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The feet of the altitudes of a simplex

by A. Gut and J. Waldvogel

(Report number 2008-08)

Abstract
We present an elegant algorithm for simultaneously computing all feet $F_0, F_1, \dots, F_n \in \mathbb{R}^n$ of the altitudes of a simplex from the coordinates of its vertices $A_0, A_1, \dots, A_n \in \mathbb{R}^n$. The algorithm which is based on projective geometry and matrix algebra, is valid for every $n \ge 1$. Coded in \textsc{Matlab}, it may be expressed by means of three simple statements using no more than 50 characters.

Keywords:

@Techreport{GW08_373,
  author = {A. Gut and J. Waldvogel},
  title = {The feet of the altitudes of a simplex},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-08},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-08.pdf },
  year = {2008}
}

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