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The paper "An Area-Preserving Parametrization for Spherical Rectangles" describes an efficient approach for sampling solid angles for rectangle light sources.

I am wondering if

  • The light source in world space is a quad shape (not necessarily a perfect rect), can I transform it to its local space which will be a rectangle, apply the above to sample the solid angle, and then transform the sampled dir back to world coordinate? Would this approach be valid for sampling quad shapes (using the method in this paper)?

  • Also (I guess this is a more general thing) if the world to object (and obj to world) transformation has shear transformation in it, would sampling in local space and then transforming the sample back to world still be a valid one?

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