Direct Mesh Extraction

[william-silversmith]

It might be possible to directly extract a triangle mesh from the crack codes by expressing the dual graph of level sets of contours. Then the level sets can be converted into a mesh. That last step might not be super easy though.

Q: Is it worth doing this vs. binary image extraction followed by marching cubes?

Each graph node would be 2 to 4 bytes + 1 byte (encoding two directional links) = 5 bytes. 5 bytes * 10% of the image = 0.5 bytes per a voxel vs a binary image would be 1 byte per a voxel.

Would it be faster? Unclear.

This mesh construction could proceed two z-slices at a time, resulting in extremely low memory usage.

paper relevant to triangle mesh construction from surfaces:
https://dl.acm.org/doi/pdf/10.1145/130881.131213

[william-silversmith]

The dual graph can also be used to answer queries like "what label is this point inside" or "what is the cross sectional area at this point"

Would this be any better than decoding to an image and sampling? For large sections probably, but would that be better than using the random access grid?

If I recall correctly, a major contributor to decoding time is connected components, so if that could be reduced (e.g. by only needing to CCL a subset of contours), maybe that would accelerate those queries.

[william-silversmith]

You could also easily extract a point cloud. You can create an approximate surface mesh from a point cloud using the point cloud library: https://pointclouds.org/