Circlewhere

Circlewhere is a term used in geometry and spatial data processing to describe two related ideas involving circles and location.

Overview

In geometry, circlewhere denotes the locus of points that are equidistant to two given circles. For circles with centers C1 and C2 and radii r1 and r2, circlewhere consists of all points P such that the distance from P to circle1 equals the distance from P to circle2. The distance to a circle is defined as the Euclidean distance to its center minus the circle’s radius, with an absolute value to account for points both inside and outside the circle. The resulting locus is a piecewise algebraic curve, often composed of several arcs, and it generalizes Apollonius-type problems.

In computational geometry and GIS, circlewhere refers to a circular neighborhood query: selecting all data points whose distance to a given center is within a specified radius. This circular range query is a common operation in proximity search, clustering, and spatial indexing.

Applications and examples

In urban planning or emergency planning, a circlewhere query retrieves all facilities within a chosen radius of a central location, such as hospitals within 10 kilometers of a city center. In geometry software, circlewhere can be used to illustrate how the equidistance locus between two circles changes as their centers or radii are varied.

See also

Apollonius problem, range query, buffer, spatial index.