JSegmenten

JSegmenten is a family of geometric primitives used in computer-aided design and geographic information systems to represent smooth curve sections between waypoints. The term is used primarily in Dutch- and German-speaking CAD contexts. Each JSegment connects two fixed points while enforcing a controlled bend described by a joint parameter J, which governs the initial curvature and overall bending behavior.

An instance is defined by endpoints P0 and P1, a unit tangent direction at P0, and a curvature-control parameter J that shapes the bend. The curve blends a straight line with a smoothly curved profile to produce a continuous transition between segments. There are common variants, such as J1 for simple transitions and J2 for higher-order curvature control, allowing designers to tailor the bend to specific geometric or engineering requirements. The construction aims for C1 continuity, with optional C2 continuity between adjacent segments.

Mathematical properties include a parameterization on the interval [0,1], a finite length, and the ability to evaluate position, tangent, and curvature along the segment. Length is typically obtained via numerical methods, and curvature bounds are derived from J. JSegments are designed to be composed into networks or polylines, enabling smooth path modeling in both 2D and 3D contexts.

Applications and usage span road and rail design, highway alignment, and general CAD modeling where smooth transitions are preferred over sharp corners. They serve as an alternative to standard Hermite or spline segments by providing a compact control mechanism through the joint parameter J, facilitating quick adjustments during design iterations.

See also: clothoids, Hermite splines, B-splines, cubic splines, polyline.