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From: rickc@agora.UUCP (Rick Coates)
Newsgroups: comp.graphics,sci.math
Subject: Re: simple spherical algebra question
Keywords: algebra
Message-ID: <1192@agora.UUCP>
Date: 16 Oct 88 14:45:16 GMT
References: <1187@agora.UUCP>
Organization: Advanced Solutions, Hillsboro, OR
Lines: 32


Many thanks to all those who sent me suggestions - especially the fellow
at Tektronix who mailed me a copy of a couple of pages from an encyclopaedia
of mathematics.

I went ahead and got off the dime and solved the problem myself - as it
turned out, I did have what I needed: my 1968 edition of the CRC Standard Math
Tables, which includes a summary of spherical trigonometry (do the new
editions still have pages and pages of numerical results for trig functions?).

I had thought that this would be a standard problem in cartography and
someone in Netland would have the solution at her/his fingertips.

For those of you who asked why I wanted to do this - the most obvious
application is to plot great circle routes on a map.  If I want to
show the course from Sidney to Seattle, I have to incrementally draw the
great circle route between the two, since the map projection is not
linear (the 'straight line' great circle becomes a curved line on the 
projection).

(The problem was: given two points in spherical coordinates (lambda from
-pi to +pi; phi from -pi/2 to +pi/2) find a function that returns the
phi for a given lambda on the great circle line between the two points;
and what is the midpoint)

Again, thanks for all the replies!

Rick Coates

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