Rotating calipers

In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points.

The method is so named because the idea is analogous to rotating a spring-loaded vernier caliper around the outside of a convex polygon.

The method of rotating calipers can be interpreted as the projective dual of a sweep line algorithm in which the sweep is across slopes of lines rather than across x- or y-coordinates of points.

Godfried Toussaint coined the phrase "rotating calipers" and demonstrated that the method was applicable in solving many other computational geometry problems.

77–82) for the rotating calipers method, which generated all antipodal pairs of vertices on a convex polygon:[2] Another version of this algorithm appeared in the text by Preparata and Shamos in 1985 that avoided calculation of angles:[4] Pirzadeh[5] describes various applications of rotating calipers method.

Sequence of probes around the convex hull of a polygon to determine its diameter using Rotating Caliper method.
An antipodal pair of vertex and their supporting parallel lines .
Rotating calipers, finding a bridge between two convex polygons