GridEdgeNetwork emits 8 vertices + 12 edges per voxel with no deduplication (~368 B/voxel)

[swahtz]

Summary

GridEdgeNetwork (src/fvdb/detail/ops/GridEdgeNetwork.cu:100-107) allocates its output as a fixed 8×/12× expansion of the input voxel count, with zero deduplication — a corner shared by 8 voxels is written 8 times, and an interior edge shared by 4 voxels is written 4 times:

buffer	size	B/voxel
outV	8V × 3 float32	96
outE	12V × 2 int64	192
outVBidx	8V int32	32
outEBidx	12V int32	48
		368

(The two *Bidx arrays are also written and then discarded for batchSize == 1 — the existing FIXME at :151.)

This was catalogued alongside the coordinate-list topology builders addressed in #711 / #712, but it is a different problem: there is no _createNanoGridFromIJK and no radix sort here. It is purely an output-size issue, so #712 does not (and should not) cover it.

This is not a speed problem. Warmed, the op runs in 0.17 ms for 212k voxels. It is memory only — but 368 B/voxel puts a hard ceiling on the grid size that can be visualized (a 100M-voxel grid would need ~36.8 GB just for the wireframe).

Proposed fix: deduplicate via the dual grid

Both halves of this were verified experimentally, not just derived.

1. The deduplicated vertex set is exactly the dual grid.

dual(c) active ⇔ ∃d∈{0,1}³ primal(c−d) ⇔ c is a corner of some active voxel. Measured on a sparse grid (V = 212,803): unique vertices = 657,710, dual_grid().num_voxels = 657,710, sets element-wise equal.

Vertex positions become dualIjk − 0.5 (index space) or tx.applyInv(dualIjk − 0.5) (world) — numerically identical to today's values, so return_voxel_coordinates semantics are preserved exactly. Only the duplication goes away.

2. Edges need a 4-voxel incidence test.

Note that "both endpoints are dual-active" is necessary but not sufficient — two diagonally-adjacent voxels satisfy it without the segment being a voxel edge. The correct rule:

Edge (c, c + e_a) exists ⇔ any of the 4 primal voxels c − off is active, where off ranges over the offsets in {0,1}³ whose component along axis a is 0.

(Voxel v has corners v + {0,1}³; the segment lies in that corner set iff c − v has a 0 in axis a.)

Validated against ground truth (the geometrically-unique edge set produced by the current implementation) on a sparse irregular grid that exercises diagonal and corner cases: 165,527 edges from both, element-wise identical.

3. Endpoint indices come from ijk_to_index on the dual grid — no sort, no separate dedup pass.

Implementation sketch

One kernel over dual-grid voxels: for each c, apply the 4-voxel test on 3 axes to build a 3-bit mask; prefix-sum the popcounts to size outE exactly; fill. O(D) work, no expansion, no sort. Removes the discarded jidx arrays at the same time.

Expected savings

grid	V	current	deduplicated
dense 128³	2,097,152	771.8 MB (368 B/vox)	128.0 MB (61 B/vox)	6.0×
dense 64³	262,144	96.5 MB	16.3 MB	5.9×
sparse (random points)	212,803	78.3 MB	31.2 MB	2.5×

On dense grids dual D ≈ 1.02×V and unique edges ≈ 3.05×V, so the win is largest exactly where V is big enough to matter. Extrapolated to 100M voxels: ~36.8 GB → ~6.1 GB.

Dependency

This should be stacked on #710, not built on main. It needs the dual grid, which is only cheap once the leaf-mask PadGrid lands — on main, buildPaddedGrid still takes the coordinate-list path, so you would trade one blow-up for another.

Compatibility notes

• This changes the size and ordering of both returned tensors. The documented contract (fvdb/viz/_utils.py:11) promises only "an (N, 3) tensor of vertices and an (M, 2) tensor of indices" and does not pin N or M, so deduplication is within contract.
• There are currently no tests for this op — edge_network appears in tests/ only as a commented-out line (tests/unit/test_ray_marching.py:433). Nothing will break, but that is because coverage is absent; tests should be added as part of any change here.
• The only consumer is fvdb.viz (grid_edge_network / gridbatch_edge_network). Rendering should look the same or better — interior edges are currently overdrawn 1.75–4×.
• If changing the default is undesirable, a deduplicate: bool = True parameter would preserve the existing behaviour.

Related

• Grid topology ops build coordinate lists where leaf-mask operations would be far cheaper #711 / Replace coordinate-list grid-topology construction with leaf-mask morphology #712 — coordinate-list → leaf-mask topology builders (this op is a sibling case, deliberately out of scope there)
• Build dual/padded grids via leaf-mask morphology to cut memory #710 — PadGrid / dual-grid leaf-mask morphology (dependency)
• MarchingCubes.cu:357 — a separate instance of the same theme (torch::unique_dim over a (3·nTri, 3) int64 tensor), also not covered by Replace coordinate-list grid-topology construction with leaf-mask morphology #712