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MathGroup Archive 1995

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Re: Spherical trig application

  • To: mathgroup at
  • Subject: [mg2252] Re: Spherical trig application
  • From: danl (Daniel Lichtblau)
  • Date: Thu, 19 Oct 1995 01:31:22 -0400
  • Organization: Wolfram Research, Inc.

In article <DGBJLI.MM8 at> Roger Uribe <ui at> writes:
> Given a roughly convex polygon on the Earth's surface - typically 1000
> miles "diameter" and 3 - 12 vertices. I need to know whether a given
> point is in it or not.  There are about 10,000+ such points to test so
> I need an effecient method.
> Any ideas, or know of any software that will do something like it.
> I guess defining the enclosing circle and discarding any points
> outside that would get rid of most of them.
> I don't want a lesson in spherical trig, I'm no expert but I know
> enough, it's the methods and short cuts I'm after.
> Thanks  Roger.

  This should improve on my last attempt.
  Orient your sphere so that the region is approximately "centered" at the  
north pole. Then translate it to the plane simply as (x,y,z) -> (x,y).  
This will give less distortion (than my last idea), and thus some bounding  
circles and/or boxes for inclusion/exclusion should suffice for most  
points, particularly if their distribution is anything like "random"  
around the whole sphere. Note that you a priori exclude points with  
negative z coordinate.

  Daniel Lichtblau, WRI

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