Apache wrote:
> 
> > ... the distribution is stronly anisotropic at the lower
> > parts of the hemisphere.
> Should the distribution isotropic then? I did my best generating a costheta
> distribution, which is an anisotropic distribution.

No.  I have explained this before, the varying density does not
necessarily mean anisotropy.  Anisotropic means the density depends on the
direction on the sphere surface (in your distribution the samples are more
dense in circumference direction than in theta direction).   

Christoph

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