I designed an algorithm that, given an octree and a location within that octree can compute the cubemap at that location. The algorithm kind of raytraces each face of the cubemap, but does this in such a way that multiple rays are traced simultaneously (aka. mass connected processing).
The faces of the cubemap are axis-aligned, which allows us to use linear interpolation rather than perspective correct interpolation (which includes 2 multiplications and a division). Because of this linear
interpolation, the algorithm only needs integer additions, subtractions, and multiplications by a power of two (aka. bitshifts).
For a more thorough explanation of the algorithm please read this article.
I’ve also written a partial implementation of the algorithm, available at Git-hub, which renders the positive z plane of the cubemap. It currently does so at 2 fps, which, considering I did not yet put effort in optimization and screen space occlusion is not yet implemented, seems promising. The data is still fully loaded into memory at startup. As background I render a fixed cubemap.
Due to space considerations, not all models have been uploaded to git-hub, but a small low-resolution model is available, such that after compiling the code, you can at least see something. The code is rather messy as it is still in an experimental state.
Images: http://imageshack.us/a/img839/7291/voxel2.png (test-scene) http://imageshack.us/a/img841/1796/voxel3.png (test-scene) http://imageshack.us/a/img708/221/voxel4.png (part of Mouna Loa) http://imageshack.us/a/img24/8798/voxel5.png (part of Mouna Loa) http://imageshack.us/a/img69/2483/voxel6.png (low resolution) _______________ UPDATE: Here is a movie made by Bauke, with his program. Moreover, here is a draft article which explains it in detail.