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## Main Question or Discussion Point

Hi,

I've researched this problem all across the web and most answers involve finding the distance between two points on a great circle, mostly in nautical terms, using latitude and longitude, etc. but that isn't the answer I'm looking for. It's generally agreed if you have two points on a great circle that are not antipodal then there is only one great circle through those points. But nowhere can i find how to generate parametric formulas for a unique great circle or how to find other points on the circle *analytically* (without graphs.) I can specify two points that lie on the unit circle: (0,.5,-.866), (.5,0,-.866). These are separated by 90 degrees on the circle. I would like to be able to compute all the points on the circle (in rectangular coordinates) starting from 0 degrees (the first point) and in increments of tenths or hundreths of a degree to 360 degrees. Can anyone help me with this? My math level includes college trig and a little differential calculus.

I've researched this problem all across the web and most answers involve finding the distance between two points on a great circle, mostly in nautical terms, using latitude and longitude, etc. but that isn't the answer I'm looking for. It's generally agreed if you have two points on a great circle that are not antipodal then there is only one great circle through those points. But nowhere can i find how to generate parametric formulas for a unique great circle or how to find other points on the circle *analytically* (without graphs.) I can specify two points that lie on the unit circle: (0,.5,-.866), (.5,0,-.866). These are separated by 90 degrees on the circle. I would like to be able to compute all the points on the circle (in rectangular coordinates) starting from 0 degrees (the first point) and in increments of tenths or hundreths of a degree to 360 degrees. Can anyone help me with this? My math level includes college trig and a little differential calculus.