Hello,
indeed, you found a bug for larger step sizes. I've never used the '-central' option with such large step sizes. Turns out that for sizes higher than 60 there is an integer overflow bug. This is fixed now and you can download a preliminary version here if you cannot wait until the next release:
Thanks for noticing. Below - just for the record - the sequence of LAStools calls that I used in my experiments to notice that things were not quite right.
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To get a closer look at what happened I had done the following. First I decided to look at only a subset of your input to be able to tell whether the algorithm picks one point per 200 by 200 meter cell that is the closest to the center of each 200 by 200 cell (hence, closest to the x/y coordinate pair that has a remainder of 100 when divided by 200).
las2las -i GCP_TEST.las ^
-inside_tile 484000 6129000 2000 ^
-odix _sub -olaz
lasthin64 -i GCP_TEST_sub.laz ^
-step 200 -central ^
-odix _central200 -olaz
lastile -i GCP_TEST_sub_central200.laz ^
-i GCP_TEST_sub.laz ^
-files_are_flightlines ^
-tile_size 200 ^
-o GCP_TEST_200.laz
lasview -i GCP_TEST_200*.laz -gui
lasview -i GCP_TEST_200_484400_6130400.laz -color_by_flightline
lasview -i GCP_TEST_200_485200_6130200.laz -color_by_flightline
lasview -i GCP_TEST_200_485000_6130200.laz -color_by_flightline
lasview -i GCP_TEST_200_484800_6130400.laz -color_by_flightline
lasview -i GCP_TEST_200_484000_6129600.laz -color_by_flightline
lasview -i GCP_TEST_200_484000_6129400.laz -color_by_flightline
Attached a before and after image for GCP_TEST_200_484400_6130400.laz with the green point that is selected being the most central one.