Regular Dual Mesh

Hi,
i try to remodel the DTC Recycleshell. I struggle to get the Dual Mesh correct. In the original structure the Polygons are aligned with the force flow. This way a sliding failure will be prevented. I used the Tri Remash Component but my Polygons are oriented arbitrarily. Also the original structure has a more staggered pattern. Does somebody know a way to get a similar pattern?

Original

Remodeled Version

Shell.gh (21.4 KB)

Hi @Thomas16

Here are a couple of different ways this can be tackled.

  1. Make a regular triangular mesh of the right shape and wrap it onto the target surface

  2. Use repulsion to distribute points then triangulate

(then take the dual after in both cases)

wrap_regular.gh (37.4 KB)
repulsion_shell_panels.gh (30.0 KB)

The first gives you most direct control over the topology. For this shape you could even use a fully regular mesh, since it has 6 sides, but you’d get more size and shape distortion of the hexagons. In my example Here I’ve used a mesh which is regular on the interior, but has some corners where it meets the boundary. See here for another example of this.

The second avoids you having to create a starting mesh, and will generally give a nicer distribution than just remeshing, but it won’t generally give perfectly regular arrangements (and not symmetrical unless you include another goal to enforce that). Also for shapes that wrap under themselves the triangulation step gets a bit more complicated (but in your case that isn’t an issue since it can easily be projected flat).

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Sorry for replying this late. Very nice solution, thanks!
But is there a way to get rid of the very small quad parts?

image

I thought that might come up, and yes there are ways to tackle it, but I didn’t want to overcomplicate things at first.
Are you looking at the regular mesh wrapping approach or the point repulsion approach?

I am looking at the point repulsion approach

Hi @DanielPiker!

Found this thread relevant. Indeed, regular mesh wrapping approach gives nice results and direct control over the topology. Thanks for the links for useful threads.

I have the same question, as Thomas asked above. Is there a way to get rid of the very small quad parts? Could you pleas help on this? (for regular mesh wrapping approach)

I have tried some changes in the corners on the original regular mesh, but without any success…small zones appears in the the other places. I hope that there are some smart ways exist hot to solve it….

Quads like those along the boundaries appear in the dual where the input triangular mesh has only 2 faces connected to a boundary point along what becomes a smooth curve when relaxed:

So we need to instead design a mesh topology that avoids such vertices. This often requires introducing some internal irregular vertices.

Coming up with such a topology from scratch that leads to a result which balances panel size and regularity takes some practice. Here’s one possibility that could work here:

wrap_regular.gh (30.7 KB)

Another possibility here would be to anchor alternating vertices along these edges, then split to create half hexagons. These are still quads, but with nicer angles. Setting this up is a bit more work because of the floating vertices beyond the boundary, and the splitting at the end.

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Thank you very much for your clear explanation.