| Re: Map Projection Woes [message #48351] |
Thu, 13 April 2006 13:45  |
David Fanning
Messages: 11724
Registered: August 2001
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Senior Member |
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Matt Savoie writes:
> Determining whether a given point is inside or outside a given spherical
> polygon is rather difficult.
Oh, oh. No *wonder* I haven't seen anything like
this around here!
Humm. Guess I'll go think about Wayne's ARRAY_OR
problem. That sounds like more fun than this. :-(
Cheers,
David
--
David Fanning, Ph.D.
Fanning Software Consulting, Inc.
Coyote's Guide to IDL Programming: http://www.dfanning.com/
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| Re: Map Projection Woes [message #48355 is a reply to message #48351] |
Thu, 13 April 2006 12:44  |
savoie
Messages: 68
Registered: September 1996
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Member |
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David Fanning <davidf@dfanning.com> writes:
> Folks,
>
> I took on this day/night terminator project to learn a
> little more about map projections. I thought I would learn
> something by doing it. I know better, and should be careful
> what I wish for.
>
> Here is my problem (I think), and you map projection
> experts probably know the answer. My program calculates
> a field of view, essentially, from the point of view
> of the sun looking towards the Earth. You could think
> of it as a circular polygon.
>
> If the subsolar point on the Earth is inside this
> polygon, that is the light part of the map. If it is
> outside, that is the dark part of the map, with
> respect to the day/night terminator.
>
> But...I don't always get a reliable answer to my question:
> "Is the subsolar point inside the polygon that describes
> the terminator?" The problem comes (surprise, surprise)
> when the polygon crosses the international date line
> and there is a jump from 180 degrees of longitude to -180
> degrees of longitude.
>
> My question is how is this handled, normally? (If you
> are an Aussie or a Kiwi this problem probably comes up
> daily.)
Don't know if this helps. But I know a website...
Directly from geospatialmethods.org:
http://geospatialmethods.org/spheres/MiscAlgorithms.html#PSP
Point in Spherical Polygon:
Determining whether a given point is inside or outside a given spherical
polygon is rather difficult. Several effective algorithms exist for making
the same determination on a plane, but those don't transfer well to the
surface of the sphere. In the spheres package we have adapted the
"point-at-a-distance" algorithm to work on the sphere for "reasonable"
polygons, but it cannot be made absolutely foolproof.
The plane is infinitely large so finding a point outside a given polygon is
relatively easy on the plane. One can simply pick (maximumX + 1, maximumY +
1) or, to be really safe, one can pick (maximumX * 10, maximumY * 10) where
maximumX and maximumY are the maximum values of the given corner
points. Indeed the algorithm is frequently refered to as the
point-at-an-infinite-distance algorithm because developers just use the point
(infinity, infinity), or substitute some absurdly large number for
"infinity", no matter what polygon they are working with.
But the sphere is a closed surface so when you go far enough away from a
given point you end up back where you started. Consequently there is no easy
way to pick a point known to be external to the polygon. The spheres package
employs a number of heuristics to guess an external point as outlined below,
and in cases where that guess it likely to be wrong the SphericalPolygon
class has a setExternalPoint() method to allow users to designate the known
external point.
Given a point known to be external to the polygon determining if a given
point is inside a given polygon is a simple matter.
1. Connect the point to the known external point with a great circle arc.
2. For each great circle arc that is a side of the spherical polygon test
if it intersects the arc constructed in step #1 and count the number of
intersections.
3. If the total number of intersections is odd the given point is inside
the spherical polygon. if the total number of intersections is even the
point is outside the spherical polygon.
Behavior is undefined if the given point is a corner point of, or on an edge
of, the spherical polygon. In cases where the great circle arc constructed in
step #1 just touches an edge of the polygon the algorithm may wrongly
designate an external point as internal. But those cases should be
excessively rare.
--
Matthew Savoie - Scientific Programmer
National Snow and Ice Data Center
(303) 735-0785 http://nsidc.org
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| Re: Map Projection Woes [message #48436 is a reply to message #48351] |
Fri, 14 April 2006 08:15 |
James Kuyper
Messages: 425
Registered: March 2000
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Senior Member |
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David Fanning wrote:
> Matt Savoie writes:
>
>> Determining whether a given point is inside or outside a given spherical
>> polygon is rather difficult.
>
> Oh, oh. No *wonder* I haven't seen anything like
> this around here!
>
> Humm. Guess I'll go think about Wayne's ARRAY_OR
> problem. That sounds like more fun than this. :-(
While the general case is very difficult, your case should be much
simpler. Your particular spherical polygon is just an approximation to
a great circle, which means that a lot of the tricky special cases
shouldn't apply. However, I don't think I know enough about the problem
that you're running into, to suggest a specific procedure for doing it.
Could you give more details?
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