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Re: Spherical trig application

• To: mathgroup at smc.vnet.net
• 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 wri.com> Roger Uribe <ui at uribe.demok.co.uk> 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