Lineextensie

Lineextensie is a term used in geometry and design to describe the operation of extending a line or line segment within a prescribed space or set of constraints until a boundary or end condition is reached. The concept appears in computational geometry, computer graphics, and planning disciplines where controlled line growth is required.

Definition. Given a domain D in the plane (or space) with boundary and a directed line segment AB contained in D, the lineextensie in the direction of AB extends AB beyond B along the ray A + t(B−A) for t ≥ 1, until it meets the boundary ∂D or satisfies a predefined constraint. The resulting segment AB′ is maximal with respect to D and the imposed constraints, meaning no further extension along that direction is possible without violating them.

Computation and properties. In practice, lineextensie is computed by tracing the line along its direction and locating the first point where it intersects a boundary or constraint boundary. Robust implementations account for multiple constraints, obstacles, and numerical tolerance. If the domain or constraints change, the extension may be recomputed. The operation is distinct from creating a new line or a generic ray, because the extension stops only when a boundary or constraint is encountered.

Applications. Lineextensie finds use in geographic information systems for planning corridor or road expansions within zoning limits, in computer-aided design to generate layout lines that terminate at boundaries, and in graphics or simulation to model line growth under space restrictions.

See also. Line, extension, ray, boundary, clipping.