Dynamic remeshing - now with feature preservation, curvature adaptivity, and minimal surfaces

This will be incorporated into future releases of Kangaroo, but because it is so much fun to play with (not to mention useful!), I was excited to share this as a standalone component right now.

This is a tool for remeshing, as I first wrote about and demonstrated here.

However, since those first videos over a year ago, this has been improved upon and developed a lot.

One of the most significant changes under the hood is that it now uses the custom half-edge mesh class Plankton developed as an open-source collaboration by myself and Will Pearson (to whom I owe great thanks for all his fantastic work on this). Big thanks also to Giulio Piacentino for sharing his great work on Turtle, and to Dave Stasiuk, Mathias Gmachl, Harri Lewis, Jonathan Rabagliati and Richard Maddock for helpful mesh discussions.

High quality triangular meshes have many applications, including physical simulation and analysis.

Since I shared some examples of remeshing scripts here, I have also added a few more features in response to discussions and requests:

Feature preservation

This allows the user to set curves and points to be preserved during the remeshing. These can be boundaries or internal curves, and can be useful for keeping sharp creases, or separate regions. (One of the major applications of this tool is creating high quality meshes for input into analysis programs.)

These features can now even be moved while the remeshing is running, and the mesh will stay attached.

Curvature Adaptivity

When a mesh contains features with tighter curvature, smaller edge lengths are needed to faithfully represent the geometry. However, applying these reduced mesh lengths across the whole surface, even in flat areas where they are not needed can be impractical, and slow everything down. A solution is to refine the mesh according to local curvature.

'Fertility' model from AIM shape repository, remeshed with curvature adaptivity. Here the edge flipping option is also set to valence based, which causes the mesh to become anisotropic in the direction of curvature.

Minimal surfaces

Relaxation based purely on 1d elements will not give accurate minimal surfaces, we need to use proper 2d elements.

However, when relaxing meshes to produce minimal surfaces, generating a high quality initial mesh can be problematic and tedious. Uneven meshing can cause the relaxation to fail or give incorrect results, especially when the relaxed geometry changes significantly from the input, causing the triangle quality to degrade even further.
By continuously updating the connectivity of the mesh to maintain even sized and nearly equilateral triangles, even very large changes to the boundaries become possible, and the surface still minimizes mean curvature.

This allows exploration of sculptural forms in a more dynamic and flexible way than I think has ever been possible before (seriously - try it out, I think you'll enjoy it).

Surfaces may 'pop' if the boundaries are moved suddenly or too far apart - as sometimes no minimal surface solution exists with the given boundary conditions.

Any plugin claiming to produce minimal surfaces which lets you move the end rings of a catenoid arbitrarily far apart and still gives a tubular solution is lying! The only proper behaviour in this case is to collapse into 2 flat disks. (As it is currently, the disks will remain connected by an infinitely thin strand, as I have not yet implemented anything to allow genus change, but maybe in the future.)

Here is the component and a basic example file. Feel free to ask any questions about its use, report bugs, or request changes or additions. This is still a work in progress.

MeshMachine.gha

Plankton.gha

Plankton.dll

Remesh_new_examples.gh

To install, unzip and place the dll and 2 gha files in your Grasshopper libraries folder (replacing any previous versions of these you may have installed - these are more recent than other releases). Make sure they are all unblocked, and restart Rhino.

Comment

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Comment by David Stasiuk on April 22, 2014 at 2:21pm: So awesome!

Comment by shima sn on April 22, 2014 at 2:17pm: Thanks Daniel, well the problem that I'm having is that the grasshopper can't load the MeshMachineComponent! I downloaded the above file and copied in my library, do you have an idea why it is not loading? It also doesn't recognize the PlanktonMesh component!

Comment by Daniel Piker on April 22, 2014 at 1:49pm: Shima - The file used in the first video is the bottom group in the example definition. Just bake the curves into Rhino and reference them back in, then you can move them while it is running.

Comment by Daniel Piker on April 22, 2014 at 1:47pm: Hi Christian,

Yes, I'll add a version with the interpolated edge lengths - Maybe as another component, as I think this one already has a lot of inputs.

One question I had here for users is about useful ways to control these edge lengths. Is interpolating between values given at a few sample points a good way to do it?

Another option might be to use mesh colours - so you could paint on regions of density using UTO's MeshPaint3d.

and yes - I'll do a timer free version too. I'm also working on a dedicated timer free version of the main Kangaroo component that keeps all the iteration internal and outputs only once final equilibrium is reached (As this is no longer the 'live' interactive physics as usual, but it's not really 'dead' I'm thinking maybe zombie kangaroo for the name!)

Comment by I_M_F [Iker Mugarra Flores] on April 22, 2014 at 1:37pm: it feels like it is Christmas! great stuff, super exited....

Thanks for sharing, fantastic research Daniel!!!!!!!!

best

Iker

Comment by shima sn on April 22, 2014 at 1:36pm: This is really awesome!

Can you share the grasshopper file that you are using in the first video?

Thanks

Comment by Christian Schmidts on April 22, 2014 at 1:14pm: Thank you - half edge meshes really rock :)

I wanted to ask if the version with interpolation between multiple target lengths will be also incorporated into kangaroo? Hope so because it is really perfect for making gradual changes in the tessellation of a structures.

I just saw you posted a version without a timer in the original thread. Would it be possible to post something similar for the interpolation between multiple target lengths example?

Because I would like to incorporate it in a automated generation process.

Comment by nick belomatis on April 22, 2014 at 12:39pm: Object: MeshMachineComponent (level 1)
{
Exception has been thrown by the target of an invocation.
TargetInvocationException
}

Object: MeshMachineComponent (level 2)
{
Could not load file or assembly 'Plankton, Version=0.3.0.0, Culture=neutral, PublicKeyToken=null' or one of its dependencies. The system cannot find the file specified.
FileNotFoundException
}