The anticomplement of a point in a reference triangle is a point satisfying the vector equation
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
The anticomplement of a line
is given by the line
The following table summarizes the anticomplements of a number of named lines, including their Kimberling line and center designations.
|de Longchamps line|
|Euler line||Euler line|
|line at infinity||line at infinity|
|Nagel line||Nagel line|
|orthic axis||de Longchamps line|
The following table summarizes the anticomplements of a number of named circles.
|de Longchamps circle||polar circle|
The following table lists some points and their anticomplements using Kimberling center designations.