Quote:Original post by Pragma
Do you care about the volume contained in each cell? Or do you just need to know the total volume?
If it's the former then you'll need to use a different trick. But if it's the latter, you can compute dot(v0, cross(v1,v2)) / 6 for all the triangles in each cell and store them in the cell. Then you can add this up for all the cells. You can easily do this in parallel over multiple machines.
Yes, I see that your suggested approach will work regardless of whether the isosurface is on one processor or shared across several processors, and it should work perfectly fine if I only needed the total volume.
However, I do need the volume in each cell. One primary reason is that I do not a priori know the total number of closed isosurfaces in the data field. Once I am done calculating the "volume" present in each cell, I will then need to search through the entire data field for connected "volumes". To be more precise, I will need to compute the volume distribution (say for instance, the pdf of sphere volumes) of the closed isosurfaces in the data field.
I can think of one **laborious** procedure at the moment: construct a table (similar to the tritable in the mc-algorithm) that contains all the triangle facets that enclose the required volume in each cube (this would mean breaking up the relevant part of the cube faces into triangular facets). I could then use your suggested approach for the tabulated triangles in each cube. So essentially I will have a "closed" volume in each cube.
Do you have other suggestions?
