Xref: utzoo comp.graphics:3363 sci.math:4645 Path: utzoo!utgpu!water!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!rutgers!gauss.rutgers.edu!math.rutgers.edu!bumby From: bumby@math.rutgers.edu (Richard Bumby) Newsgroups: comp.graphics,sci.math Subject: Re: simple spherical algebra question Keywords: algebra Message-ID: Date: 14 Oct 88 22:41:36 GMT References: <1187@agora.UUCP> Reply-To: bumby@math.rutgers.edu (Richard Bumby) Organization: Rutgers Univ., New Brunswick, N.J. Lines: 29 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? > There is ONLY ONE way to do all problems involving the global geometry of the sphere -- formulate them in the Euclidean space in which the sphere is embedded -- and there is ONLY ONE way to solve problems in Euclidean space -- use vector methods to reduce them to planar problems. Following these principles, the two give points and the center of the sphere give 3 points in space, and the equation of the plane through those points can be found easily from their coordinates. This plane meets the sphere in the required great circle. The rest of the problem is done in this plane. The midpoint of the segment joining the given points is found by a standard method. If you have followed up to this point you have a picture showing that the point you want is a point at the right distance from the center on the line joining the center to this point -- another standard problem. -- --R. T. Bumby ** Math ** Rutgers ** New Brunswick ** (in one form or another for all kinds of mail) [bumby@math.rutgers.edu]