circlesOrigin

circlesOrigin is a term used in geometry, computer graphics, and related fields to denote the origin point or seed configuration from which a set of circles is generated. Depending on context, the origin may be a fixed center in the plane or a dynamic starting point for constructing a family of circles.

In standard geometric terminology, the origin usually refers to the coordinate origin. Circles sharing a common origin are concentric, while a non-fixed origin can generate patterns in which centers lie along curves or surfaces determined by the origin and additional parameters.

In computational applications, circlesOrigin is often treated as a parameter or function that, given input such as seed points, a path, or a surface, computes circle centers and radii to satisfy constraints such as tangency, coverage, or packing density. It appears in circle-packing routines, procedural texture generation, and geometric modeling workflows.

Examples of use include generating tangent circles to a boundary from a designated origin, or producing a sequence of cross-sectional circles along a spline, where the origin guides the placement and sizing of each circle.

Related concepts include center, origin in a coordinate system, circle packing, tangency, and Voronoi-based circle generation. The term circlesOrigin is not universally standardized and can have different meanings in different disciplines.

See also Circle (geometry); Center (geometry); Circle packing; Apollonian gasket; Voronoi diagram. References are discipline-specific and not standardized for the term circlesOrigin.