A voxel is a sample in a three-dimensional grid, analogous to a pixel in a two-dimensional raster image.

A volumetric dataset with dimensions $N_x\times N_y\times N_z$ stores a value at each grid location. The value might represent density, material occupancy, temperature, medical-imaging intensity or another scalar or vector field.

Voxels are useful when the interior of a region matters, not only its boundary. They support direct volume rendering, simulation grids and conversions between sampled fields and surfaces.

Uniform voxel grids are simple but expensive: doubling resolution in every direction multiplies the sample count by eight. Sparse structures therefore store only occupied or interesting regions when most of the volume is empty.

A voxel is a sample, not necessarily a literal cube of uniform material. Reconstructing a value between grid points requires an interpolation rule, just as displaying a transformed raster image requires reconstructing values between pixels.