equator tangent or secant to the inside of the cylinder.

A map projection that transforms points from a spheroid or sphere onto a tangent or secant plane. The azimuthal projection is also known as a planar or zenithal projection.
zero length line event ...

extent east-west than north-south and in equatorial regions, while conic projections are better in mid-latitudes; transverse cylindrical projections are used for maps which are of greater extent north-south than east-west; azimuthal projections are ...

Generally, the paper is either flat and placed tangent to the globe (a planar or azimuthal projection) or formed into a cone or cylinder and placed over the globe (cylindrical and conical projections).

Locate yourself on a Craig Retroazimuthal projection map, and and use a protractor to measure the angle on the map from north to the center of the projection. This is easy to to do since all meridians are represented as parallel straight lines.

See also: Projection, Map, Azimuth, Map Projection, Equator