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