Xref: utzoo comp.graphics:3372 sci.math:4652
Path: utzoo!utgpu!water!watmath!julian!uwovax!7103_300
From: 7103_300@uwovax.uwo.ca (Eric Smith)
Newsgroups: comp.graphics,sci.math
Subject: Re: simple spherical algebra question
Message-ID: <785@uwovax.uwo.ca>
Date: 16 Oct 88 01:03:08 GMT
References: <1187@agora.UUCP>
Lines: 27
Organisation: University of Western Ontario, Canada

In article <1187@agora.UUCP>, rickc@agora.UUCP (Rick Coates) writes:
> Here is a straightforward question that I have not been able to find
> in my reference books:
> 
> 	Given two points on a sphere, what is the equation of the
> 	line (great circle) between them?  What is the midpoint?
> 
> Many thanks in advance,
> 
> Rick Coates

Suppose you take two points on the sphere. That gives you a circle; call
it the equator. Draw a meridian through one of the points to give you
a reference for lines of longitude. Then that point has coordinates (0,0),
and the other one has coordinates (a, 0), where a=longitude of second pt.
The line between them is { (x,0) : 0 <= x <= a }.

If you want to translate this back into another latitude/longitude coordinate
system, you just have to rotate; in general the equation will be
(x,y) = t(u,v), where t is a parameter, and (u,v) is one of the points.
So the lines on a sphere are like lines through the origin on a plane.
--
Eric R. Smith                      email:
Dept. of Mathematics               7103_300@uwovax.uwo.ca
University of Western Ontario      7103_300@uwovax.bitnet
London, Ont. Canada N6A 5B7    (a shared mailbox: put my name on
ph: (519) 661-3638              the Subj: line, please!)