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 |
| nine-point circle | circumcircle |
The following table lists some points and their anticomplements using Kimberling center designations.
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 | |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 | |
 | |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
 |  |
