Orthographic Projection

sc_projections_orthographic.png

 

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. This is the default Release 8 projection for new drawings, images and labels components.

 

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 the Earth, 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. The Orthographic projection is used by default within Manifold for images and drawings that are not otherwise georegistered.

 

Limitations

 

Use only for a single 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. Note 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. The Clip coordinates option clips invisible parts of objects, such as countries located on the other side of the Earth from the point of view of the projection. Note that Clip coordinates is a destructive change: parts of objects extending beyond the projection horizon will be permanently trimmed.

 

proj_ortho_s.png

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

 

proj_ortho_e.png

 

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

 

proj_ortho_w.png

 

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.

 

sc_projections_orthographic_eg02.png

 

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.

 

Using Clip Coordinates

 

The Clip coordinates option tells Manifold to cut objects so that they do not "wrap" around the Orthographic coordinate system.

 

sc_orthographic_noclip.png

 

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 have two choices:

 

 

sc_orthographic_clipped.png

 

The illustration above shows the same drawing after projection to Orthographic using Clip Coordinates. Note there is no overlap.

 

The Clip coordinates option is a convenience, not an exact cartographic instrument. It works by clipping objects using a clipping rectangle. If after using Clip coordinates in an Orthographic projection we re-project the drawing into Latitude / Longitude we will see the areas have been clipped to fit inside a bounding box.

 

sc_orthographic_cliprect.png

 

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 fast to compute.