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December 13th, 2012, 01:30 AM   #1
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Calculate the arc length between 2 points over a hypersphere

Good morning,

I'm trying to compute the arclength (geodesic distance) between two n-dimensional points over a n-dimensional sphere (hypersphere). Do you know if it is possible? If yes, please, I'd be very pleased if you, as experts, provide me this knowledge.

Thank you very much
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December 23rd, 2012, 08:00 AM   #2
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Re: Calculate the arc length between 2 points over a hypersp

Get the 2 vectors connecting the respective hypershperical points to its center, say A and B. Compute the angle (^) between A and B with Cos(^) = A.B / |A|.|B| . The geodesic arclength between the points is (^) times r where r is the radius of the hypersphere and (^) is given in radian measure.
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