Centroidal tessellation and termination criterion

[momohu]

I saw in an article that the distribution state can be adjusted by controlling λ, but I didn't find the corresponding function in the manual. What command is needed to realize this
neper -T -n 15 -domain "sphere(0.016,12):scale(1,1,1)" -o sphere -format geo
https://link.springer.com/article/10.1007/s40571-016-0129-0

[rquey]

This is a centroidal tessellation, which you can get using -morpho centroidal or, equivalently, -morpho "centroid:seed".

The expression of the termination criterion is a L1 norm. It is curious that it is not normalized by the number of cells, but I'm quite sure that the authors did normalize.

Neper's default is a L2 norm (normalized), but you can change it to the L1 norm (normalized) using -morphooptiobj centroid:L1.

The lambda value can be set using -morpho val=....

Put this in a spherical domain and you get something like your figures:

$ neper -T -domain "sphere(1)" -n 250 -morpho centroidal -morphooptiobj centroid:L1 -morphooptistop "val=0.5"
$ neper -V n250-id1.tess -datacellcol id -print lambda-0p500

$ neper -T -domain "sphere(1)" -n 250 -morpho centroidal -morphooptiobj centroid:L1 -morphooptistop "val=0.005"
$ neper -V n250-id1.tess -datacellcol id -print lambda-0p005