The feet of the altitudes of a simplex (Q1025802)

The computation of the coordinates of the feet of the altitudes of a triangle as a function of its vertices is quite a simple task. In this paper this task is generalized in order to find an algorithm to compute the coordinates of the feet of the altitudes of an \(n\)-simplex as a function of the coordinates of its vertices for any \(n\geq 2\). The algorithm is constructed using homogeneous coordinates in \(\mathbb{R}^n\) and an implementation using MATLAB is presented.