Cubic Command

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Cubic[ <Point>, <Point>, <Point>, <Number> ]
Gives n-th triangle cubic of the given triangle ABC.
Example:
Let A = (0, 1), B = (2, 1) and C = (1, 2).
Cubic[A, B, C, 2] yields the implicit curve -x³ + 3x² + 5x y² - 14x y + 7x - 5y² + 14y = 9.
Note: This command is in development, set of supported index n is changing.

Some common triangle cubics

Index n Cubic
1 Neuberg Cubic
2 Thomson Cubic
3 McCay Cubic
4 Darboux Cubic
5 Napoleon/Feuerbach Cubic
7 Lucas Cubic
17 1st Brocard Cubic
18 2nd Brocard Cubic

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