nearcircularity

Nearcirularity is a term used to describe how closely a planar shape resembles a circle. In practice, it is quantified by several related indicators that compare a given region to an ideal disk. Common measures include circularity, the isoperimetric deficit, and distance-based metrics to the class of circles.

For a planar region with area A and perimeter P, a widely used dimensionless measure is circularity C = 4πA / P^2. This value lies in (0,1], with C = 1 if and only if the region is a circle. The isoperimetric deficit δ = P^2 / (4πA) − 1 is another equivalent description, with δ = 0 precisely for a circle and δ ≥ 0 for all other shapes. The two measures are related by δ = (1 − C) / C.

Beyond area–perimeter based indices, distance-based approaches assess nearcirularity via how far the boundary deviates from a best-fit circle. One method fits a circle to the shape (often by least squares or minimum-maximum radius criteria) and reports radial deviation statistics or the Hausdorff distance between the boundary and the circle. Another approach uses the symmetric difference in area between the shape and a congruent disk as a metric of dissimilarity.

Applications of nearcirularity measures appear in computer vision, pattern recognition, materials science, and biology, where shapes are evaluated for roundness, quality control, or morphological characterization. Related concepts include the isoperimetric inequality, circle geometry, and shape analysis techniques.