# Delaunay mesh irregular connections

Hi !

I want to make a regular delaunay mesh, but as soon as the surface makes an important angle with the base plane, the triangles aren’t regular anymore. Does someone have a way to fix this ?

Delaunay triangulation is meant to work in two-dimensions, not three! If you use it like you do, the z-component of each point probably gets ignored. Imagine each point being projected to the XY-plane and treated there, and that is also where your problem stems from.
In your case, it might still work though! You just need to provide a plane where no future triangles would overlap, while being projected to the same plane!

Yes you’re right, when I orient the plane differently I have a better result, but still not perfect. As you said, I was rather looking for a way to make a delaunay “in 3D”

You can use Remesh from Kangaroo or the one from Ngon or MeshMachineStatic.

Remeshing will change the vertex positions too though and produce something irregular (I could add an option to only do the flips, but it’s not there yet without scripting).

Where are these points coming from? - it looks like they’re on a surface, in which case it’s better to just generate the regular triangulation on the plane then map it to the surface.

Thank you @laurent_delrieu, I tried it with the remesher provided by NGon and it works !
Apparently @DanielPiker, the remesher of NGon gives the possibility to fix the vertices, but I’m really interested in a solution based on the plane mapped onto the surface, because it would be far more adaptable to all kind of surfaces

Ah yes, if you fix the vertices and give an edge length longer than any in the mesh, then only flips will happen anyway, so forget what I said about it not being possible without scripting in the remesher - you can do this with SimpleRemesh too just setting all vertices as corners.

Still, mapping points to a curved surface, then doing a planar projected Delaunay, then flipping the edges is a very roundabout way to get a regular triangulation on that surface.
When you have the surface, you can simply map to it (which also means the surface can even fold over itself, which would stop the planar Delaunay from working):

map_triangulation.gh (16.9 KB)

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If your surface is regular and untrimmed as the one in the focus of your reference image you could do something like this:

Which is a component from: