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 8.2 Duality.
Points on the coordinate system
Corresponding dual line
What is duality for a point?
A point in the plane has two parameters: its x-coordinate and its y-coordinate. A (non-vertical) line in the plane also has two parameters: its slope and its intersection with the y-axis. Therefore we can map a set of points to a set of lines, and vice versa, in a one-to-one manner.
This application shows dual of a point as a line in xy-coordinate system. You will immediately see resulting line orientation at the right pane. At the right pane, above figure shows inner angle of concave points and below is their intersection.