Dimensionality

Terms

Spatial dimensionality (D)

The number of spatial axes in the coordinate system of a ZVF store. The most common value is D = 3 (x, y, z). Values of D = 2 (planar data) and D = 4 (e.g. x, y, z, t for time-series tractography) are also valid. D is declared in the store’s root .zattrs metadata and must be consistent across all arrays and all resolution levels.

Position array shape

The shape of the vertices/ array within a single chunk group: (N, D), where N is the number of vertices in that chunk and D is the spatial dimensionality. N varies per chunk (ragged); D is fixed for the store.

chunk_shape / bin_shape tuple length

Both chunk_shape and bin_shape are D-tuples. They must have exactly D elements, one per spatial axis.

Axis names

Optional string labels for each spatial dimension, stored in the OME-Zarr-compatible axes field of the multiscales metadata block. Typical values: ["x", "y", "z"], ["r", "a", "s"] (RAS), ["col", "row", "slice"] (voxel index).

Axis units

Optional physical unit strings associated with each axis (e.g. "micrometer", "nanometer", "voxel"). Stored in the axes field alongside axis names.

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Introduction

The Zarr Vector Format is not inherently three-dimensional. The spatial dimensionality D is a property of each individual store, declared at write time and embedded in the root metadata. All format rules (chunk grid, bin grid, VG index addressing, bounding-box queries) generalise straightforwardly to arbitrary D.

In practice, the vast majority of ZVF stores are three-dimensional (x, y, z), matching the dimensionality of the volumetric image data they are registered against. Two-dimensional stores arise in planar microscopy contexts. Four-dimensional stores (x, y, z, t) are an emerging use case for time-series tractography and dynamic cell tracking.

This page documents how dimensionality is declared, enforced, and used throughout the format.

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Technical reference

Declaring dimensionality

D is inferred from the length of chunk_shape at write time and stored in the root .zattrs under the key "spatial_dims":

{
  "zarr_vectors_version": "1.0",
  "geometry_type": "point_cloud",
  "spatial_dims": 3,
  "base_bin_shape": [50.0, 50.0, 50.0],
  "chunk_shape": [200.0, 200.0, 200.0]
}

There is no mechanism to change D after a store is created. Adding a resolution level with a different dimensionality will raise ValueError.

Effect on array shapes

Every dimensionality-dependent array shape in the format uses D explicitly. The table below shows how shapes vary with D:

Array	Shape	Notes
vertices/ (per chunk)	(N, D)	N varies per chunk
vertex_fragments/ (per chunk)	opaque uint8 blob, length depends on F	Fragment-index binary blob; size grows with the number of fragments in the chunk, independent of D
link_fragments/ (per chunk)	opaque uint8 blob, length depends on F	Same structure as vertex_fragments/ but indexes links/0/<chunk> rows
links/<delta> (per chunk)	(E, 2)	E varies; independent of D
links/<delta> (per chunk, mesh)	(F, 3)	F varies; independent of D
object_index/data	ragged uint8 (concatenated manifest blobs)	Each blob’s chunk_coords words have D int64s; total size grows with manifest count and complexity
object_index/offsets	(n_objects,) int64	Independent of D
cross_chunk_links/	(L, 2)	independent of D

The chunk_grid of the vertices/ Zarr array reflects D:

{
  "chunk_grid": {
    "name": "regular",
    "configuration": { "chunk_shape": [65536, 3] }
  }
}

Here 65536 is a soft cap on vertices per chunk (the actual number is ragged; the array is extended as needed); 3 is D.

Effect on chunk and bin addressing

The chunk coordinate of a vertex with position (p_0, p_1, …, p_{D-1}) is:

chunk_coord[i] = floor(p[i] / chunk_shape[i])   for i in 0..D-1

The bin coordinate within a chunk is:

bin_coord[i] = floor((p[i] % chunk_shape[i]) / bin_shape[i])   for i in 0..D-1

The number of bins per chunk is:

bins_per_chunk = product(chunk_shape[i] / bin_shape[i]   for i in 0..D-1)

For D = 3 with chunk_shape = (200, 200, 200) and bin_shape = (50, 50, 50): bins_per_chunk = 4 × 4 × 4 = 64.

For D = 2 with chunk_shape = (500, 500) and bin_shape = (100, 100): bins_per_chunk = 5 × 5 = 25.

The VG index array is always (bins_per_chunk, 2) regardless of D; the bin coordinate is flattened to a scalar index using C-order (row-major) ravelling:

bin_flat_index = ravel_multi_index(bin_coord, bins_per_chunk_shape)

where bins_per_chunk_shape = tuple(chunk_shape[i] / bin_shape[i] for i in range(D)).

Bounding-box queries

A bounding box is specified as a pair of D-dimensional arrays:

bbox = (
    np.array([100.0, 100.0, 100.0]),   # lower corner, shape (D,)
    np.array([300.0, 300.0, 200.0]),   # upper corner, shape (D,)
)

For D = 2:

bbox = (np.array([0.0, 0.0]), np.array([500.0, 500.0]))

The query engine computes the chunk range as:

chunk_min[i] = floor(bbox[0][i] / chunk_shape[i])
chunk_max[i] = floor(bbox[1][i] / chunk_shape[i])

and then the bin range within each overlapping chunk. All arithmetic is D-dimensional throughout.

Axis metadata

For stores that will be visualised or processed by OME-Zarr-aware tools, axis names and units should be provided via the multiscales metadata block. Example for a 3-D RAS store in micrometres:

{
  "multiscales": [
    {
      "version": "0.5",
      "axes": [
        {"name": "z", "type": "space", "unit": "micrometer"},
        {"name": "y", "type": "space", "unit": "micrometer"},
        {"name": "x", "type": "space", "unit": "micrometer"}
      ],
      "datasets": [...]
    }
  ]
}

Axis order in the axes array must match the axis order of chunk_shape, bin_shape, and vertex coordinates. zarr-vectors-py defaults to z, y, x order (slowest to fastest varying), matching the OME-Zarr convention for volumetric image data.

Four-dimensional stores

For time-series data (D = 4, axes t, z, y, x), the temporal axis is treated identically to the spatial axes for chunking and binning purposes. chunk_shape and bin_shape include a temporal component:

write_points(
    "timeseries.zarrvectors",
    positions_4d,                        # shape (N, 4): (t, z, y, x)
    chunk_shape=(10.0, 200.0, 200.0, 200.0),   # 10 time units × 200³ space
    bin_shape=(5.0, 50.0, 50.0, 50.0),
)

Bounding-box queries may include a temporal range:

result = read_points(
    "timeseries.zarrvectors",
    bbox=(np.array([0.0, 0.0, 0.0, 0.0]),
          np.array([5.0, 200.0, 200.0, 200.0])),   # t in [0, 5)
)

There are no special-case code paths for D = 4; the general D-dimensional logic handles it uniformly.

Validation

The validator enforces:

• spatial_dims in .zattrs equals the length of base_bin_shape and chunk_shape (L2).

• Every vertices/ array’s second dimension equals spatial_dims (L3).

• Every bin_shape and chunk_shape tuple at every resolution level has length spatial_dims (L2).

• Bounding-box arguments passed to read functions have shape (D,) (runtime assertion, not a stored validation level).