ok, May be as a beginner, I may overestimate the power of PGA. Especially if I consider the main problem I would like to work on : How to re-construct the brain gray matter surface from a MRI acquisition. I get very exited by the PGA approach, as it looks as being the proper tool to use (and not just an other tool …) I may be wrong since I did not find any work mixing the PGA framework to do surface reconstruction but it worth a try. (especially if I can find collaborations through this forum)
To come back to the particular technical question of this thread, the “PGA magic” I need seem to be obvious: it has oriented surface, (so an easy test to separate inside from outside) and it also has the volume formula, that should make the computation easy. Indeed, the end result is just to compute the inner and the outer volume of the surface intersection with a cube.
What is not clear to me, is how to choose the surface and the voxel cube representation in PGA. For the surface, I also would be very interested by @enki work “Clean up your meash !” as mention here #393 (is there a first version available ? or any other related works ?)
May be a naive question, can the voxel cube be an element of the algebra (as points, lines and planes ) ?