Oval/ellipse centres

[brianhr]

I have some ovals and ellipses for template work and I need to establish the exact centre. Any ideas how to do this would be appreciated.

 

[Steve Maskery]

I take it these are male templates (ie you draw round them rather than inside them) with no axes marked on?

Hmm, tricky dicky.
How big are they? If small enough, Id lay them on graph paper and adjust the position until the squares are coverd by the same amount in all four quadrants. Then you can mark the NSEW positions on the edge using the graph paper as a guide. The you can draw the axes from those marks and you have your centre.

HTH
Steve

 

[9fingers]

This seems so basic I can only assume there is some difficulty I've not thought of?

Measure the major and minor axes and bisect then use dividers to check and refine if necessary.

Bob

 

[Yetty]

Here is one method to find the ellipse centre (school tech drawing was fun, but a long time ago so I think this is correct…).

1) Draw 2 parallel lines (AA, BB). Draw a 3rd line between their centres (ab).

2) Repeat above but in another position, giving lines (CC,DD) and (cd)

3) Where the line (ab) and (cd) overlap is the centre (O) - done!

I dare say there may be simple methods - this is the one I was taught… Do let us know how it goes!

and good luck!



PS Should you then want to find the major and minor axis, continue like this:

4) Draw a circle, centre (O) ensuring the radius is sufficient that the circle touches the ellipse in 4 places (P,P, Q, Q).

5) Draw a line between (PP) and also between (QQ). Draw a line between their centres (pq) and extend this line to touch the ellipse edges (MjMj). This is the eclipse major axis.

6) Minor axis (MiMi) is a perpendicular line from centre of major axis.

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[9fingers]

And you remembered that lot :shock:

I'm very impressed indeed!

Bob

 

[Steve Maskery]

=D> =D> =D> =D> =D>

 

[9fingers]

This has got me thinking (always dangerous!!)

The Op asked about ellipses and ovals. Are these one and the same?
Ellipses are defined by (x^2)/(a^2)+(y^2)/(b^2)=1
I think ellipses are conic sections but quite what is an oval?
Are all "squashed circles" in fact ellipses?

1 have 2 O levels and 2 A levels in maths but it was a long time ago!

Bob

 

[Steve Maskery]

Well I wold define "oval" as any closed curve that was longer than it is wide. A running track, for example, would be oval even though it is not elliptical.

I don't think that "oval" has a mathematical definition, it's a much more generic term.

S

 

[Shultzy]

From Wiki

In technical drawing an oval (from Latin ovum, 'egg') is a figure constructed from two pairs of arcs, with two different radii. The arcs are joined at a point, in which lines tangential to both joining arcs lie on the same line, thus making the joint smooth. Any point of an oval belongs to an arc with a constant radius (shorter or longer), whereas in an ellipse the radius is continuously changing.

 

[David C]

Joyce shows a carpenters Ellipse which I would assume is an oval, based on two different radii.

David C

 

[Mr Ed]

If you draw a rectangle around the oval so it touches at the four tangent points you can then easily measure off the minor and major axes. Where these cross could be described as the centre.

To determine the 2 foci of the ellipse you draw a circle from one corner, with an arc the length of the short side of the rectangle. You then draw a tangent to this arc, from the corner at the other end of this long side of the rectangle. The distance along this line to the tangent with the arc is the distance between the 2 focal points, which can then be plotted on the major axis equally either side of its centre point.

Not sure that makes sense written down, but I know what I think I mean...

Ed

 

[Steve Maskery]

The problem with that method, Ed, is knowing where the tangent points are. I mean, EXACTLY where the tangent points are. I think that's what he's trying to find in the first place, is it not?

S

 

[brianhr]

I'm beginning to regret I asked this question now. My little Oxford Dictionary describes an ellipse as a 'regular oval'. An oval is 'egg shaped'. Presumably, therefore an oval is an ellipse with irregular curves. So, what I want is to find the precise centre of an ellipse.

I already have the ellipse. I know how to draw one and can create one on up to A4 size with Corel Draw.

I will enjoy trying the various methods.

Thanks to everyone for their explanations and methods.

 

[Mr Ed]

The problem with that method, Ed, is knowing where the tangent points are. I mean, EXACTLY where the tangent points are. I think that's what he's trying to find in the first place, is it not?

S

Well to coin a phrase, if thats where you're going you don't want to start from here. I would start with a rectangle, within which I wanted the ellipse to fit and then draw it using the string and 2 pins method, based on foci determined as I described earlier. That way the tangents don't need to be found.

I was trying to reverse engineer the way I would draw an ellipse, but I agree its not straightforward. At least if you construct the ellipse you know what the setting out points were.

Ed

 

[xy mosian]

Surely the foci of the ellipse:-
Draw a rectangle Major axis by Minor axis.
Focus is where an arc, radius half major axis, centre where minor axis cuts the long side of the rectangle, cuts the major axis. Two of these of course.
Length of string, for two pins and pencil method, is length of major axis.

xy

 

[Kalimna]

Brianhr - Im sure you know this already, but in CorelDRAW you could create one any size you like, print off using a grid of A4 pages, then stick em all together afterwards on your 4x2m tabletop. I have done this with a panoramic-d photo previously.

Adam

 

[Benchwayze]

Gawd... The things that crop up on this forum!

I have forgotten the little geometry I was taught.

However, I always believed that an 'oval' (ellipse or otherwise) has a perimeter that is always 'curving' whereas a running track surely has straight sides, with a semi-circle at each end?

Or have I got it wrong again Dad?

John :lol: