Kaarikuviot

Kaarikuviot is a Finnish term used to describe geometric figures formed from circular arcs. The word kaari means arc and kuviot means figures or shapes. In Finnish contexts, kaarikuviot can refer to both the curves themselves and the planar regions bounded by such curves.

Definition and representation: A kaarikuviot is typically a planar curve made of a sequence of circular arcs joined at common endpoints. Each arc is defined by its center and radius. Junctions aim for tangent continuity (G1) to produce a smooth appearance; higher-order smoothness depends on design.

Construction: Methods include arc interpolation and bi-arc interpolation, where two circular arcs are used to connect two boundary conditions with a smooth transition. In practice, designers specify a series of points and tangents, and an algorithm computes the arc sequence and centers.

Properties: On each arc, curvature is constant; at joints, curvature changes abruptly unless the joints are tangent. The total length is the sum of the constituent arc lengths, and the enclosed area can be computed piecewise using sector areas.

Applications: Kaarikuviot are used in graphic design and logo work for rounded aesthetics, in typography and font design for arc-based strokes, in architectural ornamentation, and in computer-aided manufacturing to approximate smooth curves with circular segments.

Relation to other concepts: They are related to arc splines and bi-arc curves, and contrast with polynomial spline methods such as Bezier or B-spline curves. In Finnish literature, the term is sometimes used interchangeably with arc-based curves in CAD and vector graphics.