I guess most of you are familiar with environment maps, they represent distant lighting distribution, and are used to render objects given their BRDF or SVBRDF distribution. Many papers map the spherical environment maps to 2D representation via a octahedron as described by Spherical parametrization and remeshing (E Praun - 2003). Wavelet transform is applied on 2D representation, for the resultant sparsity in representation. Is there a code available for Domain to sphere mapping described in the above paper. If not anyone can help explaining me the implementation.
Here are few doubts I have about the paper. The mapping from Domain to Sphere according to the paper is done the same way Sphere to Mesh parameterization is done, that is (according to what I have understood), the Domain (octahedron) is reduced to a tetrahedron using a progressive mesh favouring triangles with good aspect ratio (described in section 3.5), then progressively they apply vertex split transformation and optimize the vertex positions around the inserted vertex. This doesn't make sense to me because they could directly fit a octahedron to a sphere ( as it is also an regular polygon) rather than reducing to tetrahedron.
Another doubt I have is how they calculate the inverse function's Jacobin (mentioned in 3.4). They say that estimate it from the stretch calculated from the planar approximation of circular triangles.
I think there aught to be an implementation of this spherical parameterization to 2D in internet because alot of people have used to parameterize environment maps.