This page is adapted the algorithm from a book Computational Geometry - Algorithms and Applications, 3rd Ed by Berg et. al. You can see details in chapter excersise 8.16.
Line segment on the coordinate system
Checking stabbery existence?
A line l that intersects all segments of S is called a transversal or stabber for S.
This application shows dual of a line segment in xy-coordinate system. You will immediately see resulting wedge at the right pane. At the right pane, corresponding wedge has the same color with the segment.
Black region shows intersection of the wedges. If intersection exists there must be a stabber which intersects all line segments.