Planarize mesh

Hi Daniel,

I have a problem about flattening out the mesh's faces.

I have a mesh, which at first, I equalized its edges length and angles .Then I am trying to planarize the faces.

I did as your example titled "Planar Quads", but when I increase the force in order to flatten faces, unfortunately the mesh fails.

Please help me.

Thanks in advance.

Replies to This Discussion

Permalink Reply by Hans Rebel on November 6, 2015 at 8:55am

I think you try something impossible.

With all those goals you ( and Kangaroo ) can't get total total plan faces.

If you try you break it.

Permalink Reply by Daniel Piker on November 8, 2015 at 4:35pm

Hi Hengameh,

I agree with Hans that this looks impossible.

In general you can get a mesh of planar quads on any smooth surface, but this does not hold if you want to also fix the boundaries and connectivity of the mesh too.

For instance, consider a tube with a mesh aligned on a diagonal like this:

Keeping this grid and boundaries, no amount of nudging can ever make the panels close to planar while remaining close to the surface. Imagine we make the two green quads planar. The three highlighted points then determine the plane the yellow panel must lie in, and if we extend this we end up with all the panels lying in one plane, so it can never wrap around to form the cylinder.

To get a planar mesh on this surface what we would really need to do is make a new grid aligned with the axis and circumferential directions of the cylinder, but we cannot get there just by incremental shifts of the existing vertices.

With an open surface like yours, what can sometimes help is to planarize a smaller mesh which fits within the boundaries of the surface(or equivalently, extend your surface so the mesh fits within it), so the mesh can slide around and find an orientation better aligned with the curvature. Attached is an example which does this, and if you slowly increase the planarization strength you do get planar quads - it has to pull away a bit from the surface though. I suspect the only way to get a really good match is to start from a mesh with some irregular vertices.

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