3d fractal object generation process

These objects, as I said previously,
have very small details, so the polygonization grid should be very fine.

The result is that in order to get sufficient detail, a huge number of triangles is generated, even for regions where the surface is locally flat, and in theory a much larger grid could have been used.

I have not found any way of implementing adaptive refinement, so I am left with billions (literally) of triangles. In addition to take a large disk space (1 triangle equals 3 vertices, 1 vertex equals 3 floating point values, this makes 36 bytes per triangle), this amount of triangles is far beyond what is possible to display interactively (I think current limit of graphics hardware is about 10 million tris/second).

The solution is called decimation . It simply consists of generating an object with less triangles, taking into account the fact that some areas are almost flat, and thus require less triangles. Of course this usually comes with variable loss of original shape, but it maybe not noticeable, depending on the quality of the implementation.

Over the years I have found many implementations of meshes decimation, here is a survey of common ones.

The real key point for me is that the decimation implementation must be Out Of Core, that is it must work on data (much) larger than available memory. Not all implementation support this, but I found a little Gem, cluspartred by Heiko Lippmann.
Heiko has been kind enough to send me the Linux executable of his program, and I must say it works very well for my purposes.

Starting from a 1 billion triangle mesh, it can generate a 5 million triangle mesh that is almost perfect looking and usable (displayable) on standard machines.
It creates partitions on disk and loads on demand these partitions to decimate them in memory, handling all the details of contiguous partitions. On a recent machine (Xeon 3.2Ghz, see below full specs), this process only takes a few hours.

I then convert the resulting triangle soup to a custom format that I wrote a viewer for, and eventually convert it to the STL format suitable for 3d Printers.

The generation of the initial triangle soup is multi threaded using Intels'TBB parallel_for, and is very efficient, using a grid size of 12000x9671x8417 only takes a few hours on a 8 core 3.2Ghz 2x6 MB cache 16 GB memory Xeon machine (cpuinfo x5482, not a bad machine...)