A cubic curve through nine points

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The following diagram shows a cubic curve passing through nine points \(A,B,C,D,E,F,G,H,I\) in the plane. By moving these points around you can see how the curve changes.

This construction uses the paper Ruler Constructions in Connexion with Cubic Curves by Robert Russell, and builds on the work of Chu Khoon Hwa's honours thesis.

I will add some more information about Russell's construction in the future. For now, the following pages contain various constructions associated to cubic curves.

The Cayley-Bacharach theorem.
The coresidual of four points on a cubic.
The coresidual of seven points on a cubic.