Medial Axis for Euclidean Distance in nD

by Eric Remy and Edouard Thiel

This page is an appendix to our paper:

Here you can download the program sources (in C langage) to compute the Look-Up Tables and the Neighbourhoods in several dimensions: LutEucli2D.c , LutEucli3D.c ; for larger dimensions, see npic-mlut.c.

To compile, type cc LutEucli2D.c -O2 -o LutEucli2D and to run, type ./LutEucli2D (the same for 3D). The program will print its usage with command line arguments.

The beginning of the Lut masks are presented in the paper in 2D and 3D, Figures 10 and 13. Here are wider Lut masks saved in text files (first column the appearance rank i, next columns the coordinates x,y or x,y,z or ... or x,y,z,t,s,r, last column the appearance radius R) ; same datas are also given in Npic .nmask format :

Dimension Vector number Rverified radius in pixels Text format "i x y z R" Npic format "z y x R" OEIS reference
2 350 23500000 4847 txt nmask A171988
3 10000 126929 356 txt nmask
4 144979 30000 173 txt.gz nmask.gz
5 491945 10000 100 txt.gz nmask.gz
6 158129 2500 50 txt.gz nmask.gz


  1. Page 168, section 2.3, 1st paragraph, 2nd line: replace    vg = G(v)    with    vg = G( sigma(v) : sigma in SG(n) ) .
  2. Page 172, 1st paragraph, 2nd line: replace    4a(8b+7)    with    4a(8b+7) .

Last update 25 may 2009