Orthographic Projection

The "view from space" projection: An azimuthal, perspective projection that is neither conformal nor equal area. Range is no more than one hemisphere at a time.

Best used for viewing data for local regions, such as a province or a compact country.   The need to "clip" objects that extend beyond a single hemisphere makes it inconvenient to use Orthographic for very large regions or worldwide data sets.

Scale

True at the center and along any circle having its center at the projection center but only in the direction of the circumference of the circle. Scale decreases with distance from the center.

Distortion

Only the center is free from distortion, which increases rapidly away from the center. Distortion is extreme near the edge of the hemisphere.

Usage

Pictorial views of a geographic region, resembling those seen from space. This is a perspective projection of the globe onto a tangent plane from an infinite distance (i.e., orthogonally); thus, the map has the look of a globe.    Orthographic is a very popular projection for local regions, such as the region surrounding a city,  where scale and relative appearance are to be preserved.

Limitations

Use only for a single hemisphere, and only for data sets containing objects that entirely fall within that hemisphere. Defined only for a sphere, specifically a sphere that utilizes the same major axis as the WGS84 datum, 6378137. Note that although WGS84 appears as a datum for Orthographic projection, the flattening of the WGS84 ellipsoid is ignored and only the major axis is used to define the sphere.  That this is different than the explicitly enumerated Sphere datum, which utilizes a major axis of 6370997. Use the Stereographic projection instead of Orthographic if non-spherical datums are to be utilized.

Origin

Apparently developed by Egyptians and Greeks by the 2nd Century BC

Options

Specify the center of the projection by setting latitude origin and longitude origin. Specifying a non-Equatorial or non-polar origin causes an oblique projection.   Illustrations below use data sets that have been manually trimmed so objects exist only in the hemisphere shown.

The Southern Hemisphere view above is created using a latitude origin of -90 and a longitude origin of 0.

The Eastern Hemisphere view above is created using a latitude origin of 0 and a longitude origin of 90.

The Western Hemisphere view above is created using a latitude origin of 0 and a longitude origin of -90.

If more than one hemisphere is displayed, countries will be "wrapped" from the invisible side of the world and displayed anyway in mirror image.

Above is an Orthographic projection centered on latitude 68 North longitude -70. The original map included areas and a graticule for just the Northern Hemisphere. If zoomed far into the latitude and longitude origin we would see essentially zero distortion.

Clipping Undesired Objects.

When using the Orthographic projection to show the entire world, we should cut away objects so that they do not "wrap" around the Orthographic coordinate system.

If we use a drawing showing the entire world and then re-project it into Orthographic centered on the default 0, 0 origin we will see that some areas, such as Australia and New Zealand are "wrapped" around the edge of the Orthographic system. This effect arises because the Orthographic projection is not intended to deal with more than one hemisphere's worth of data at a time.

To avoid this effect we must edit the drawing in advance so that only areas in the hemisphere of interest exist. This is the method used to create the screenshots in the previous section of this topic.

The illustration above shows the same drawing after projection to Orthographic after editing the drawing.

We can usually get a good effect by trimming objects to a rectangle.   For example, the screenshot above was created based on the objects as seen below in Latitude / Longitude, where it is clear how the areas have been clipped to fit inside a bounding box.

Using straight lines to clip objects at the Orthographic horizon is an imperfect approximation (it leads to a "lumpy" horizon sometimes at the edge of the Earth), but it is reasonably easy to do.