Grasshopper

algorithmic modeling for Rhino

# Marching Cubes: Curve Wrapping & More Metaballs

UPDATE: 30-Jan-2014

140130_marching_cubes.gh

I have added breps as an input for wrapping geometry (it also can take lines now), as in the above definition. It has been updated for some efficiencies...now you can taper a curve at both ends if you choose, you only need to feed one radius, although you can feed as many as you like (it acts like the longest list component). The definition uses kangaroo, weaverbird and nudibranch, although I ahve also included some internalized geometry...but I highly recommend playing with those! Kangaroo and weaverbird are better-known essentials, but nudibranch is really fantastic too. Enjoy!

Some of the work posted lately by Nick Tyrer has gotten me thinking about marching cubes again...I had done some stuff with marching tetrahedra and cubes a ways back, and with some new inspiration (and a little time I could carve out today) I figured I'd take a stab at trying to make it more flexible and robust. There was a lot of room for improvement...certainly there still is. This is really a work in progress, so all caveats apply to the script...it can probably break, hasn't been thoroughly tested, etc. But I probably won't be able to do too much more with it for a bit, so I figured I'd put it out there if anyone wants to play with it.

The short of it is that the inputs can take any combination of points and curves, along with variable radii of influence for each geometry object. Also, if you're using curves, and want to "taper" the effect of it over its length (from start to finish) you can do so. For example, an untapered curve versus a tapered curve:

The marching cube stuff is derived from the amazing Paul Bourke's work. I'm calculating fields around points and curves using a standard metaball fall-off function. The trick to its (relative) quickness is in using rTrees to determine which sample points should have their fields updated by various geometry objects, and also in ensuring that points aren't sampled more often than they need to be. The use of the rTree has some up-front computational expense, but with larger geometry sets it saves a ton of time.

The definition has some examples in it, as well as a description of the inputs...but here there are again anyway:

G = A list of base Geometry, which can be any combination of curves or points

R = Radius...this is a list of the radius of influence for each geometry object. The number of elements in this HAS TO BE EQUAL to the number of elements in the geometry list

res = resolution...the edge length of each sampling cube, so smaller numbers reflect higher resolutions. Watch out...the lower this number is, it exponentially increases the calculation time!

iso = iso value for cutting the surface...the lower the number, the bigger the mesh will be

smooth = an integer equal to the number of smoothing passes you want to do on the mesh(es) after they've been created

taper = a boolean...if you're using curves, and want the mesh that wraps around the end of the curve to be tapered smaller, then set this equal to true

ratio = the taper ratio, a double between 0 and 1...this is how much of your base radius you want your tapered edge to be...so if your taper = 1, then your tapered edge should have the same radius as the beginning, 0.5 then it'll be half, etc.

run = a boolean to execute the code...it still can be pretty slow with a lot of geometry, so you can toggle this off to adjust your settings

Anyway, I hope you enjoy!

140120_marching_cubes.gh

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Comment

Comment by Artc Quang on November 30, 2015 at 1:45am

GOOD JOB!

Comment by Henrique F on November 25, 2015 at 12:42pm

thanks for sharing!

Comment by Neo on August 4, 2015 at 12:59pm

Thanks for your help Nik, I learned a lot from your post.

Comment by Neo on August 4, 2015 at 12:18pm

Thanks for your patients Nik, I tried to figure out all these terminology . so "iso" just means one certain surface because within one 3D field, there is a lot of surfaces where all the value at this surface are the same. just like the electric field, at different distance from the center charge there is always a Gaussian Surface where the field strength is the same. so the value only means which surface to choose. am I right?

Comment by Neo on August 4, 2015 at 11:33am

Hi Nik, "it samples the eight corners of each sample cube in a big XYZ grid around your object for the overall field value at each of those eight points" here, is the sample cube similar to the bounding box?  "by summing the contribution of all geometric objects or at least the closest point to each one"  is the geometric objects a cube unit or a object ? I don't understand it clearly. Thanks

Comment by Neo on August 4, 2015 at 11:20am

Thank you Nik, I know the marching cube algorithm but what is the relationship between marching cube and iso value??

Comment by Neo on August 1, 2015 at 12:22pm

Hi David,

Your Job is awesome. but I am not clear how "iso" this parameter influence the final result. As I tried to increase the number then I found these spheres getting smaller.Can you explain a little bit on how does it work?? Thanks

Comment by Oliver Tessin on June 15, 2015 at 4:16pm
I understand. So any further smoothing attempt of the output isn't really proportional to its effort...

I'll have a look into that library you mentioned later. Many thanks for the hint!

And should you find the time to refine your MC... I would highly appreciate it!
Comment by David Stasiuk on June 15, 2015 at 10:49am

Hi Oliver...this is one of those things that I really wish I had more time to update...the smooth that I built into the script in is a very basic Laplacian operation, and the topology that results from the MC algorithm isn't well suited to being nicely smoothed from this. What I really should do is one final pass post-Laplacian smooth that reevaluates each vertex in the iso-field and relocates it. This should produce a much smoother result, especially after a WB loop sub-D pass.

Daniel Piker started up a very interesting approaching using a small library he built called Æther that may be worth looking at. Unfortunately, I am just in the middle of a lot of things, so won't have time to code up these (and other) desired changes for improving this MC implementation, probably for a few months yet.

Comment by Oliver Tessin on June 15, 2015 at 10:07am

Hi David,

I uninstalled Kangaroo 2 before I posted. Your scripts works fine. I already got some nice results.

My main opbjective is to create a fibrous structure based on agent-behaviour design regarding stresslines and strand thickning through load values. I posted earlier about it http://www.grasshopper3d.com/forum/topics/extract-fem-volumetric-po...

Btw, might their be another way to solve the uneven srf than cranking up the res and smooth values? I'm already using mesh subdivision and smooth with weaverbird. It's lots of geometry, I know, and it will get much more, but I was wondering if I could improve something. Can't find an attach button for the file here...