baryoncentric
Barycentric refers to a system of coordinates used in geometry and physics. In its simplest form, it describes the position of a point relative to a set of reference points. For example, in a triangle with vertices A, B, and C, any point P inside the triangle can be expressed as a weighted average of these vertices. These weights, known as barycentric coordinates, are non-negative and sum to one. If P = uA + vB + wC, where u, v, and w are the barycentric coordinates, then u + v + w = 1. The values of u, v, and w indicate how "close" the point P is to each of the vertices. For instance, a point near vertex A would have a large u value and small v and w values.
The concept extends to any set of n+1 reference points in n-dimensional space. In this case, a