Relaxing Lines on a mesh

Hello, I was wondering if anyone had any thoughts on the best way to relax the jagged edges of a triangular mesh into smooth lines that still followed the contours of a base mesh. I came across the mesh burner python script written by Anders Deleuran, which helped me organize my initial mesh into concentric layers starting from the naked edges. Now I would like to relax the edges of each group into smooth lines. I managed to somewhat smooth them out with the length and smooth goals but they are still quite wobbly. Attached is an image of what I am trying to achieve as well as a working gh file.


Eventually I would like to translate them into develop-able surfaces for production. Previously, I have been doing it all manually in rhino. Below are some previous iterations of lights that we’ve made to get a better idea of the smooth lines that I am looking for.

Any help or advice on would be greatly appreciated!

meshRelaxedLines.gh (170.4 KB)

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You can smooth polylines using rhinocommon:

private void RunScript(Polyline x, double t, ref object A) {

Polyline poly = new Polyline(x);
poly.Smooth(t);
A = poly;
}

running this smoothing in a for loop is also good way.

then I suggest to project vertices to original ones just for being more accurate

if you want to add more stuff use kangaroo second 36:
https://vimeo.com/181328695

B A L L O O N S !

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Wow amazing! I’ll give that a try. This video is amazing, are those surfaces or meshes that you are constructing in the video at 0:38? How are you keeping them singly curved?

Thanks for the quick reply Petras, really incredible work.

Here’s a quick way of just smoothing the boundaries of the regions, if I understand correctly what you mean:
smoothregions.gh (104.5 KB)

smoothregions

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Yes this is what I was looking for. I was distorting the mesh too much with the length goal. Thanks Daniel.

The other solution is to use geodesic and mesh iso splitting


A bit better with subdivided mesh but takes 6 min to calculates. I have to rewrite geodesic script.

And one solution to flatten the strip is to suppress inner points. I don’t know if it is somewhere available. I wrote mine for my projects.

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Laurent, where is the gh file with vb and c# only (without milipede) ?

I didn’t keep the script I wrote for the example. You can recreate if you need
Geodesic is there:


I followed this publication
http://hhoppe.com/geodesics.pdf
but didn’t implement the simplification. So it is too long for “big mesh”.

Mesh iso splitting here

thanks, do you think the smoothness of offsets in the paper is just more mesh subdivisions or they use some sort of weights from laplace function?

It could be arc. It is quite “simple” to get the arc as all the information is available. But it is subdivision of mesh where needed. See this paper