Splines & Arcs

[Bill Tillman]

I was not a bad student in Geometry class but apparently I've really lost it with this layout. I can only post bits and pieces of this thing due to NDA's I'm bound to. So here goes.

 

The drawing is composed of a block which in turn contains two blocks. I'm not sure if this was done intentionally but my suspicions are it ended up this way when it was exported from Revit or other BIM software to a DWG file...that's my guess anyway. Through a process of elimination I can see that once you open the block in the block, that's the end of the thread. Now why the person who drew this thing did it this way is beyond me, thus my conclusion that this file was exported from another software program.

 

In essence, the object is made up of a bunch of splines. Which makes locating the center of the arcs/radiuses almost impossible. The only way I did locate something close was by establishing two non-parallel chords, adding perpendicular bisectors to them and then filleting these lines. Well that gets me kind of close but the information people are telling me I don't have it right. Close but no cigar.

 

If anyone with more expertise on this using splines, maybe can shed some light on this for me...I still think it's an issue of exporting to DWG file which causing some very sloppy drafting practices to happen. I've saved the attachment down to 2010 format.

Drawing21.dwg

[Dadgad]

Hi Bill I use Spline leaders all the time and I am quite proud of how nice I make them look, typically by grip stretching with a crossing window.

Which has absolutely no bearing on your problem.

I downloaded your Dwg and played with it a bit.

 

I used the Burst command on the multiple blocks, then used Polyline Edit to Convert to Polylines MULTIPLE.

I then used the PE JOIN option.

Splines are really interesting and they look great, but most folks tend to try to avoid using them, as far as I can tell.

 

Another command which might help you is SPLINEDIT.

 

 

Drawing21.dwg

Edited August 18, 2021 by Dadgad
Dwg attached

[Dadgad]

I am having difficulty uploading an edit, so hopefully this will do it.

 

I used my quick properties to set all the Splines to FIT, from Control vertices>

Polyline Edit Multiple selection to JOIN.

Having done that a Midpoint grip appears for each bit with the Convert to Arc option as in the screenshot.

Appreciably less than ideal, presumably there is a much better way to do this, looking forward to

leaarning it when a member of the Splinerratti weighs in. 

Drawing21.dwg

Edited August 18, 2021 by Dadgad
typo correction

[Dadgad]

This might be helpful, I am inclined to suspect that @lrm is the Grand Wizard of the aforementioned Splinerratti.

[eldon]

I think that no human drew this. There are odd bits of line all over the place!!

 

Is this structural? It looks to me as if it could be an ellipsoidal lining of a tunnel.

 

How important is the shape of it? I would go at it by drawing a polyline with the Nearest Object snap at suitable intervals and then curve fit.

 

 

[eldon]

However, the shape is not an ellipse that AutoCAD knows about!

 

 

[CyberAngel]

If the shape is a curve but not a spline or an ellipse, it may be a spiral. I know nothing about spirals, but that may put you on the right track.

[lrm]

It is not clear what your management wants for the representation of the curves in the imported drawing.

 

To get a better feel for the shape I created short chords for several of the small mid-span splines (cyan curves) and then perpendicular bisectors (yellow).  If you want to approximated the curve by arcs you could use the intersections of these bisectors as arc center points as you have discussed.  However if you want to approximate the shape with a spline I would take the following approach.

To simplify the task I will assume the shape is symmetric.  The vertical cyan line is an approximate line of symmetry.

Before creating the spline create a horizontal line at the top center vertex as shown below.  The left end of the line will be the right most vertex of the spline and the left end of the line will be referenced to define the spline's tangency.  This will ensure that the curve when mirrored will not have an inflection point at the top and will produce a smooth curve.

 

 

Now create a spline using fit points that pass through points (going from left to right) on the spline segments.  After clicking the right most point at the the centerline enter "t" for tangency and click the right end of the horizontal line.  The result should look something like the following (magenta spline).

 

 

 

[Bill Tillman]

Thanks all. The designers on this project tell me that there are three different radiuses on each side of the centerline and it is symmetrical about the vertical centerline. But once again when I request they send me the work, the send me something that no matter how you look at it, it just doesn't add up. The day will soon come when I can force their hand but until then they are playing their cards close to the vest.

[eldon]

Is the geometry such a secret that they cannot just tell you??

 

Or is  it a test for you and CADTutor?

[Bill Tillman]

Eldon,

 

LOL! No, it's just a big bureaucracy. The detailers are not allowed to speak to outsiders and the PM's are clueless.

[BIGAL]

It may have started life as 3 arcs then been splines in some way or as in road designs as suggested some form of parabolic spiral added between the 3 arcs. They are not giving the formula used to create.

 

When construction  started this was same problem how to build these concrete shells with changing radius.

 

 

Edited August 19, 2021 by BIGAL

[Dadgad]

Presumably, if there are ONLY 3 different radii, then this should be able to be drawn with 3 arcs and mirrored across the centerline.

The drawing supplied seems to fly in the face of that revelation, assumption, or should I say allegation? 

 

It is worth noting that in lrm's treatment in his post, there do appear to be 3 strong contenders for arc centers, guessing that the fourth, at the bottom might

be the one which is unused? 

Edited August 19, 2021 by Dadgad

[BIGAL]

My $0.05

 

I did look at road vertical curve it takes into account, start point and grade at that point ie tangential, end point again grade at that point, I have  a paper copy of the formula looking for jpg for y=x something then can see if can replicate. But looking at shape maybe this, but note it has a R value which controls the 2 parabola curve answer. I think that is what has been used.

http://onlinepubs.trb.org/Onlinepubs/trr/1994/1445/1445-010.pdf

 

 

 

[eldon]

There may be only three different radiuses, but they are NOT tangential according to the drawing provided. Did they not tell you about the discontinuities?

 

Is it too much to hope that you will tell us when you know?

[hugha]

This adds nothing to the search for a solution to OP's difficulty (sorry) but it may come as a (or no) surprise that the Opera House sails are all derived from the surface of a single sphere:

 

https://www.sydneyoperahouse.com/our-story/sydney-opera-house-history/spherical-solution.html