3dimensional

Three-dimensional, often abbreviated 3D, refers to objects and space characterized by three independent spatial dimensions: length, width, and height. In mathematics, physics, engineering, and computer graphics, 3D describes the physical world and digital representations that convey depth along a third axis in addition to two-dimensional plane coordinates. In everyday usage, 3D is contrasted with two-dimensional (2D) representations and with higher-dimensional theories that include time or additional spatial axes.

In mathematics, three-dimensional space is modeled as R^3 with coordinates (x, y, z). Distances are measured by the Euclidean metric, d = sqrt(x^2 + y^2 + z^2). Common coordinate systems include Cartesian, cylindrical (r, θ, z), and spherical (ρ, φ, θ). Vectors, dot products, and cross products describe directions and areas within this space.

In computer graphics and modeling, 3D objects are represented as meshes consisting of vertices, edges, and faces. Rendering pipelines convert 3D scenes into 2D images by projecting 3D points onto a view plane, applying shading, textures, and lighting. Applications include video games, simulations, architecture, animation, and virtual reality. 3D printing creates physical objects by layer-by-layer additive fabrication from digital models.

Perception of depth relies on cues such as perspective, occlusion, and binocular disparity. Some displays, including stereoscopic and autostereoscopic systems, aim to present true or convincing 3D visuals. In physics, three spatial dimensions are complemented by time as a fourth dimension in spacetime models; many theories treat higher-dimensional spaces beyond ordinary experience as mathematical abstractions.