The return of the 3-pipe elbow, but this time with PERFECTLY round pipes. The critics said it couldn’t be done, but Professor 3D Dave digs deep into his mysterious bag of semi-magical 3D hacks.
If you watch on YouTube, be sure to click the LIKE or SUBSCRIBE buttons because I am shallow and desperate for superficial attention.
Another great video! Thanks for sharing this Dave-
Hey @theoutside
Thank you, Kyle. I appreciate it.
Nice use of SubD. 
The rebuilt surface is not an “perfect” surface. It deviates from a perfect circle by up to 0.01% (correction: up to 0.06% of the diameter) so not a lot but could be enough to cause a problem in some situations.
NICE tutorial Dave, Thanks for sharing!
Hey @davidcockey
Very intriguing! Two follow up questions:
Glad you liked it. 
Circle comparison.3dm (55.3 KB)
I used the Circle command to create a perfect circle with diameter of 100 units. The Circle command creates circles with are rational (weights other than 1) degree 2 NURBS curve which are perfect circles.
It is mathematically impossible to create a non-rational (all weights = 1) NURBS curve which is a perfect circle. Rebuild always creates non-rational curves.
Rebuild was used to rebuild the perfect circle into non-rational degree 3 NURBS curves with 8 and 16 control points, The maximum deviation between the rebuilt curves and the original perfect circle was found using CrvDeviation.
Rebuild degree 3 with 8 control points: Maximum deviation 0.0575831 which for a circle with diameter 100 is 0.06% (Deviation of 0.01% posted above was erroneous and has been corrected.)
Rebuild degree 3 with 16 control points: Maximum deviation 0.00320616 which is 0.003% of the diameter.
In general rebuilding with more control points will decrease deviation from the original curve. However Rebuild command works by interpolating to a set of discreate points equal to or less than the number of control points. This can result some input curves the maximum deviation not decreasing monotanically as the number of control points is increased.
The Rhino 9 WIP includes Elmo, an alternative command for rebuilding curves, which fits the rebuilt curve to the input curve by minimizing the deviation. Usually Elmo will result in curves which deviate less than Rebuild from the original curve.
Elmo degree 3 with 8 control points: Maximum deviation 0.00320616 which is 0.003% of the diameter.
Elmo degree 3 with 16 control points: Maximum deviation 0.00171293 which is 0.002% of the diameter.
@davidcockey
I appreciate all of the math and explanation. All I can say is ‘wow’ and ‘I just want it to look cool.’
But … I think I’ll have to trade tolerances used in a particle accelerators or rcoket engines for being able to tweak and hack.
the position of the faces and vertices can be optimised and constructed by using the rotary-symmetry. (violet lines).
(red axis) - and this allows also to use
_radiate
I also teach:
@schultzeworks
nice video, nice style and exercise - I like the starting “augmented reality” - intro.
comment to your workflow:
after subdividing at 5:02 the red edgeloop is not nice and does not represent a nice approximated cylinder / circle. - (in my opinion) you should delete the orange FaceLoop and stitch the cylinder at this position, closer to the transition.
And also make sure that the face-size, at least the first Faceloop in the cylinder has similar spacing / edge length than in the connection/transition area.
at least 2 FaceLoops or 3 Edgeloops (“Circle-like”) are needed to get a perfect parallel (last) approximated cylinder-section.
here is my file.
ThreePipeConnection_00_tp.3dm (3.4 MB)
kind regards -tom
