[OSRS-PROJ] Orthographic Projections and MapServer

[Duncan Agnew]

Some thoughts that might be useful. This discussion suggests a way of
classifying projections:

	A. Map the sphere to a finite region on the plane; most projections
do this, even those defined for limited regions (in the sense that the math
will go from [lat,long] to [x,y]). (NB I am using "map" in the mathematical
sense).

	B. Map the sphere into an infinite region on the plane; eg Mercator.

	C. Map only a part of the sphere to a finite region on the plane;
eg orthographic.

	D. Map only a part of the sphere to an infinite region; eg gnomonic.

	It seems to me that this discussion raises a legitimate question about 
class C, and one that does fall within the domain of projections: how do we
want to define the mapping for the "unmapped" part of the sphere? We can
	
	1. Declare that the mapping function to be undefined, and return an
error code.

	2. Map such points to the edge of the mapped region on the plane.

	Option (2) would be historically nonstandard, but is just as much a
"valid function" as option (1)--there is no reason (that I can see) not to
define a "proj orthographic" (say) to map points on the rear hemisphere to the
edge, rather than declaring an error--and if this makes the graphics easier,
why not? (It does not solve the problem of how to continue a line to the
edge, but I agree that this is a graphics problem, not a projection one).
A quick review suggests that the number of projections in class (C) is small,
so perhaps a move from Option 1 to Option 2 would not be that difficult to
implement.

	Any of this make sense?

Thanks
Duncan Agnew
dagnew at ucsd.edu

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