bensegment

Bensegment is a geometric construct defined as a pair of line segments that share a common endpoint. The shared point is called the apex, and the other endpoints are denoted B and C. Thus a bensegment can be described as the ordered pair (AB, AC). The two segments form an angle θ = ∠BAC and together bound a wedge-shaped region unless the three points are colinear.

Basic properties include that the lengths of the two segments are |AB| and |AC|, and the convex hull of {A, B, C} is the triangle ABC when the points are non-colinear; if they are colinear, the bensegment reduces to a single segment AB (or AC) along the same line. The region between AB and AC, the wedge, has area 0.5 · |AB| · |AC| · sin θ.

Notationally, bensegments appear naturally as elements of polygonal chains and in vertex fan constructions used in mesh generation and rendering. They can be generalized to a set of k segments sharing a common endpoint, forming a fan, sometimes described as a k-segment or multi-segment fan.

Terminology and usage: the term “bensegment” is not widely standardized in classical geometry and may appear in informal discussions or niche literature as a descriptive label for a two-segment fan. In formal texts, the same object is typically referred to as a pair of segments with a common endpoint or as a simple two-edge polygonal chain.

See also: line segment, polygonal chain, wedge (geometry), vertex fan, triangle.