# [OSRS-PROJ] Orthographic Projections and MapServer

Strebe at aol.com Strebe at aol.com
Thu Aug 21 18:41:39 EDT 2003

```With regard to Option (2) and analysis, it seems very unwise to fail to distinguish between "unprojectable" and "horizon". There are critical reasons one might want to know whether a point is unprojectable:

a) A path construction engine will know to clip the path, rather than construct a crazy, manifold, bloated, "unidimensional" polygon. A crazy polygon cannot be edited practically afterward using vector graphics software, and may severely degrade performance in rasterization and color fills, or even cause such operations to fail entirely.

b) Distortion analysis software will know to discard the point from consideration rather than spuriously including it in statistics.

Regards,

daan Strebe
Geocart author
http://www.mapthematics.com/

_______________

Duncan Agnew <dagnew at ucsd.edu> writes:

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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