Unable to join surfaces

I’m confused:
I have two surfaces they have matching number of control points, matching spans, their edge control points coincide but I cannot join them.

Can someone explain to me how/why they have different number of isocurves and knots?

I’ve never had such problem before. Rebuilding a surface to match another surface control points and degree was enough for them to join.

extract.3dm (80.6 KB)

using “joinedges” I get:

that seems a pretty huge jump in tolerance.

zooming in on the bend I see this:

Yes, I know.

I do not understand why.

Hello - the points along the edges are not actually coincident, - a couple of mm apart where I checked. The pink surface is non-uniform
-Pascal

I’m using setpt command to set them all and still there is a gap between the surfaces.

Still inexplicable is the difference of the number of isocurves.

What does that mean? I thought all surfaces in Rhino are non-uniform.

Hello - run `MakeUniform` on these - you’ll see the isocurves even out, for one thing. Mr Pink has a fully multiple knot at the top end of the curved part, which Mr Green does not - that makes the isocurves appear different, and introduces a kink at that location.

-Pascal

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Does that change the curvature?

Yes - if a curve or surface is non-uniform, in general the shape will change if made uniform.

-Pascal

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If I remember correctly the difference between uniform and non-uniform (or at least one of the differences) was that the weight of the control points in one of the are all 1s and the points are 3d whilst the other are 4d and you can modify the weight.

Is there some way in Rhino that these are shown as being different? Because currently in Object Description I see no difference.

Hello - all weights are 1 here as far as I can see. The difference is in the knot vector. Use `UntrimAll` and then `List` to see the knots (among other things) - you’ll see one in the pink surface that has a knot of multiplicity 3 that is not at one end of the list. That is the kink.

-Pascal

What does this mean? It has 3 knots more?

Hello - see

-Pascal

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Thanks @pascal.

Just one last question @pascal,

What do you call a `kink`? What does the `kink` do?
I am unfamiliar with this term.

Hello - a kink (or potential kink - it may not actually be a kink) occurs where there is an interior fully multiple knot. If you move a quad point on a circle you’ll see a link in action.

It is a location where there is at least potential for a break in tangent continuity.

-Pascal

so kink is like a knuckle on a surface?
what is a crest then? <- UPDATE: I meant crease

I do not know that term, but that does not mean much… my guess of the moment is that it is a 3d thing - a locally highest point or series of points on a surface- something like that. I do not know if it applies to surfaces as NURBS things or 3d topography, so to speak…

-Pascal