Please delete semicolons from links... :-)

thanks brian,

didn't notice that.

Hi Anthony,

> i was saying that i'm trying to find a definition of an ellipse
> that works equally well in real life and moi.

Well, an ellipse is sort of a mathematical concept - you can't actually create an actual 100% exact one in real life, stuff like the paper you use is not 100% flat but has little tiny bumps in it, if you draw it with a pen it won't have 0 width like an actual true ellipse, etc, etc...

Do you mean a method to make a sketch representation of an ellipse in real life just using a pencil and paper?

Some kinds of pencil and paper sketch methods can translate well into MoI when they involve stuff like drawing some auxilary shapes and finding intersections between them for where to start new lines at and stuff like that.

But an ellipse is a continuously changing curve, it's a lot different than drawing a line - methods that involve some kind of continuous change applied to the pencil won't really have a very good direct equivalent in MoI. I guess you could try using the Sketch command to do a brush stroke type approximation, but it will be really difficult to get a high quality approximation without wiggles in it - meanwhile if you use the actual ellipse or conic drawing tools you get a super precise ellipse.

I guess if you were really intent on simulating a pencil or pen draw method you could write a script that basically drew a curve that was plotted with a whole lot of control points in it. If you've seen some of the function curve plotting commands that Brian has posted earlier, that's how those were made. But I really can't see how that would be of any benefit for the case of an ellipse though, since with NURBS an ellipse does not have to be approximated it can be formed exactly instead which is what the ellipse and conic commands do.


One of the sketch based ways for drawing an ellipse is to put 2 pins in at the foci points and then have a length of string between them, then if you hold the string taut with a pencil and drag it, it will trace a sketch of an ellipse. That's again though the kind of continuously changing pencil stroke type operation that doesn't really translate very well into MoI as a construction technique.

If you wanted to define an ellipse mathematically instead of by some kind of "pencil sketching with apparatus" method then that would translate more directly into MoI's ellipse or conic drawing commands though...

Again though, I'm still not entirely sure if I completely understand what you're looking for. Just in general in the more abstract environment of CAD systems you can't necessarily use drawing methods that involve some kinds of physical processes like tension or friction with various moving parts and apparatus or stuff like that... But on the other hand with CAD you are more free to make exact mathematically defined stuff more directly instead of trying to simulate them with physical processes....

- Michael

hi michael,

"Do you mean a method to make a sketch representation of an ellipse in real life just using a pencil and paper?" yes that's what i mean

"Some kinds of pencil and paper sketch methods can translate well into MoI when they involve stuff like drawing some auxilary shapes and finding intersections between them for where to start new lines at and stuff like that." yes this is what i'm trying to do at the moment

i have been able to add points and run a spline through them. i wasn't too fond of that method however. when you make a solid, using this method, it comes out all lumpy.

as i mentioned, moi is working fine. the ellipse tools you have are great. brian already made a script to solve the main problem, using the moi conic tool. i'm just curious about trying to see if there is a simple way to define and draw an ellipse in real life and with moi. and yes by real life i mean make an approximate sketch with paper and some sort of drafting tools. what i'm really curious about is how a draftsmen would have went about this in the 1950's and if that method would work in moi. again, only out of curiosity, not to implement for daily use in moi.

i have found several sketching methods for real life, and of course many equations to calculate points. i'm most curious if you can use lines and arcs to approximate an ellipse, possibly the five center method.

please don't spend any more time on this. i know you have more important things to do. i will figure it out eventually. you helped me find the center of an ellipse created with the moi conic section tool. brian helped me create the whole ellipse using the conic section tool and mirror/rotate. with that added information, i could confirm the ellipse created with the conic section tool to that of one created with the ellipse tool. now i'm just learning.

Hi Anthony,

> and yes by real life i mean make an approximate sketch with paper
> and some sort of drafting tools. what i'm really curious about is how
> a draftsmen would have went about this in the 1950's and if that
> method would work in moi. again, only out of curiosity, not to
> implement for daily use in moi.

I guess check out "The Draftsman's method" that's described here:
http://www.uwgb.edu/dutchs/MATHALGO/Ellipses.HTM

Seems to be an approximation based on sampling several points and then I guess connecting them with line segments - you can repeat the same steps in MoI if you want, but the result will be a polyline approximation of an ellipse and the approximation will be kind of rough as far as CAD accuracy goes.

An approximated sketch on paper is a lot different kind of a thing than actual geometry that you then want to use directly as a basis for further 3D construction in MoI.


> i have found several sketching methods for real life, and of
> course many equations to calculate points. i'm most curious
> if you can use lines and arcs to approximate an ellipse, possibly
> the five center method.

The five center method is described there as well, I was not familiar with it. Since it involves drawing circles, lines, and arcs and finding intersection points I think you should be able to repeat the process in MoI. The result will however be again by CAD standards a pretty rough approximation, probably without a known error bound, and will again be a segmented series of curves rather than just one smooth curve.

It would not be desirable to use a segmented approximation like that as the generator for further 3D shapes, because extrusions and stuff like that which you construct off of it will inherit the segmentation and inaccuracies as well.


So although you could use one of those old drafting methods for constructing some approximation of an ellipse in MoI, it would be a kind of pointless exercise since it would not work well to use the result for much of anything after that.

Meanwhile using one of the ellipse tools generates a mathematically exact ellipse that's made up of just a single totally smooth segment, with a lot less effort involved as well.

So I do not see how one of those methods would be very practical for use in MoI.

- Michael

hi michael,

i agree with you 100%. i have narrowed this down to the draftsmen method, that you mentioned, as well. i'll let you know if i get this to work out and post a pic of it. i have ruled out the other methods mentioned.

if the draftsmen method works out, and you intended to have an elliptical leading edge, you should be able to define the ellipse by its length and width. the moi ellipse tool could easily generate the ellipse with that info. i just need to see if i can make that ellipse with the draftsmen method.

thanks for the suggestions

Hi Anthony,

I appreciate you're not UK based, however perhaps this might be of passing interest to someone.

The London Science Museum's permanent Mathematics exhibition http://www.sciencemuseum.org.uk/visitmuseum/galleries/mathematics.aspx has a collection of truly beautiful mechanical drawing instruments dating back 190+ years. I highly recommend a visit to anyone with even a passing interest in the history of technical drawing. My recent visit really put into perspective for me just how far we've come in 200 years. Actually, what really did it, and still makes the hairs on the back of my neck stand on end just thinking about it, was being able to touch Stephenson's 'Rocket', built in 1829 in the same room as look inside the actual Apollo 10 capsule!

Back to Earth now, here's a couple of London Science Museum links showing instruments for drawing ellipses. One is an ellipsograph from 1817, the other a trammel from 1876.
http://www.sciencemuseum.org.uk/objects/mathematics/1909-191.aspx
http://www.sciencemuseum.org.uk/images/I032/10302774.aspx

There's also quite a nice animation of a trammel here:
http://en.wikipedia.org/wiki/Trammel_of_Archimedes


Cheers,
Hamish

hi hamish,

i didn't know trammel's really existed, really neat:

http://www.sciencemuseum.org.uk/objects/mathematics/1876-662.aspx

this tool is awesome too:

http://www.sciencemuseum.org.uk/objects/mathematics/1909-191.aspx

i remember playing with these as a kid:

http://www.sciencemuseum.org.uk/objects/mathematics/1976-61.aspx

thanks for the links, awesome.

hi,

here is an example of the draftmen's method. the results are pretty typical of what I have gotten trying some of the other methods. they just don't seem to work. i could be doing something wrong. but it seems the error is quite large. if i have done everything right, that would leave some of the mechanical drawing tools in the previous link as the only way to draw an ellipse accurately in real life. i imagine you could still define the ellipse by its height and width and that definition could be used by the mechanical tools and cad programs such as moi.

Hi Anthony, from what I can see that you have drawn there, it looks like you are not using "The Draftsman's Method" as described in that previous link (http://www.uwgb.edu/dutchs/MATHALGO/Ellipses.HTM) but rather the "Five-Center Method", is that correct?

The page there mentions the following:


So yes as far as I can tell that method produces a pretty rough approximation which gets worse as the width to height ratio increases.

An ellipse is a continuously changing curve and you simply cannot make a very good approximation of a rather elongated one using only a couple of arc pieces...

- Michael

Just to follow up on this and out of pure curiosity I made an ellipse in NX and simplified it, NX has a tool which can simplify splines into true lines and arcs to the closest approximation.
Anyway, NX simplified a 100mm x 50mm ellipse into 28 arcs.

-

thanks guys, i would have to agree. the pictures are of the draftmen's method. however i tried a bunch of methods and nothing seemed to come close. in their examples they show good agreement. but with the ellipse i have, i don't get good agreement.

the example ellipse i'm working with has the following characteristics:

the height from center is 9.5313263 mm, the width from center is 3.5668193 mm, the foci from center is 8.8387771 mm, and the rho value of the conic section the ellipse started from is 0.4632322 mm.

at this point i'm assuming that if it was the 1950's and i wanted an ellipse with a certain height and width, it would be generated with a special mechanical drawing tool, as shown in previous links.