A 2 dimensional object embedded in a 2+ dimensional space.
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.
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.
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?
Computation Geometry for Design and Manufacture by Faux and Pratt is/was a standard reference which was originally published in 1979. It uses “curve” and “surface” as the general terms. It also uses “patch” a topologically rectangular two parameter surface, which may be part of a larger surface.
I didn’t think I’d get into this thread… oh well.
In 't nederlands is 't toch ook ‘oppervlakte’ - en een zeepbel heeft ook een oppervlakte, met oppervlaktespanning…
Een zeepbel wel, die heeft een binnen en buitenkant, maar ik zou “oppervlak” niet gebruiken voor een niet-gesloten, eindig vlak. Wel met betrekking tot vierkante meters, maar niet met betrekking tot de vorm. Maar ja, een beter woord heb ik ook niet. “Vlak” is wiskundig gezien correct, maar klinkt alsof het niet te veel gebogen mag zijn.
Interessant. Dus als je een zeepbel in 2 zou kunnen delen, zou die opeens geen oppervlakte hebben?
Maar je hebt in elk geval gelijk - zover ik kan zien, is er geen één woord dat helemaal dekkend is voor het begrip. Als je het mij vraagt, is het daarom dat men bij conventie het eens wordt (zonder daarom het aan iedereen te vragen) en gewoon een bepaald woord gebruikt.
heb nog een prettige avond!
Ha, so funny reading discussion about people trying to find words for abstracts concepts to express actual things. That is bound to get the brain in a knot.
Een zeepbel gedeeld in twee is gelijk aan twee zeepbellen. Dat betekent dat je dan twee binnenkanten en twee buitenkanten hebt.
i don’t know… both skin and membrane, by definition, have a thickness… which to me, makes both of those words no good for 3D modeling surfaces… (unless you offset the surfaces into a solid in which case sure, skin/membrane could work)
Spatial structures made from tensioned surfaces are called membranes. Technically a NURBS surface also is a tensile structure formed by the “pulling forces” of its control points. (Although the weights may also be negative… but that’s a different story.) Following that logic a NURBS surface also is kind of a membrane.
But since the control points can be placed anywhere the resulting surface can have any shape. In most cases NURBS surfaces do not look like natural membranes in between its boundaries (also known as minimal surfaces). Therefore I think calling NURBS membranes would simply be confusing. I mean there are still designers around who believe that one needs to know mathematical equations to model with NURBS…
