++Tutorial: "Mathematical Transformations of Spatially Balanced Samples" by falkmielke · Pull Request #364 · inbo/tutorials · GitHub

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A brief writeup of some useful tweaks I first implemented here for the MNM project.
I found this of general relevance, and spiced it up with references to spatially balanced sampling and basic application of functional programming.

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Hi Falk, this is a very interesting tutorial! I am not an expert in spatial sampling (but I'm trying to learn it on my own), but everything is conceptually clear to me (I'll have to deal with the mathematics of Halton sequences another time). As a non-expert, I would mainly benefit from having more examples in the tutorial, maybe in the form of references to specific applications. Some examples:

(3) Choose Your Distribution Pattern: And in many applications, it is a valid strategy to give points closer to the center a higher chance of being chosen [?? EXAMPLE ??], or to have a sampling pattern that reduces likelihood with distance from center, or just the opposite (i.e. bias towards the rim) [?? EXAMPLE ??].
Spatial Balance - in a Weird Way: Close to the center, it is high, but it reduces towards the edges of our circle. Logical, if you think about it: the orbits close to the center are much shorter, yet they house equally many points as the distant orbits. This outcome might be fine in some situations [?? EXAMPLE ??], but undesired in others [?? EXAMPLE ??].
If you would have real-life examples for the special variants (line 508 and further) that would be cool, but the tutorial is fine without.

On line 339 there is a typo: it refers to apply_transform but it was coded as apply_trafo.

Thanks for writing this nice tutorial!

thanks to suggestion by @bserrien

Hi Falk, this is a very interesting tutorial! I am not an expert in spatial sampling (but I'm trying to learn it on my own), but everything is conceptually clear to me (I'll have to deal with the mathematics of Halton sequences another time). As a non-expert, I would mainly benefit from having more examples in the tutorial, maybe in the form of references to specific applications. Some examples:

(3) Choose Your Distribution Pattern: And in many applications, it is a valid strategy to give points closer to the center a higher chance of being chosen [?? EXAMPLE ??], or to have a sampling pattern that reduces likelihood with distance from center, or just the opposite (i.e. bias towards the rim) [?? EXAMPLE ??].

Spatial Balance - in a Weird Way: Close to the center, it is high, but it reduces towards the edges of our circle. Logical, if you think about it: the orbits close to the center are much shorter, yet they house equally many points as the distant orbits. This outcome might be fine in some situations [?? EXAMPLE ??], but undesired in others [?? EXAMPLE ??].

If you would have real-life examples for the special variants (line 508 and further) that would be cool, but the tutorial is fine without.

On line 339 there is a typo: it refers to apply_transform but it was coded as apply_trafo.

Thanks for writing this nice tutorial!

Great suggestions, thank you for reviewing, @bserrien !

I have added (fully made-up) examples; and although I would prefer actual applications, I hope they serve the purpose of illustration.

Note: I have also moved the figures to /static, which is "good practice" for hugo but seems not common practice on this website. I have tested and it should work on the website, but please double check.

Hello Falk, thank you for adding some real-life examples for the spatial patterns of sampling more towards the center or more towards the edge. I found them very helpful to understand the rationale for the tutorial. Nice work!

trafo_spat_bal: initial draft

6550835

falkmielke added the proposal tutorial label Aug 23, 2025

falkmielke added 3 commits August 25, 2025 06:53

trafo_spat_bal: note on interval

e007f87

trafo_spat_bal: additional figure

3963087

trafo_spat_bal: proofread - ready for review

29afa29

falkmielke requested a review from florisvdh August 25, 2025 05:31

falkmielke added 2 commits August 25, 2025 08:39

trafo_spat_bal: ++Gaussian

47adb7c

trafo_spat_bal: minor typo

2f35cf1

falkmielke requested a review from EmmaCartuyvels1 September 4, 2025 13:38

falkmielke requested a review from wlangera February 24, 2026 13:20

wlangera mentioned this pull request Feb 24, 2026

Potential improvement for randomisation options within circle b-cubed-eu/gcube#143

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bserrien reviewed Jun 2, 2026

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falkmielke added 4 commits June 11, 2026 08:17

trafo_spat_bal: merging main for update

761fa59

trafo_spat_bal: moving images to /static

744e8bc

trafo_spat_bal: wrong function reference

489567c

trafo_spat_bal: proefread and more examples(*)

290cd81

thanks to suggestion by @bserrien

falkmielke requested a review from bserrien June 11, 2026 07:20

bserrien approved these changes Jun 12, 2026

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falkmielke merged commit c56ccbe into master Jun 12, 2026
1 check passed

falkmielke deleted the transform_spatial_balanced branch June 12, 2026 08:07

++Tutorial: "Mathematical Transformations of Spatially Balanced Samples" by falkmielke · Pull Request #364 · inbo/tutorials · GitHub

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++Tutorial: "Mathematical Transformations of Spatially Balanced Samples" - #364

++Tutorial: "Mathematical Transformations of Spatially Balanced Samples"#364
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++Tutorial: "Mathematical Transformations of Spatially Balanced Samples" by falkmielke · Pull Request #364 · inbo/tutorials · GitHub

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++Tutorial: "Mathematical Transformations of Spatially Balanced Samples" - #364

++Tutorial: "Mathematical Transformations of Spatially Balanced Samples"#364falkmielke merged 10 commits intomasterinbo/tutorials:masterfrom transform_spatial_balancedinbo/tutorials:transform_spatial_balancedCopy head branch name to clipboard

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++Tutorial: "Mathematical Transformations of Spatially Balanced Samples"#364
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falkmielke commented Aug 23, 2025 •
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