[OSRS-PROJ] Orthographic Projections and MapServer

[Strebe at aol.com]

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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