SubD to Nurbs G0 continuity problem

Zero! This is one of those things that math nerds like to drone on about for eons. (Pro tip - don’t invite me to a party.) Something can be perfectly GN everyplace except a single point.

It’s a little easier to think about with curves.

At a subd “star point” it is often the case that the the curvature simply does not exist. But it is alwasy the case that at every single point nearby but not equal to the star point, the SubD surface is G2.

There is at least one serious issue with the approach you suggest. The boundaries of subd object have zero cross boundary curvature. That means you can’t “trim the star point” without modifying the nearby surface location AND having that surface get very flat across the boundary.

Detail from Star Hole.3dm

Star Hole.3dm (308.1 KB)

There’s two different ways to answer the question about how far the discontinuity propagates.

Dale has the correct answer for true SubDs.

However, it is generally not possible to convert a SubD directly to Nurbs, especially around extraordinary regions (star points / n-gons). So anyone that is doing a SubD -> Nurbs conversion is doing some kind of approximation, which will either increase the degree of the Nurbs surfaces or decrease the continuity locally near the star point / n-gon.

The answer for how far the discontinuity propagates in the Nurbs conversion depends on the approximation used. I’ve seen approximations that are G2 everywhere, even at the extraordinary point, although G0 or G1 are more common.

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Makes sense. I’d love to party with you!

BY trimming, I meant after converting _ToNurbs.

Take a look at this…

The sphere cut is a lot more drastic change since I’m ‘eroding’ a bunch of stuff.

file here for proper inspectionXnurbs_on_corner_starpoint_gf_201014.3dm (1.7 MB)

Since the discontinuities are only 'at a point, I tried this other approach of trimming all the T/star points with micro spheres. It’s pretty impressive I think:

rhino file…
micro_trim_spheres_stars_gf_200514.3dm (5.7 MB)

I’m explorating this because I’m trying to convince @XNurbs guy to release a grasshopper components so we can identity all T-joints and Star joint and give them one of these microspheres skin smoothing treatment. Like this:



Gustavo! You never give me all the details. If you’re willing to use goo to improve your models, just rough it out in Rhino and finish it with a good dose of this.


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I know, I know… our clients have been tooling from our files with star points and all, I think they just polish the tool and that’s it. No Bondo or Microbeads cream needed. I just need cool tricks for cocktail parties.

mold polish hides a multitude of sins. :wink:

I know, one of our crazy clients send us some files today to see if we could make them better. We looked and said: “you are crazy, these are great, stop wasting money, ship them!

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i seem to remember a similar conversation with one of my old clients… now…who could that have been?..


Probably someone who was also sick, and finally went back into the real world after rehab.