nearcircle

Nearcircle is not a standard mathematical object with a single definition. In informal usage, the term may refer to a shape or region that is approximately circular, or to a specific construction in computational geometry where a curve is constrained to stay within a small radial deviation from a true circle. A common formalization defines a nearcircle of center c and tolerance ε > 0 as a simple closed curve C for which every point p on C satisfies ||p - c|| ∈ [R - ε, R + ε] for some fixed radius R. Such a curve lies in the annulus between two concentric circles of radii R - ε and R + ε.

In polygonal contexts, a nearcircle may refer to a polygonal approximation of a circle where all vertices lie inside or near a circle of radius R, with maximal radial deviation δ. In data analysis or GIS, “nearcircle” can denote a circular search region that is robust to small measurement errors; e.g., points within distance r of a specified center, allowing for tolerance.

Relationship to circles: all circles are nearcircles with ε = 0; not all nearcircles are perfect circles. Algorithms for nearcircle recognition and fitting include least-squares circle fitting, RANSAC-based circle fitting, and evaluation of deviation metrics such as maximum radial deviation or area difference.

The term appears in niche literatures and may be used narratively to describe approximate circularity in geometry processing, computer graphics, and spatial querying.