twosegment

A twosegment is a geometric object consisting of two straight line segments that share a common endpoint, forming a broken line with a single bend. It is commonly described by three points A, B, and C, where AB and BC are the two segments and B is the joint.

In the planar case, let the lengths of the two segments be l1 = |AB| and l2 = |BC|. If the base point A is fixed and the joint at B is free to rotate, the reachable positions of the end point C form an annular region centered at A, with outer radius l1 + l2 and inner radius |l1 − l2|. Consequently, the distance AC can vary between |l1 − l2| and l1 + l2 as the angle at B changes. The exact locus of C depends on the joint constraints and whether the segments can cross or overlap.

Applications of the twosegment concept appear in robotics, where a two-link planar arm (consisting of two rigid links connected by a joint) serves as a canonical model for inverse kinematics and reachability analysis. In computer graphics and computational geometry, two-segment polylines are used to approximate curves, plan paths, or represent simple narratives of motion. They also arise in geographic information systems and GIS when modeling polyline features with a single bend.

Variants and generalizations include polylines with more segments (three-segment, n-segment chains) and extensions to three dimensions. The term twosegment is informal and can be used interchangeably with two-link or two-segment polyline, depending on the context.