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From: vkr@osupyr.mast.ohio-state.edu (Vidhyanath K. Rao)
Newsgroups: comp.graphics,sci.math
Subject: Re: simple spherical algebra question
Keywords: algebra
Message-ID: <943@osupyr.mast.ohio-state.edu>
Date: 16 Oct 88 16:26:05 GMT
References: <1187@agora.UUCP> <6337@watcgl.waterloo.edu>
Reply-To: vkr@osupyr.mast.ohio-state.edu.UUCP (Vidhyanath K. Rao)
Organization: Dept of Math, Ohio St U at Newark, Newark OH 43055
Lines: 18


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?
If one wants a parametric equation for the great circle, you
have two choices: Translate and scale to get the Unit sphere.
Let the two points be r_1 and r_2. Let s_t = r_1 + t(r_2 - r_1)
and r_t = s_t/|s_t|.

The other method may be quicker if you have some quick and dirty way
of getting sine and cosine of an angle at the same time. [some fpp's
will give you unscaled values]. Find \alpha so that the two
points are u and u \cos\alpha + v \sin\alpha. with u and v
orthonagonal. Let r_t = u \cos\theta + v \sin\theta with \theta
ranging from 0 to \alpha. This is also well suited for theoretica
work.