Google Earth's Projection

The Google Earth User Guide contains a brief statement about Google Earth's projection, reproduced in the figure below.

The statement that "Google Earth uses Simple Cylindrical projection with a WGS84 datum for its imagery base" is oversimplified to the point of being misleading. The diagram is not helpful, either. It seems likely that what the authors really meant was something like this: "Google Earth uses geographic coordinates on the WGS84 datum for internal coordinate storage. Data in this form imports easily into Google Earth, but data from some other coordinate systems can also be imported."

So the above "note about projections" doesn't actually describe the Google Earth projection. In spite of what the note says, it is obvious that the projection is not the Plate Carree projection or any other cylindrical projection.

It is equally clear that the Google Earth display simulates how the earth looks from space. There are two classes of projections that accomplish this:

• Orthographic projections show the earth as viewed from deep space. That is, the point of perspective is an infinite distance from the earth.

• General Vertical Perspective projections show the earth as viewed from finite distances above the surface. The projection plane can be vertical or tilted:

A photograph taken with a hand held camera from the window of the Space Shuttle (or from an airplane or any other elevated platform) has a tilted vertical perspective projection.

Google Earth allows viewing the earth's surface from nearly ground level to about 39,000 miles above the surface. It allows any angle of tilt from true vertical (the default startup condition) to almost horizontal. So the Google Earth projection is almost certainly a general vertical perspective projection.

The left image above is from Snyder, and shows a general vertical perspective view of the earth with central meridian 90W, from 35,900 km above the surface (geosynchronous satellite position). The right image is a screen shot of Google Earth from the same perspective.

Compared to the simple regular cylindrical projections of most Internet maps, the mathematics of this projection are complex. Snyder (1987) provides complete equations for the sphere and ellipsoid, vertical and tilted. The equations for the simplest case -- vertical perspective on the sphere -- are online here. It is fairly easy to study Snyder's equations and see the basic conceptual outline of how Google's system works, but I can't begin to guess how they made it so fast.

Because the general vertical perspective projection shows the earth as it looks from an airplane or from space, it can create an illusion that the display has lower distortion or is somehow fundamentally different from displays that use more common map projections. Google's elegant and dynamic implementation powerfully enhances this illusion.

References:

Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. 1987.

Snyder, John P. and Voxland, Philip M. An Album of Map Projections. U.S. Geological Survey Professional Paper 1453, 1994.

Larry Moore
larmoor -at- gmail -dot- com
Last updated September 2007