Details

A triangle center is said to be even when its barycentric coordinates can be expressed as a function of three variables , , that all occur with even exponents. If the center of a triangle has constant barycentric coordinates, it is called a neutral center (the centroid is the only neutral center). A triangle center is said to be odd if it is neither even nor neutral.

Standard barycentric coordinates of a point with respect to a reference triangle are normalized to have a sum of 1.

Reference

[1] Encyclopedia of Triangle Centers (ETC). https://faculty.evansville.edu/ck6/encyclopedia/etc.html.