Point-Line Duality

This page demonstrates the concept of point-line duality in a simple, visual way. In the primal space on the left, you have the usual Cartesian coordinates (x, y). On the right, you have the dual space with coordinates (m, b), representing lines of the form y = m x + b.

Try adding points in one space by clicking on the canvas (i.e., pressing down and releasing without dragging). Observe how those points become lines in the other space. Conversely, adding a point in the dual space (m, b) creates a line y = m x + b in the primal space. You can also click and drag on existing points in either canvas to move them around. Notice how multiple lines in the primal space intersect at specific points, and these intersections correspond to points in the dual space that satisfy multiple linear equations simultaneously.

Primal – Cartesian
Dual – m x + b