Hi, I would like to ask about 2D skeletonization. I know this issue was addressed in quite a lot of threads by @laurent_delrieu and @DanielPiker. The issue: I have quite standard cases of 2D outlines resulting in forks and beams, but during the pruning process I most often have some little branches left. So it is not clear how many pruning steps are needed or whether the result would be good. More simply, it is difficult to have an error-less process when i.e. a beam would result in 1 central curve, or fork - 3 central curves. Smoothing of polylines does not help much either. For now I was doing mesh triangulation from closed polyline, and extracting skeleton based on mesh face adjacency. I attached the set of 2D curves I have in Rhino file. I also tried Capybara plugin on 3D closed meshes, but the CGAL wrapper does not work on some computers, so I would like to stay with 2D cases. [Branches] [Question] Curves.3dm (153.7 KB)

One common interpretation of the medial axis is actually “…the locus of the centres of maximal circles”. See for instance this paper by Pablo Miranda Carranza: https://www.diva-portal.org/smash/get/diva2:679788/FULLTEXT01.pdf Another approach is using Voronoi discretisation and post-processing this, as described here: http://www.labsimurb.polimi.it/11EAEA/T03/paper/EAEA11_PAPER_T03_p419_DELEURAN.pdf

Any ideas what would be a logic behind circle/fitting?

Maybe circle packing? Another idea using contours PCA3.gh (622.2 KB) [image]

Thank you for the references, maybe you have a code to test? :slight_smile: I wondering if this would work when outlines are very irregular? The prunning in that case often have lots of little branches. I am projecting 3d cloud to 2d, then applying 2d marching squares to get a mesh, from that I get the biggest outline for the skeleton.

I think the idea in the paper I linked above was to prune based on the angle between the 2 lines from the centre of the circle to the 2 closest points on the curve. [image] Any point which can have circle centred on it tangent to more than 1 point on the curve is part of the medial axis, but I think if the angle between these lines is small, it is more likely to be just a bump rather than what you want as a real branch

[image] Petras_Vestartas: I wondering if this would work when outlines are very irregular? Reducing small features (and/or smoothing out) of the input domain geometry is definitely a good idea to reduce the complexity of the medial axis. Or just having clean/minimal inputs in the first place, which is admittedly easier to ensure with e.g. floor-plans (which has been my main application of the medial axis). [image] Petras_Vestartas: maybe you have a code to test? I’m afraid the stuff I wrote is owned by my old employer. That said, I think the stuff Pablo did was made open source as I recall (as part if the EU project we both contributed to). Also, here’s the presentation for the paper I wrote that expands a bit on the modelling steps: TopologicalInfrastructureAnalysisSlideshow.pdf

For one of my project I continue to work on Medial Axis. And for answering @ore [image] Get skeleton more organic Grasshopper @laurent_delrieu Sounds interesting! Any timeframe for the release? I would appreciate if you could notify my once it is available… here is a component I will include in my plugin (partially free) Medial Axis From Curve [image] Curve must be planar and closed. No hole at the moment it will output the lines from the border [image] The circles that approximate the shape (useful to use cloud points algorithms) [image] And the medial axis with one polyline between each node [image] The lines are ordered so it will be possible to make sort tweens curve of one closed curve [image] I use that to put some circles inside the shape [image] In order to make a lamp. Cluster tool, rivet tool will be in the plugin. [image]

[image] Laurent Delrieu: Curve must be planar and closed. No hole at the moment it will output the lines from the border I guess it is difficult to also support holes, but it would be fantastic, if it would! Oliver

Bonjour, comment c’est va? Votre plugin a fière allure, heureux d’en acheter une copie lorsqu’il sera disponible. Merci encore

Hello that was not so difficult but I didn’t put great effort to finish it. I decided to make it with the same logic as some other components. So it generate alone the region (contour and holes) [image] Medial axis is outputted as polyline so it could be possible to filter short parts, [image] … but it works not perfectly, it depends on the tolerance chosen here 0.001 and the curve division [image] here 0.005 curve division 0.2 [image] here 0.005 curve division 0.5 [image] I have thinks to tweak things (ratio tolerance curve division …) It works on whatever planes Circles could be sorted so it is possible to have the biggest in-circle for labeling [image]

2D skeletonization

Grasshopper

LauraB (LauraB) December 29, 2023, 8:55pm 32

nice tools and good approximation @laurent_delrieu!
Since this is a mesh I think could be countouring. probably @DanielPiker could adjust his heat method tool.
this example is a bit different because uses 2 open curves…

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2D skeletonization

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