probability distribution over a sphere
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I am trying to create an orientational average of a stiffness matrix. The stiffness matrix is for a generic aligned composite fibre.
However, the fibres in the part i am trying to analyze are at various angles, creating nearly a gaussian distribution starting at zero, peaking at 25, and back to zero at 50 (degrees).
in order to create the orientational average, i need to come up with a normalized probability density function.
Ultimately i picture that this will look like a surface that is a planar (1-D) gaussian distribution revolved around an axis.
Is there any existing tool in matlab to do something like this?
I am currently looking into multivariate gaussian distributions, but not certain how much success i will have.
Another thought that has crossed my mind was trying to integrate the gaussian distribution about an axis, and normalize it by dividing by the surface area - does that make sense?
Any help would be greatly appreciated.