Modelling with implicit surfaces


I started thinking about providing implicit function modelling to Rhino.

to get the discussion started here some possible applications: patching complex holes or connecting 6 tube endings. Please see the uploaded examples.
grafik ![grafik|353x370]

(upload://uOcrHQW0IAtQsQBlending3Surf.3dm (2.1 MB) 6-tubes.3dm (863.6 KB) CaL2vL8oGZKST.png)

the workflow would be to specify boundary curves with normals, shaping curves, points and parameter for the implicit parametrization, then a mesh of the solution is created, auto-trimmed with the boundary. In case you need it you can then use your favorite Mesh2Nurb tool to convert the mesh into nurbs.

My main question is if that kind of modelling worklflow would bring any benefit?
And what would be the most important quality features of the generated implicit surfaces?
smoothness, position/tangency to connection surfaces?

Hope to get some valuable feedback from the community.

You maybe want to look at the XNurbs plug-in

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Dendro is an implicit modelling plugin for Grasshopper

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One of the advantages of implicit functions is the topological freedom like demonstrated in 6-tubes. xnurbs can not handle that.

Hi Stefan,

i would asume that if a user has edges and normals he is expecting to build nurbs surfaces, preferably having control over edge conditions and individual edge influence ratios. Getting a mesh (or surface) which bulges out unexpected may not be desired. Even if i would have a dense perfect mesh of the 6 Pipe example, i do not think that there is something available to easily go from mesh to nurbs. RR comes close, but the tangency is far away from usable in production and the dense trimmed surfaces it generates are impossible to handle as there is no way to match along trims (*).

It can. While it offers a lot of freedom to control edge continuity the generated surfaces are pretty light and require no further matching.

I would be curious how this compares to results built with RR from your example mesh provided above.

(*) This would be something… :wink:

Any references about implicit function modeling and the math used?

@stefan.schmaelzle How do you solve for the explicit surface with the position and tangency (normal) continuity conditions along arbitrary curves? Do you solve for a field equation in 3D space using a discrete mesh solver?

What is meant by " implicit parametrization"? Is it obtained prior to the solution?

Hello I have done something that could still be used to make node. I never really finished it as I have no use of it. But the logic could help making some good surfaces

The sources are still there (for the moment)

I have to more precise about xnurbs here. As you demonstrated xnurbs can be used to fill the void, but not without manually design the individual patches. In implicit surface modelling iit would suffice to select the 6 circular pipe boundary curves then hit a button to get the mesh.

The algorithm finds an implicit solution to the given position and normal fields in 3d. This solution is then discretized to yield the mesh.

Any publications describing the methodology or is it confidential?

Not confidential at all. You can start digging here: