NURBS surfaces should be called NURBS membranes

i believe that was not the question, the OP was suggesting a REdefinition and not how we define it currently. also when i logically think, the word boundary would suit in exact this specific case far better, since a surface would imply etymologically correct that something would be attached to it which in this case with this abstract, mathematical, in the real world non existing entity would not apply.

not only sometimes. traditionally we mess words and their meanings up, they get scattered into different languages getting different meanings and sometimes even meaning the exact opposite, leading to different groups of people talking about different kinds of things when they meet. that is one reason to keep terminologies dynamic to recalibrate and realign each other.

That’s clearly a pristinely ironed Kobe period handkerchief with minmalist Yukarashi graphics applied. A rare masterpiece and collectible item.


The question is, rather, in the driveway or on the driveway…

If one throws the OP’s suggestion under the bus, will the bus have enough ground clearance to roll over?

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Ergo, since you can’t actually do anything with the etymologically correct abstract, mathematical, in the real world non existing “surfaces” that you imagine you see on your computer screen, Rhino is actually useless.

Good, yes, myself guessed myself have yours meaning, prevent, that’s only way to abstract of I tiny little brain, then myself would do continuity using words this myself and most other people around my with able to understand…

Yup, rendering/raytracing is all fake. Some fake just looks better than other fake. And I love working with fake.


P.S. I am a linguist

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3D is a fad. Use your unlimited degree of freedom milling and chiselling machine. All above G0 is a con.


valid in real life qantum mechanically and of course also virtually binary either on, or off, or both.



Call it whatever you want, while working with curves, closed curves, surfaces and solids: the name may not necessarily reflect its true description. i.e. in the 1960’s they named a band the Beatles, they didn’t look like bugs, smell or act like bugs, but they sang great music. You know them for what they do or did.



To be completely pedantic about it, I think it should be called NURBS Patch. A (mathematical) surface can do a lot of things that nurbs surfaces can’t (complex topology, disjoint regions), a “boundary” must always delineate a volume or at least separate two regions of space, a “skin” implies that it is wrapped around an interior (again connotations of volume and enclosed regions), “foil” has no mathematical meaning as far as I know, but it does conjure images from fluid dynamics.

Coordinate patches are mathematically speaking most similar to the UV domain of a nurbs surface. They’re also called “charts” within topology because they make up an “atlas” which covers an entire mathematical manifold. The only problem is that patches are usually considered to be open intervals whereas nurbs surfaces have a clear, valid boundary.



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There’s two common ways to approach this:

  1. A 2 dimensional object embedded in a 2+ dimensional space.
  2. An N-1 dimensional object embedded in an N dimensional space.

Let’s keep it simple for the time being and limit ourselves to 2-d surfaces and 3-d embedding spaces, as that is what almost all CAD programs deal with. In such a setting a surface can be defined as the set of loci along with adjacency relations (in topology I think these are called ‘neighbourhoods’ or ‘localities’, not 100% sure those are exactly the same thing.) When you have adjacencies, you can ‘walk’ along a surface by stepping from one locus onto any nearby locus, and as such travel along a path from one point to another. Not every mathematical surface is continuous, it can be made up of disjoint regions that share no neighbourhoods between them.

Add a distance metric to this entity and you graduate from topological surfaces to geometric surfaces.

Yes it’s an example. As are Nurbs surfaces and meshes. They are all types of surface, but the core notion of a surface is far broader than you could achieve with either nurbs or t-splines.

See me response to point #2.

Implicit surface equations and iso-surfaces are also types of surfaces that you often cannot represent with a single nurbs surface.

I was specifically talking about mapping of open sets to other open sets within a mathematical space. Trims are a B-Rep implementation details well beyond the generality of what surfaces are, and the fact that there’s a command called _Patch is entirely incidental and unrelated.

Translating surface into german “Oberfläche”, you basically can describe everything as a surface which describes a border to something touchable. Its basically a boundary to a physical object.

That actually means you can name everything expressing this, like it. However my guess is, that the reason why predominantly NURBS-surfaces are called “surfaces” is because you explicitly model a surface directly, and not by creating it out of regular forms (solids) or by modifying “boxes” - traditional mesh-box-modeling.
Furthermore a shape described in NURBS-patches(in automotive this is equivalent to a single untrimmed/unfaced and trimmed/faced NURBS-surface, so David proposal is quite right I guess), can exactly represent any point on that shape, whereas a mesh can only do this exactly at the vertex location… (unless the mesh has a link to a formula, which then would be a true surface anyway).
I see meshes as way to visualise a surface, whereas a NURBS-surface is a surface, owing a rendermesh). Its like comparing apples and peaches.

Would Oberfläche work for a soap-film stretched within a frame?

yes , I think so

but who knows, maybe in some decades we can model a rhinoceros in soap-film-surfaces only

Not trying to argue with you here, German isn’t a native language of mine, but in what sense is it still ‘ober’ if it’s just hanging in space? What exactly is it that’s underneath?

even a soap film has a thickness, but yes, sometimes words are not excat… “ober”/over is more like the topmost particles I guess…

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Well if you think that’s superficial, then underneath may be subficial? :wink: