Analytical Functions Wrapped Around Spheres Shape Change

8 Analytical Functions Wrapped Around Spheres Shape Change 

The Fitting Probiem. In many studies in particular of natural fibers, orientation distributions are picked from spherical arcs in scattering patterns and then fitted by Gaussians or Lorentzians. The result is the finding of an isotropic background. At least part of this background is not related to structure, but to a fundamental misunderstanding. 

Pathway to the Solution. All orientation functions are defined on the orientation sphere. At the best, their period is k. Thus the mapping of an analytical function h (jc) on the orientation sphere is equivalent to 

Solution for Lorentz Distributions. For Lorentz distributions the solution is the Poisson kernel 

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