Segmentoid

Segmentoid is a term used in geometry and computer graphics to denote a generalized, parameterizable segment-like object. The concept is not standardized and appears in niche or emerging literature as a way to extend the idea of a line segment to accommodate additional structure, such as a parameter space, variable length, or morphing behavior.

In its simplest form, a segmentoid is defined by a pair of endpoints A and B in a given space, together with a continuous mapping φ from a parameter interval, typically [0,1], into the space, such that φ(0) = A and φ(1) = B. If φ is affine, the segmentoid reduces to the ordinary line segment AB. Allowing nonlinear φ yields a curved or otherwise nonstraight trace that remains contained within the convex hull or a specified region related to A and B, depending on the chosen metric or geodesic structure.

Key properties include the parameterization by t in [0,1], which assigns a point φ(t) on the segmentoid, and the possibility of defining a length through an integral of the speed |φ'(t)| over the interval. Segmentoids can be concatenated when the endpoint of one aligns with the start of another, creating longer or more complex segmentoid chains. Transformations such as isometries or affine maps act on segmentoids by transforming their endpoints and their parameterizations accordingly.

Applications are proposed in areas where simple straight segments fail to capture needed flexibility, such as modeling flexible cables, morphing vector graphics, segmented path planning, and geometric modeling where a segment’s shape can adapt under constraints or time-varying conditions. The term remains informal and context-dependent, serving as a flexible descriptive tool rather than a universally defined object.