Piirded

Piirded is a term used in geometry to describe planar regions whose boundary consists of a finite number of simple curves, each of which is either a straight line segment or a circular arc, forming a closed, non-self-intersecting loop. Such regions are bounded and connected, i.e., they are Jordan domains with a piecewise smooth boundary. The concept generalizes polygons, which use only straight edges, and curved polygons, which may incorporate more general curves.

Formally, a region R in the plane is piirded if there exist curves C1, C2, ..., Ck such that the boundary ∂R equals the union of these curves, each Ci is a straight segment or a circular arc, the pieces meet only at endpoints, and R is the bounded interior. This implies a finite perimeter and a well-defined interior, making piirded regions a subset of Jordan domains with piecewise smooth boundaries.

Examples include a rectangle, a disk, a stadium shape (a rectangle with semicircular ends), or a rounded polygon composed of straight and circular-arc edges. Non-examples are regions whose boundaries require infinitely many pieces or feature fractal structure.

Applications of piirded regions appear in computer-aided design, computer graphics, geographic information systems, and various computational geometry algorithms, particularly those involving boundary representation, offsetting, and mesh generation. See also polygon, curved polygon, Jordan curve, and mesh generation.