Distantsides

Distantsides is a term used in geometry to describe a specific relationship between pairs of sides in a polygon. In this usage, a distantside refers to a pair of parallel sides whose supporting lines are the farthest apart among all parallel side pairs of the polygon.

Formally, for a polygon P, identify all pairs of sides that are parallel. For any such pair (s1, s2), let d(s1, s2) be the perpendicular distance between the lines containing s1 and s2. The distantside pairs are those for which d(s1, s2) attains the maximum value across all parallel-side pairs of P. A polygon may have one, several, or none of these pairs, depending on its geometry.

In polygons that possess parallel sides, distantsides typically correspond to opposite sides with maximal separation along their common normal direction. The concept generalizes to non-convex polygons by applying the same distance criterion to all parallel side pairs; if multiple pairs share the maximum distance, they are all distantsides.

Applications include shape analysis, pattern recognition, and computational geometry tasks that require robust orientation information or bounding constraints, such as collision detection or bounding-box computations. The term distantsides is not standard in all textbooks, and many writers describe the same idea using the language of width in a given direction or parallel-side pairs. See also width, diameter, supporting line, convex polygon.