General Perspective projection
Encyclopedia
The General Perspective Projection is a map projection
of cartography
.
When the Earth is photographed from space, the camera records the view as a perspective projection. If the camera precisely faces the center of the Earth, the projection is Vertical Perspective. Otherwise, a Tilted Perspective projection is obtained.
The Vertical Perspective is related to the Stereographic projection
, Gnomonic projection
, and Orthographic projection
. These are all true perspective projections, and are also azimuthal (the projection surface is a plane tangent to the sphere, and directions from one central point to any other point are correct). The point of perspective for the General Perspective Projection is a finite distance. It depicts the earth as it appears from some relatively short distance above the surface, typically a few hundred to a few tens of thousands of kilometers.
Tilted Perspective projections are not azimuthal (see second figure below); directions are not true from the central point, and the projection plane is not tangent to the sphere.
Some forms of the projection were known to the Greeks and Egyptians 2,000 years ago. It was studied by several French and British scientists in the 18th and 19th centuries. But the projection had little practical value; computationally simpler nonperspective azimuthal projections could be used instead.
Space exploration led to a renewed interest in the perspective projection. Now the concern was for a pictorial view from space, not for minimal distortion. A picture taken with a hand-held camera from the window of a spacecraft has a tilted vertical perspective, so the manned Gemini and Apollo space missions sparked interest in this projection.
Currently (2006), general perspective projections are of interest for another reason. The latest generation of Internet mapping applications, including Google Earth
and NASA World Wind
, show the globe as it appears from space. These applications permit an impressive variety of interactive pan and zoom operations, including fly-through simulations. They are digital simulations of pictures or movies taken with a hand-held camera from an airplane or spacecraft. Though their documentation does not explicitly say so, their math models are almost certainly based on the general perspective projection, both vertical and tilted.
Map projection
A map projection is any method of representing the surface of a sphere or other three-dimensional body on a plane. Map projections are necessary for creating maps. All map projections distort the surface in some fashion...
of cartography
Cartography
Cartography is the study and practice of making maps. Combining science, aesthetics, and technique, cartography builds on the premise that reality can be modeled in ways that communicate spatial information effectively.The fundamental problems of traditional cartography are to:*Set the map's...
.
When the Earth is photographed from space, the camera records the view as a perspective projection. If the camera precisely faces the center of the Earth, the projection is Vertical Perspective. Otherwise, a Tilted Perspective projection is obtained.
The Vertical Perspective is related to the Stereographic projection
Stereographic projection
The stereographic projection, in geometry, is a particular mapping that projects a sphere onto a plane. The projection is defined on the entire sphere, except at one point — the projection point. Where it is defined, the mapping is smooth and bijective. It is conformal, meaning that it...
, Gnomonic projection
Gnomonic projection
A gnomonic map projection displays all great circles as straight lines. Thus the shortest route between two locations in reality corresponds to that on the map. This is achieved by projecting, with respect to the center of the Earth , the Earth's surface onto a tangent plane. The least distortion...
, and Orthographic projection
Orthographic projection (cartography)
An orthographic projection is a map projection of cartography. Like the stereographic projection and gnomonic projection, orthographic projection is a perspective projection, in which the sphere is projected onto a tangent plane or secant plane. The point of perspective for the orthographic...
. These are all true perspective projections, and are also azimuthal (the projection surface is a plane tangent to the sphere, and directions from one central point to any other point are correct). The point of perspective for the General Perspective Projection is a finite distance. It depicts the earth as it appears from some relatively short distance above the surface, typically a few hundred to a few tens of thousands of kilometers.
Tilted Perspective projections are not azimuthal (see second figure below); directions are not true from the central point, and the projection plane is not tangent to the sphere.
Some forms of the projection were known to the Greeks and Egyptians 2,000 years ago. It was studied by several French and British scientists in the 18th and 19th centuries. But the projection had little practical value; computationally simpler nonperspective azimuthal projections could be used instead.
Space exploration led to a renewed interest in the perspective projection. Now the concern was for a pictorial view from space, not for minimal distortion. A picture taken with a hand-held camera from the window of a spacecraft has a tilted vertical perspective, so the manned Gemini and Apollo space missions sparked interest in this projection.
Currently (2006), general perspective projections are of interest for another reason. The latest generation of Internet mapping applications, including Google Earth
Google Earth
Google Earth is a virtual globe, map and geographical information program that was originally called EarthViewer 3D, and was created by Keyhole, Inc, a Central Intelligence Agency funded company acquired by Google in 2004 . It maps the Earth by the superimposition of images obtained from satellite...
and NASA World Wind
NASA World Wind
World Wind is an open-source virtual globe developed by NASA and the open source community for use on personal computers. Old versions need Microsoft Windows but the more recent Java version, , is cross platform and provides a suite of . The World Wind Java version was awarded in November 2009...
, show the globe as it appears from space. These applications permit an impressive variety of interactive pan and zoom operations, including fly-through simulations. They are digital simulations of pictures or movies taken with a hand-held camera from an airplane or spacecraft. Though their documentation does not explicitly say so, their math models are almost certainly based on the general perspective projection, both vertical and tilted.