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

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Forum topic by PRGDesigns posted 01-18-2013 03:58 AM 2518 views 1 time favorited 34 replies Add to Favorites Watch
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PRGDesigns

207 posts in 978 days


01-18-2013 03:58 AM

Topic tags/keywords: resource question miter saw joining traditional

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.

-- They call me Mr. Silly


34 replies so far

View SnowyRiver's profile

SnowyRiver

51450 posts in 2145 days


#1 posted 01-18-2013 04:31 AM

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

-- Wayne - Plymouth MN

View MonteCristo's profile

MonteCristo

2097 posts in 853 days


#2 posted 01-18-2013 04:47 AM

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 . . .

-- Dwight - "Free legal advice available - contact Dewey, Cheetam & Howe""

View Jorge G.'s profile

Jorge G.

1526 posts in 1140 days


#3 posted 01-18-2013 04:51 AM

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.

-- To surrender a dream leaves life as it is — and not as it could be.

View Mark Shymanski's profile

Mark Shymanski

5113 posts in 2378 days


#4 posted 01-18-2013 05:33 AM

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

-- "Checking for square? What madness is this! The cabinet is square because I will it to be so!" Jeremy Greiner LJ Topic#20953 2011 Feb 2

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shipwright

5000 posts in 1463 days


#5 posted 01-18-2013 06:04 AM

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.

-- Paul M ..............If God wanted us to have fiberglass boats he would have given us fiberglass trees. http://prmdesigns.com/

View RonInOhio's profile

RonInOhio

720 posts in 1529 days


#6 posted 01-18-2013 08:28 AM

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.

View FirehouseWoodworking's profile

FirehouseWoodworking

625 posts in 1938 days


#7 posted 01-18-2013 09:04 AM

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!

-- Dave; Lansing, Kansas

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RonInOhio

720 posts in 1529 days


#8 posted 01-18-2013 02:34 PM

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))

View Underdog's profile

Underdog

545 posts in 700 days


#9 posted 01-18-2013 02:50 PM

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

1364 posts in 1034 days


#10 posted 01-18-2013 02:57 PM

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

-- - The mightiest oak in the forest is just a little nut that held its ground.

View Underdog's profile

Underdog

545 posts in 700 days


#11 posted 01-18-2013 02:58 PM

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….

View CharlieM1958's profile

CharlieM1958

15702 posts in 2883 days


#12 posted 01-18-2013 03:21 PM

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”?

-- Charlie M. "Woodworking - patience = firewood"

View junebug's profile

junebug

82 posts in 1069 days


#13 posted 01-18-2013 03:21 PM

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

View helluvawreck's profile

helluvawreck

15893 posts in 1532 days


#14 posted 01-18-2013 04:54 PM

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

-- If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away. Henry David Thoreau

View helluvawreck's profile

helluvawreck

15893 posts in 1532 days


#15 posted 01-18-2013 04:58 PM

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

-- If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away. Henry David Thoreau

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