# Anyone know how to divide an ellipse into 24 equal chords? Solution found - subject closed



## PRGDesigns (Jan 25, 2012)

I have been seeking out a formula or method to accurately and repeatedly divide an ellipse into multiple equal chords. My current design needs to be divided into 24 equal chords. I have AutoCAD and have tried the array command w/o success. Will Aspire or V-Carve do this instead? Is there a mathematical formula for doing this? Any help is always appreciated. Thanks in advance for any consideration you can give this matter.


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## SnowyRiver (Nov 14, 2008)

I would try seaching on Google. There is a lot of discussion there regarding this.


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## MonteCristo (May 29, 2012)

I have not heard of any formula for this sort of thing (my background is pure math). The ellipse is a much more difficult beast than a circle so my guess is that it's not an easy task, especially given the fact that the eccentricity of an ellipse is not a fixed parameter.

Symmetry would demand that there be 6 chords per quarter of the ellipse. I would then use trial and error to dial that in. It shouldn't take long to get pretty darn close. If you're trying to do a variety of ellipses, then this obviously wouldn't be ideal . . .


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## JGM0658 (Aug 16, 2011)

Listen to Montecristo. I tried the formulas for drawing an ellipse and it went over my head. Then again you might be smarter than me and can easily understand it, if you do, then get the formula and divide the result by 24.


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## FatherHooligan (Mar 27, 2008)

Would drawing it out in Sketch Up help you to empirically get your chord lengths?


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## shipwright (Sep 27, 2010)

Why do you need it divided in equal chords? 
I ask because I've been in a situation where I wanted to do that. I decided instead to divide it to suit my eye which turned out to be equal angles rather than equal chords.
Maybe your project is similar. This was my project.

Just a thought.


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## RonInOhio (Jul 23, 2010)

I tried google and most of what I found involved a lot of geometric, trig, and calculus gibberish. Not something I wanted to try to decipher.

I also saw where a similar discussion was going on in a Turbo-CAd forum.

Then I found this link. Might be what you are looking for.

CADpower Tip of the Week

sorry.


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## FirehouseWoodworking (Jun 9, 2009)

I would draw it out full scale on a piece of scrap luan or stiff cardboard. Carefully cut the ellipse out. Then take a dressmaker's tape measure (very flexible) and carefully measure the circumference.

Divide that measurement by 24 and you should have it. Might need to do just a little tweeking, depending on how carefully you measured. Good luck.

Cheers!


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## RonInOhio (Jul 23, 2010)

Wheres Ptolemy or Hipparchus when you need them ?

Found the following Lisp routine,(below the link) that you may want to try. Supposedly it works. User enters the arc, and number of segments.

source: CADTutor.net

(defun c:Segs (/ ENT EPAR I INC PTS UFLAG)
(vl-load-com) ; Lee Mac ~ 29.01.10

(setq *doc (cond (*doc) ((vla-get-ActiveDocument (vlax-get-acad-object)))) 
*segs (cond (*segs) (10)))

(while
(progn
(setq ent (car (entsel)))

(cond ( (eq 'ENAME (type ent))

(if (vl-catch-all-error-p
(setq ePar
(vl-catch-all-apply
(function vlax-curve-getEndParam) (list ent))))

(princ "\n * Invalid Object *")
(progn
(initget 6)
(setq *segs (cond ((getint (strcat "\nSpecify Number of Segments <" 
(itoa *segs) "> : "))) (*segs)))

(vla-StartUndoMark *doc)

(setq inc (/ (vlax-curve-getDistatParam ent ePar) (float *segs)) i -1)

(repeat (1+ *segs)
(setq pts (cons (vlax-curve-getPointatDist ent
(* (setq i (1+ i)) inc)) pts)))

(entmake (append (list (cons 0 "LWPOLYLINE")
(cons 100 "AcDbEntity")
(cons 100 "AcDbPolyline")
(cons 90 (length pts))
(cons 70 0))
(mapcar (function (lambda (a) (cons 10 a))) pts)))
(entdel ent) 
(vla-EndUndoMark *doc)))))))
(princ))


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## Underdog (Oct 29, 2012)

My question is how in the world you can have equal chords in a construct that has an increasing/decreasing radius around the entire circumference?


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## BinghamtonEd (Nov 30, 2011)

I like Dave's idea of using the dressmaker's tape. It's simple, foolproof, and takes out all the hard math.


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## Underdog (Oct 29, 2012)

As for drawing an ellipse, the simplest way to think of it is to think of a moving pencil drawn tight against a loop of string placed around two nails. Keep the pencil tight as you move it around the two nails, and you soon have an ellipse.

The loop of string is a constant length, and the distance between the nails is a constant length. From that you can deduce that as one radius (distance from the nail to the pencil) increases, the other decreases by the same amount.

So, you could plot 48 points around the nails using this method, then draw three point arcs around that, and have your 24 chords….


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## CharlieM1958 (Nov 7, 2006)

I'm confused. A chord is a straight line connecting two points on a curve. So when you say "equal chords" do you mean you want 24 lines of equal length? Or are you just trying to divide an ellipse into 24 "pie wedges"?


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## junebug (Oct 26, 2011)

If in fact you are just looking to divide the ellipse into 24 equal lengths, the divide command in autocad will take care of that


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## helluvawreck (Jul 21, 2010)

If you want 24 equal cords around the circumference couldn't you simply draw the ellipse that you want to use along with it's major and minor diameters and then simply take a pair of dividers and go to work until you got the points set at the right distance where the dividers will do the job for you. As a matter of fact the two diameters separate the circumference into four equal curves so what you want is six equal chords on each section. With a pair of dividers it shouldn't take long at all to find the length that works. Or maybe I'm missing something in my thinking.

helluvawreck aka Charles
http://woodworkingexpo.wordpress.com


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## helluvawreck (Jul 21, 2010)

Try Turbocad it's very inexpensive and I have used it for years. It's not at all difficult to learn.

helluvawreck aka Charles
http://woodworkingexpo.wordpress.com


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## Underdog (Oct 29, 2012)

One should also differentiate between a true ellipse, and an oval. Do you want a true ellipse, or an oval?


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## REO (Sep 20, 2012)

you have a difficult task. Roninohio will be the closest to finding it w/ autocad. the lisp routine will give you equal Arc lengths that may be close enough. the divider method is a tried and true method that most certainly will give you equal chords and not Arc lengths or degree arcs.


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## DS (Oct 10, 2011)

I did this once… I stored the formula on my hdd… one sec.









Ok, I found this from before…. I suppose you want me to interperet now…

That will take another minute.

If I remember, I had to use a spreadsheet to define how many chords to calculate, then I plotted them manually and then cut it on a cnc machine. I was a bit worried that it would come out properly, but it worked out sweet. 
If I can remember the job name I can probably find the CAD notes and help you out some more.


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## Underdog (Oct 29, 2012)

So why did you need the ellipse divided into chords?


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## DS (Oct 10, 2011)

Found it. It was on a conference table.

Just FYI, for those unfamiliar with it, an elipse is very different from an oval. You decide the chord resolution and each chord makes a different radius based on a formula. The more chords, the more precise the elipse.


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## DS (Oct 10, 2011)

Okay, I started with the X, Y graph and placed my points for each chord. Then I simply used a 3 point arc to connect subsequent points and came up with the elipse.

This is the plot that I used to make the conference table in the previous post.

Once I had one quadrant I flipped and mirrored it to get the other three.


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## PRGDesigns (Jan 25, 2012)

I am cutting an ellipse on a CNC with features around the perimeter at 24 equal locations, which appears to be similar to what DS251 did, and wanted to be able to offset the features on a subsequent ellipse, similar to a scroll saw basket, except with a CNC, which requires more precision. I wanted to be able to design any size ellipse (not an oval) and various features at precise locations around said ellipse (not an oval). Thanks to everyone for their time and energy into solving this mathematical riddle!


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## oldnovice (Mar 7, 2009)

*Am I missing something?* In post #22, those chords do not look equal to me!


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## junebug (Oct 26, 2011)

so, if I'm understanding your description, you want 25 evenly spaced "features" around the circumference of the ellipse, correct?


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## DS (Oct 10, 2011)

All I did was the inverse of what he is asking for. Look at the intervals along the Y (Horizontal) axis line-they are all equal. Maybe he's looking for something different, but This is how I did it and it worked wonderfully.

Any point along the elipse can be figured for, but I used whole numbers along the Y axis for my determinations. I suppose you could go back and find equal spacing along the elipse and refigure at those points. It wasn't important to what I was doing at the time, though.

I was looking around for the photos of this finished conference table, but haven't found it so far. The edge was a 1 1/2" thick knife edge in Solid Maple, which looked stunning. I was able to offset the elipse ( a series of radii at that point) and cut the solid Maple in eight segments around the perifery.


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## PRGDesigns (Jan 25, 2012)

I was unable to use the "divide" command in my AutoCAD to divide an ellipse. It could be my version or lack of intelligence. My AutoCAD would also not calculate the circumference of the ellipse so I am assuming I am doing something wrong along with the divide command, or it could be simply that I don't know what I am looking at if it is doing it. Wouldn't be the first time.

I did find this on e-How:

An ellipse is a type of closed geometric curve that is made by intersecting a cone with a plane (a flat surface). Calculating the exact circumference of an ellipse involves calculus (advanced mathematics). However, when the ellipse's minor axis (the height) is 1/2 the length of the major axis (the length), it's possible to create a good approximation of an ellipse's circumference, c, using the formula c=a/2*square root(93.2886751), where "a" is the arc length.

I also found this:

http://www.csgnetwork.com/circumellipse.html

Knowing the circumference would also allow me to divide the ellipse into 24 equal parts, or 23 equal parts or whatever combination I may want for any given project that has an ellipse.

Again, I am trying cut an elliptical basket with indentations evenly spaced all the way around the perimeter on both the inside and outside of the basket. The basket would be composed of layers. The next layer would be an inverse of the first layer so that it appears to be woven. There are several scroll saw patterns out there that do something similar, except they are not as precise as I would want for the CNC. I also want to replicate this process using different size and/or shaped ellipses.

Thanks again for all of the suggestions!


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## junebug (Oct 26, 2011)

regarding the "divide" command, are you sure it didnt work? Make sure your "node" osnap is on and then try again.

With regards to the circumference issue, use the "list" command on the ellipse. Should tell you the circumference.

If you'd prefer, I can do that for you if you tell me the width and height of the ellipse.


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## DavidBethune (Feb 9, 2009)

Here you go.. If you use CorelDraw you can use this MACRO
http://www.corelvba.com/index.php?pages=cad_1
It will do exactly what you want to do..
Then you can simply export the file in whatever format you want to drag it into CAD


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## PRGDesigns (Jan 25, 2012)

I re-tried "junebug's" method and added "nodes" in my osnap command and the division points showed up perfectly. Thank you very much. It worked perfectly! Score another one for LJ!

I am unsure how to do the "list" command. I typed in "list" and selected the ellipse, but lost my cursor and had to exit the drawing. I must have hit the wrong key or something.


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## Triumph1 (Dec 20, 2009)

Isn't there a "divide" command in AutoCad. I know I used it on a straight line. I wish I would have seen these before I left work. Maybe something you cold do if you tun it into a polyline.


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## Cabman (Jul 4, 2012)

Ok if you have autucad use the divide command divide into 24 parts it should drop nodes around the circumference of the ellipse. Or use the list command to find the circumference length and divide by 24 then use the measure command on the ellplse


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## LepelstatCrafts (Jan 16, 2011)

Now here is an idea and I don't know if you can approach this problem the same way but, why not find the center of the ellipse, draw a circle around the center point, then divide the circle into 24 equal parts. Once the lines are laid down, delete out the circle. This would allow you to have 24 equal angled sections. If you want the area within the wedges to be the same and have the angles all the same, that is impossible. If you want the area of each section to be the same and can accept that the angles of the wedges are different, that is another story all together. I think we just don't have enough information to create the proper solution for you.


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## RonInOhio (Jul 23, 2010)

Maybe this thread should be edited to show its solved. Good example for future cad problems involving
ellipses.


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## PRGDesigns (Jan 25, 2012)

Edited per RoniOhoio's suggestion. Thanks again for everyone's assistance in this matter.


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