We have two methods.

For your special case, after cutting the cube (but it's optional to cut it), you could simply sweep a circle with the edge (created by the cutting) as the rail.
Why it is optional to cut ? if you use the function Curve/Project, you could create the rail withut cutting.

The second method is for to find the center curve.
You could use two opposite edges, then you loft between these two curves to have a surface.
Then with the ISO function, you have a center curve as you wanted.

I will post the file with step by step.

The file with step by step...

It follows your idea. But I don't think you need Grasshopper, Phiros step-by-step guide is excellent!
If you want to try out Grasshopper I post the .gh-file here.

Something i don't understand

A simple circle by 3 points taken on the cubic "tube" Sweeping on a internal perimeter is not sufficient ?

And you can adjust the radius/diameter of the final tube in real time at the end after the sweep...

Phiro:
Thank you very much for your efforts. I really appreciate it. It looks like a very smart way.
I probably need to get it spelled out though sorry :-/. I'm still pretty new in Moi.

In step two - what did you do? Did you join those connected edges and copy them so you have the next step? Did you choose those because together they seemed to be the best approximation for at surface going through the center line?





In the step after you just make a loft it seems when I replicate. In the step after that do you do an offset to make that midpoint line? And the final step why didnt you just make a sweep? But maybe you did?

Again thank you very much.

renklint: Thanks a lot. I will look into it. If the beginning solid shape is more complicated I don't think its possible to do in any other way so still probably good to know that function.

Pilou: I dont know if I understand you correctly but in the meantime before I got all those great suggestions/solutions i tried to do something more like Phiro did. Not as sophisticated but anyway.
First I took one of the selected curves he made. Then I made a sweep:













Is that what you mean is good enough? I agree that its definitely close to acceptable.

Hi Michael

Sorry for my late answer. I wanted to wait with a reply until I gained a little bit more knowledge in general.

Even though I still don't think I understand why there is no surface like you stated?

For a calculation of the center curve I am thinking of first slicing the tube/solid/shape in little pieces. Then find the midpoint for each piece by integration. Then connect the midpoints to a single center curve and finally smooth out the edges if need by some smooth algorithm.

The smaller pieces (and thereby larger amounts) the better approximation for the curve. And of course calculation and processor time will increase:

Example with tube and cuts.








I briefly checked the skeleton about dividing the surface into minor shapes. I might have to dig deeper into this.


>Sorry I'm not really understanding what the end goal is here. Do you want the tube to slice away additional area of base solid to extend the cut out area?

<Or is the tube going to sit on top of the solid like as if you put a line of grout squeezed onto it or something like that?

Yes exactly - well a bit of both. My idea is that I can cut out an interesting shape and then change the surface on that shape. For example it could be some kind of wall design where the wall goes "in and out". Along the wall there could be a cut out for wires. The cut out could come from a curve and there after the wire gets put in the hole.

It could also be to slice additional area as you suggested and then put a wire in that fit that cut (the same wire).

@Pilou

>>> A simple circle by 3 points taken on the cubic "tube" Sweeping on a internal perimeter is not sufficient ?
>>> And you can adjust the radius/diameter of the final tube in real time at the end after the sweep...

I think, because of the cutting made in the problem presented, the cubic tube don't have a regular section square.
So it doesn't match .

When I tested it, it didn't match.
I tested a double rail too, and the size if circle was not regular.

Hi Hans,

re:
> Even though I still don't think I understand why there is no surface like you stated?

I meant that in your post you showed this:


Were those meant to be planar cross-section surfaces? Those are the ones you don't have in your .3dm file. But it sounds like there is a Grasshopper method to generate those for you automatically?


> For a calculation of the center curve I am thinking of first slicing the tube/solid/shape in little pieces.
> Then find the midpoint for each piece by integration. Then connect the midpoints to a single center
> curve and finally smooth out the edges if need by some smooth algorithm.

Sounds good - I thought that you were asking for a fully automated calculation.


> Yes exactly - well a bit of both. My idea is that I can cut out an interesting shape and then change the surface on that shape

Ok, but to get a tube like that another approach that would be simpler could be to project just one curve onto your solid and then sweep with that rather than cutting out a channel with 2 curves:

For example, just one profile curve:



Construct > Curve >Project to project it onto the solid:



Construct > Sweep using the projected curve as the rail curve for a one-rail sweep:



- Michael

Or another method for making a type of groove is to use boolean difference with one profile curve to cut a chunk out and then fillet those edges:











- Michael

@HansChristian

Sorry, I think I have made more steps and forget explaining.
It's a reverse thinking from result to conditions.
The first question was to do a "middle curve" and my solution is based on doing an Iso curve from a surface.
This surface is done with initial conditions given, the "squared tubular cutting".

To do an iso curve, I need a surface and only one surface, not a joined surface.
To have an only one surface constuction, lofting need to have "soft curves" (no angular point on the curves).
So I use a "reconstruct curve" with many points to have these two soft curves.

The middle curve is not an ofset, it's an iso (V iso I think).
Iso permit to have the center curve of the surface even if the distance between the 2 initial curves is not regular.

Next I use the iso curve to do the sweeping.



But I think, the initial question was to do a circular border.
The easier way for this (I think it, but perhaps I'm wrong) was the first method explained, with a "Curve/Project" to have a curve and to sweep a circle with this projected curve.
This method is in my file too.
I used "reconstructcurve", but it's optional here.

Hi Michael

First of all. Im sorry for the late reply. I had a very busy day yesterday and today.


<Were those meant to be planar cross-section surfaces? Those are the ones you don't have in your .3dm file. But it sounds like there is a Grasshopper method to generate those for you automatically?

Yes excactly you don't have those surfaces. But by slicing a solid tube into small pieces you could find the cross section midpoints for each and then connect them all.




<Ok, but to get a tube like that another approach that would be simpler could be to project just one curve onto your solid and then sweep with that rather than cutting out a channel with 2 curves:

<For example, just one profile curve:


Thank you very much for your reply. The suggestion of projecting the curve alle around the solid was a brilliant idea and much easier. I think thats the solution :-).

I really appreciate all the response and kindness here.

Hi Michael
That's an interesting option too with filleting. I have to experiment with that also. Thanks for taking all the time to help!

Hi Phiro

Thanks for that detailed explanation. Im sorry the answer took so long. I have to try it myself and dig into it. I will try making that isocurve and so on and report back :-). Thanks.