The anticomplement of a point in a reference triangle is a point satisfying the vector equation
(1)

where is the triangle centroid of (Kimberling 1998, p. 150).
The anticomplement of a point with center function is therefore given by the point with trilinears
(2)

The anticomplement of a line
(3)

is given by the line
(4)

The following table summarizes the anticomplements of a number of named lines, including their Kimberling line and center designations.
The following table summarizes the anticomplements of a number of named circles.
circle  anticomplement 
circumcircle  anticomplementary circle 
de Longchamps circle  polar circle 
ninepoint circle  circumcircle 
The following table lists some points and their anticomplements using Kimberling center designations.