voxel

A voxel is a discrete element used in constructing and representing a three-dimensional space in a voxel-based model. The term combines volume and pixel, referring to a value on a regular grid in 3D space, analogous to a pixel representing color on a 2D image. A single voxel is typically a cube with coordinates i, j, k in a grid; in practice each voxel stores a sample of a 3D field such as density, color, material, or occupancy.

Voxelization is the process of converting geometric data into a voxel representation, used in medical imaging, computational geometry, and 3D graphics. Common forms include occupancy grids, density fields, and signed distance fields. To manage memory, voxel data is often stored in sparse structures such as sparse voxel octrees or hybrid grids rather than a full uniform grid.

Rendering and processing: Voxel data can be rendered by ray casting or ray marching in volume rendering, or converted to polygonal meshes via iso-surfaces (for example, marching cubes) for traditional rendering. Real-time engines use optimizations such as sparse voxel octrees, voxel cone tracing, and GPU-accelerated voxelization.

Applications: Medical imaging uses CT/MRI scans to produce voxel-based representations for visualization and analysis. In geology, meteorology, and computational fluid dynamics, voxels represent volumetric data. In entertainment, voxel-based games and terrain editors model deformations and volumetric effects; some engines store terrain as voxels for dynamic editing.

Limitations: Volumetric representations can require substantial memory; efficiency depends on data structure and level of detail. They are often used in combination with polygonal meshes, with voxel data converted to meshes for rendering, or used directly in volumes for effects and simulation.