Note the difference in returned Location for BRep_Tool::Tolerance and BRepTool::Surface:

const Handle(Poly_Triangulation)&
BRep_Tool::Triangulation(const TopoDS_Face& F, TopLoc_Location& L)
{
L = F.Location();
return (*((Handle(BRep_TFace)*)&F.TShape()))->Triangulation();
}


const Handle(Geom_Surface)& BRep_Tool::Surface(const TopoDS_Face& F, TopLoc_Location& L)
{
Handle(BRep_TFace)& TF = *((Handle(BRep_TFace)*) &F.TShape());
L = F.Location() * TF->Location();
return TF->Surface();
}

See https://www.opencascade.com/system/files/forum/20180122_122046.jpg

Hi Roman,

Thank you very much for the detailed explanation.
I am starting to understand the difference between topology and geometry. And yes, ideally, I would like to split a complex topology like that into a number of patches: https://imgur.com/a/9eXjm

One thing I don't understand is why it wouldn't be possible to split the topology into smaller patches with OCC. I noticed that there are a number of splitting classes. The degrees and continuity might make it difficult I think.

Another thing, OCC is able to triangulate topology. I don't know how that works exactly, but I was hoping that there would be a way to create similar results using nurbs patches.

I would understand if OCC has no functionality for this, maybe it's simply not one of its use-cases. In that case I'll have to look around for an alternative for this final step, though I'd prefer to do it all in OCC of course.
And of course I would really like to avoid having to do this manually.

Alternatively, it would be possible too on my end to work with (rational) Bezier surfaces. But I expect OCC cannot split the topology in that case either.

Either way, thanks for the help, it already helped me understand this better :)


Nathaniël

Hi Nathaniel,

Glad this helped ;-).
Thanks for attaching the picture. Yeah, I see where you are leading to. Now imagine that your external wire contains twice as many edges. How would that affect your expected result ?

Anyway, no splitting in OCC would do this job to the best of my knowledge.

As for triangulation, that's a different story. Triangulation is essentially an approximation of a 3D model with the help of planar triangles. There is always a trade-off between precision of such approximation and number of triangles (read memory footprint).

So you could certainly apply triangulation and convert each triangle into a NURBS surface of degree 1 (both U and V) with one degenerated side. But that would be a hardly feasible model in any CAD/3D application - the size will be enormously large and data quality is extremely poor. Nothing beyond visualization I bet. If Maya does not accept faces but does accept meshes then you could feed it with results of triangulation indeed but not with the degree 1 NURBS surfaces.

My 2 cents of course.

Roman
P.S. Yep, Bezier won't make any good comparing to NURBS in this scenario. Effectively Bezier is just a single span of a NURBS.

Hi Roman,

I'm going to have to be a bit more creative to solve my problem, but it's very nice to have some certainty (even if that means that what I'm trying is not very doable).

Just for clarity: I'm not actually writing a Maya plugin; Maya can import STEP (sort of, I think it's not perfect). My project is similar in the sense that I can't use trimmed nurbs/brep. But now at least I am starting to understand the difference and the problem of obtaining simple nurbs patches from trimmed nurbs.

And don't worry, I'm not going to make a nurbs patch for each triangle. I think my machine would explode

Hi Roman,

One more thought actually. Maybe you could tell me if it makes sense.

So say I have only (non-planar) nurbs faces with no holes, so only a single closed boundary for the face. I think it should be possible to at least force this into "simple" nurbs patches. I understand the edges and surface would have to be (converted to) consistent degrees and types. And some shapes will be hard to deal with automatically (e.g. complex concave boundary). But I think for these faces it should be possible and doable, even if it has to be done (partially) by hand. Or am I missing something?

Hi Nathaniel,

Let's imagine quite a simple example - a single "convex" boundary (as we are in 3D, not in 2D, convex is kind of conditional).

Even in that case, what you would need to do is to (automatically) split the face domain into quadrangle-like shapes. The latter are required as you need a rectangular grid of knots in 2D UxV space. Hope the referenced image - https://ibb.co/dGF5Jb - is of some help.
Internal rectangles defined by knot iso-lines which are completely inside the face domain should be easy - they map just "as is". For those at boundaries you will have decide how to distribute your sample points. In such case those patches will not be fully equal to your original surface anyway. They will deviate from your original surface and you will certainly have gaps (cracks) between adjacent NURBS patches. So your model will no longer be watertight.

To overcome that, even in a simplified example you will need a more sophisticated approach - e.g. splitting the entire face domain with a dense grid of isolines. In that case, I would look at ShapeUpgrade_FaceDivide and feed its ShapeUpgrade_SplitSurface tool with required U/V values. But even then there will be a lot of corner cases - e.g. tiny edges due to splitting with dense grid, etc.
Something really challenging...

Hope this helps somehow anyway.
Roman