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daemon2008

Points on a sphere

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Hi there, Was just wondering if anyone had an example C or Java file, or formula for calculating the spherical distance between two 3d vector locations on a sphere. I made a method for Euclidean distance but its not as accurate. Is it as simple as just finding the dot product between two vectors? Thanks! Dan

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Off the top of my head i would say get the angle between the two and then multiply by the radius of the sphere to get the distance.

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Quote:
Original post by ibebrett
Off the top of my head i would say get the angle between the two and then multiply by the radius of the sphere to get the distance.

Indeed. BTW, the most robust and accurate way to get the angle between two 3D vectors is θ = atan2(||A×B||, A·B).

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Thanks for the fast reply!

By : θ = atan2(||A×B||, A·B).

I know AxB is the cross product, but what are the lines surrounding the cross product, it looks like the cardinality.

Sorry im new to Geometry.

Thanks!
Dan


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Quote:
Original post by daemon2008
Thanks for the fast reply!

By : θ = atan2(||A×B||, A·B).

I know AxB is the cross product, but what are the lines surrounding the cross product, it looks like the cardinality.

Sorry im new to Geometry.

Thanks!
Dan
The above equates to:
angle = atan2(length(cross(A,B)), dot(A,B))
Does that clear things up?

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Quote:
Original post by DonDickieD
Shouldn't it be:

theta = atan2( length( cross( A, B ) ), dot( A, B ) / length( A ) / length( B ) )
You might be thinking of the method that uses acos().

The method posted above works because:
|AxB| = sin(angle(A,B))|A||B|
A.B = cos(angle(A,B))|A||B|
And:
atan2(sin(angle(A,B))|A||B|, cos(angle(A,B))|A||B|) = angle(A,B)
That's rather informal, but should show (more or less) why it's not necessary to factor in the product of the lengths explicitly.

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In what sense is that method better than the more direct R*acos(dot(v1,v2)/(R*R))?

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