Global Positioning System Reference
In-Depth Information
FIGURE 4.6. Orthographic projection. This projection looks like a view of the world (or
more accurately half the world, mostly the eastern hemisphere in this case) from
space. Our minds are easily able to allow for the distortion produced by this type of
azimuthal projection. Adapted from a Wikipedia image.
If you think about it, you can also see that the sphere has to be stretched
in varying degrees to project it onto the cone. For example, two points
on the sphere that are close together, one just east of the South Pole
and one just west of it, will be projected onto opposite sides of the cone.
The distance between the points will thus be greatly exaggerated. On the
other hand, consider the points of contact between sphere and cone: these
points form a circle, a parallel at a latitude that depends upon the cone
angle. Any point on this contact circle (shown in fig. 4.5b) is not moved
by the projection. Consequently, along this circle distances are preserved,
and near this circle the shape of the map on the cone will look very much
like the shape of the map on the globe. Distortions will increase with
increasing distance away from this ''circle of contact'' between the sphere
and the cone.
Here we have a di√erence between azimuthal and conical projections.
For azimuthal projections, the plane is tangent to the globe at only one
point, whereas for the cone it is tangent at a set of points that form a circle.
 
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