The Darboux cubic of (orange curve) is the set of all positions of such that its pedal triangle is in perspective with . In other words, the three gray dashed lines meet at a single point if and only if the point is on the cubic.

Let , , be the side lengths and let , , be the excenters of .

Then the equation of the Darboux cubic of in barycentric coordinates is given by

, where the sum is over all six permutations of the variables , , .

The Darboux cubic passes through the points , , and the Kimberling centers , , , , , , [1].

You can drag the vertices , , and the point .