arcbackarc

Arcbackarc is a term found in discussions of geometry and computer graphics to describe a composite curve formed by two circular arcs connected by a shorter connecting arc, sometimes used to approximate rounded, elongated shapes. The term is not standardized and tends to appear in niche discussions or informal descriptions rather than formal literature.

Construction and properties: A typical arcbackarc consists of three circular segments: arc A, a connecting arc C, and arc B, arranged so that the endpoints of A and B are joined by C. Continuity at the joints can be chosen to be tangent (C1) or curvature continuous (C2) depending on design goals. The radii of the arcs and the length of the connecting segment determine the overall shape, curvature distribution, and turning direction, including a backtracking portion where the path reverses direction along the curve.

Applications: In vector graphics and font design, arcbackarc-like shapes can approximate smooth contours with a small number of control parameters. In path planning or motion design, they offer a compact representation of rounded corners or twin-arc profiles. They can be produced by simple parametric formulas or derived from converting a piecewise circular path into a single parametric description.

Etymology and scope: The name comes from combining “arc” with a “back arc,” signaling the bridging segment that connects two primary arcs. Because there is no formal standard, the term is used flexibly in discussions and may describe any two-arc-with-connector configuration rather than a unique mathematical object. See also arcs, circular arcs, splines, Bezier curves.