Description
Budget exact additional voxel cells for a symmetric integer halo around a supplied positive cuboid, counting edges/corners once; no boundary clipping or memory overhead.
A voxel is a cell on a three-dimensional integer lattice. Coordinates use [x, y, z] order; a box uses an inclusive low corner and exclusive high corner, so its dimensions count cells rather than physical distance. Occupancy records can repeat the same cell without creating extra occupied space.
Budget exact additional voxel cells for a symmetric integer halo around a supplied positive cuboid, counting edges/corners once; no boundary clipping or memory overhead.
When to use this tool
Use this tool to budget exact additional voxel cells for a symmetric integer halo around a supplied positive cuboid, counting edges/corners once; no boundary clipping or memory overhead.
How to use the tool and how it works
- Enter dimensions, halo using the field definitions below.
- Run the operation. Correct input errors before interpreting an output.
- Read result.core, result.expanded, result.haloCells. Use the ordering, boundary rules and absence conditions described below.
Multiply the core dimensions and dimensions enlarged by twice halo. Return both exact volumes and their difference as decimal strings.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| dimensions | Three positive cell counts [sizeX, sizeY, sizeZ]. | Dense list of at most 128 finite numbers; integer/shape constraints above also apply. |
| halo | Nonnegative integer cell thickness added on both sides of each axis. | A finite safe integer within the operation’s stated bounds. |
| Output field | Interpretation |
|---|---|
| result | Object containing the named fields below. |
| result.core | Exact core cell count as decimal text. |
| result.expanded | Exact expanded cell count including the halo, as decimal text. |
| result.haloCells | Expanded count minus core count, as decimal text. |
{
"input": {
"dimensions": [
2,
3,
4
],
"halo": 1
},
"output": {
"result": {
"core": "24",
"expanded": "120",
"haloCells": "96"
}
}
}Limitations and assumptions
- Halo counts cells on both sides of every axis, including edges and corners.
- Voxel components are integers from −1,000,000,000 through 1,000,000,000; dimensions are three integers from 1 through 1,000,000. Counts or strides returned as decimal text use exact integer arithmetic. No physical voxel size is assumed.
- Every declared top-level input field is required and unexpected fields are rejected. Ordinary strings are limited to 8,192 UTF-16 code units and lists to 128 entries, with tighter operation-specific bounds where stated. JSON text has bounded nesting and node counts.
- Numeric outputs must be finite and no larger in absolute magnitude than the safe-integer limit; operations returning exact large integers use decimal text. Positions are zero-based and spans end exclusively unless the operation explicitly states a different convention.
Alternative or Complementary methods
Keep cell coordinates, storage order and physical scale separate. Use coordinate conversion for a different memory layout and a separate meshing or geometric model for rendered surfaces.
References
Similar or alternative tools
- Voxel Box Boundary Cell Count
Count distinct boundary voxel cells of a positive-size integer cuboid as total minus strictly interior; edges/corners count once.
- Voxel Box Overlap Cell Count
Count integer voxel cells in the intersection of two half-open integer boxes; touching faces have zero cells and no physical-volume inference.