VoxelGrid

A voxel grid is a three-dimensional grid-based representation of spatial space in which the continuous volume is divided into discrete, uniform units called voxels. Each voxel corresponds to a small cube of space and can store attributes describing that portion of the scene, such as occupancy, color, density, or distance to a surface.

Typical implementations use a uniform 3D array, where the grid resolution is determined by the voxel size. The mapping between voxel indices (i, j, k) and real-world coordinates is defined by the grid origin and voxel edge length. Voxels can be binary (occupied or free), probabilistic, or store richer fields such as a signed distance function.

Uniform grids are straightforward to index and well suited for simple volumetric queries and rendering techniques like ray casting and marching cubes. However, memory usage grows with the cube of the linear resolution, making dense grids impractical for large scenes. To scale, many systems use sparse voxel grids, hierarchical structures such as octrees, or specialized formats like OpenVDB, which store only occupied or near-surface voxels.

Voxel grids are widely used in robotics for 3D occupancy mapping and in computer graphics for volumetric effects and reconstruction. In surfaces reconstruction, truncated signed distance function (TSDF) voxel grids fuse depth data to produce smooth surfaces. In medical imaging, volumetric data from CT or MRI naturally aligns with voxel grids. Variants include color or multi-channel grids and dynamic or streaming voxel grids for time-varying data.

Related concepts include point clouds, which represent sampled surface points, and meshes, which encode surface geometry with polygons. Voxel grids differ from these by representing space volumetrically and enabling straightforward volumetric processing, at the cost of potential memory and quantization trade-offs.