Nearplanar

Nearplanar is a term used to describe objects or structures that are almost flat, lying close to a single plane within a small tolerance. In geometry and modeling, a set of points, a polygonal mesh, or a surface is called near-planar if all points are within a bounded distance δ from some plane, so the maximum perpendicular deviation to that plane does not exceed δ. When both the distance and the orientation are restricted, the object is described as being close to planar in a stronger sense, such as C0 or C1 closeness, depending on whether only positional or both positional and directional deviations are considered.

In practical applications, near-planar approximations simplify analysis and computation. For example, when a nearly flat polygonal mesh is projected onto a plane for rendering, collision detection, or geographic information processing, the near-planar assumption reduces complexity without introducing significant error within the tolerance δ. In surveying, construction, and manufacturing, recognizing near-planarity helps determine whether a surface meets required flatness tolerances.

In graph theory, near-planar is an informal descriptor for graphs that are almost planar. This includes graphs that become planar after removing a small number of edges or vertices, or graphs with small crossing numbers. Although not a formal classification, the concept highlights a continuum between planar graphs and more complex networks.

See also Planarity, Flatness, Tolerance.