Question regarding MoI's conic section abilities  1-20  21-32

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 From:  Unknown user
4835.1 
Hi,

I just learned about this tool from burrman. I really like it but am having a problem. I have a model where I fit a conic section in. It appears to be an ellipse based on the rho value shown as you are creating the conic section. However, after the creation of the curve I can't figure out how to see the rho value. Also, I can't determine where the center of the ellipse would be. I would like to recreate the conic section as an ellipse for other purposes. The tool is great as is, I just need to figure out more about the curve it creates after the fact. Does anyone know how I might go about this. I tried several things, but am stuck.

Thanks,

Anthony
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 From:  BurrMan
4835.2 In reply to 4835.1 
Hi Anthony,
I dont think there is a property set on it to retrieve, but here is some discussion on it from the past:

http://moi3d.com/forum/lmessages.php?webtag=MOI&msg=3042.13

Also, the conic command will accept a "Negative Value!" for going the other way on an existing conic. You may be much better at the math to get a perfect ellipses out of an existing conic as opposed to some type of parab/hyperparab or something...

Interestingly enough, if you do a negative rho on an existing conic, then turn on control points for both, you get a triangle!!
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 From:  bemfarmer
4835.3 
"The parameter rho is a measure of the eccentricity of the curve and is defined as the ratio of two distances as shown in the Figure..."




rho is also a measure (from 0 to 1), of the angle of a plane intersecting a cone...

EDITED: 6 Jan 2012 by BEMFARMER

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 From:  Unknown user
4835.4 In reply to 4835.3 
Thanks guys. I'll study this info some more. I'm still a little confused, but I think you've answered my question.
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 From:  BurrMan
4835.5 In reply to 4835.4 
I'm stuck on the center of a true ellipses also..
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 From:  Michael Gibson
4835.6 In reply to 4835.1 
Hi Anthony,

> It appears to be an ellipse based on the rho value shown as
> you are creating the conic section. However, after the creation
> of the curve I can't figure out how to see the rho value.

The rho values are something that's only used by the Conic command itself as parameter for building the curve - once the Conic command has ended then you won't see rho value after that.


> Also, I can't determine where the center of the ellipse would be.

If you build an ellipse segment with the conic tool then there should be an object snap available to snap on to at the ellipse's center point. Make sure you have "Object Snap" enabled in the bottom toolbar then you can draw a point and place it there.

So for example if you've built an ellipse segment conic like this:



If you then go to draw something after that, if you have object snaps enabled you will see this little target marker where the ellipse center is at:



And then if you move the mouse there the "Cen" object snap will kick in and snap to the ellipse's center point:



- Michael

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 From:  Michael Gibson
4835.7 In reply to 4835.5 
Hi Burr,

> I'm stuck on the center of a true ellipses also..

Exact ellipse curves (including both regular fully closed ones and also ones that are just partial segments of an ellipse like the conic command will build) should be getting a center object snap point set up for them - do you have one where that's not happening?

One thing to note is that if the curve is a kind of small piece of a much larger ellipse then the ellipse center can be a fair ways away from the curve.

- Michael
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 From:  BurrMan
4835.8 In reply to 4835.7 
""""""do you have one where that's not happening?""""""

It could be a misunderstanding on my part. Once the rho value extends to .5 or greater, I lose the snap.

.49, I find it a bit down.
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 From:  Unknown user
4835.9 In reply to 4835.8 
thanks michael,

that helped a lot. is there a way to get the width of the ellipse. i'm trying to use the center snap you pointed out to recreate an ellipse. moreover, i'm trying to confirm the geo coming out of the moi conic section tool. you have an ellipse tool in moi, so i was trying to create an ellipse with that tool and see if it agrees with the output from the conic section tool. of course the problem is not enough info about what is coming out of the conic section tool to do this.

i'm trying to use stevens' method to create an ellipse. i've been able to do that, just can't match the dimensions yet. ultimately, what brian posted is the best final solution to the main problem. i'm just trying to learn and check things out.

got a big headache at the moment, lol, literally.
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 From:  Michael Gibson
4835.10 In reply to 4835.8 
Hi Burr,

> It could be a misunderstanding on my part. Once the rho
> value extends to .5 or greater, I lose the snap.

The way rho values work is that a rho value of 0.5 creates a segment of a parabola curve, not an ellipse.

For greater than 0.5 and less than 1, it's a segment of a hyperbola.

It's only when the Rho value is less than 0.5 that it will generate an ellipse conic section.

If you generate a parabola or hyperbola conic section, those do not get center snap points on them currently, only ellipse and circle conics get that.

- Michael
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 From:  BurrMan
4835.11 In reply to 4835.10 
I knew it was something like that...:o
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 From:  Michael Gibson
4835.12 In reply to 4835.9 
Hi Anthony,

> that helped a lot. as with burrman, i may be finding it is a
> bit off. not sure yet. is there a way to get the width of the
> ellipse.

Currently there is no way to get the full ellipse major or minor axis width from an ellipse segment.


> i'm trying to use the center snap you pointed out to recreate an ellipse.

What are you using for the orientation of the ellipse? The ellipse segments that are created by the conic command are not restricted to have their major and minor axis only aligned to the world x/y axis directions, the ellipse that it is a part of can be rotated around.

So you've got an orientation and also size in the x and y axis directions that you would need to all be specifying in order to manually draw a new ellipse on top of the existing ellipse segment.

If you are creating en ellipse that shares the same center point but has a different orientation or major/minor axis sizes then that's why they would not match.


> i guess what i'm trying to do right now is confirm the geo
> coming out of the moi conic section tool.

If it has a center point snap then it means that internally MoI has analyzed it and confirmed it to be an exact ellipse segment already...

If you need more confirmation than that, you maybe need to take it into some more specialized software that might give you more detailed mathematical data about the ellipse segment than what MoI is currently set up to show in its UI.

- Michael
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 From:  Unknown user
4835.13 In reply to 4835.12 
thanks michael,

i think you've explained it. the rotated axis may be the missing link. i can use the center point and eyeball the width and overlay an ellipse. however, it doesn't agree with stevens' method. the rotated axis aspect, may be why. having the width and the center, in the future, may be a useful thing. however, i think my curiosity is satisfied at this point.

thanks
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 From:  bemfarmer
4835.14 
Notes on Conic command, rho, ellipses, and eccentricity.







For a given ellipse, there is one value for the eccentricity.

For a given ellipse, there can be many rho values.

The conic involves two tangent lines.
The tangent lines do not need to be symmetric.

The conic is determined by 3 points plus rho, or 4 points. (start, end, apex, through or rho).

rho = vertex distance from chord center / apex distance from chord center.

rho is rounded off, in MoI, to two decimals. (EDIT Incorrect, see next post) :-)

rho can be calculated by using custom distance.

The maximum positive rho value is 1 for a conic.
For a hyperbola, 0.5 < rho <= 1.
For a parabola, rho = 0.5.
For an ellipse, rho < 0.5.

A negative rho has the through point opposite the chord center, from the apex point.
This is a "negative" distance. rho < 0. (examples: rho = -.3, -.6, -1.2, -4.5, -52.0 ...)

When MoI does a conic ellipse, the center point of the ellipse is determined, and can be revealed by drawing a line near to it.
Draw a line from the apex, through the chord center point, to where the center pops up.
Create a line segment from the conic intercept point to the center.
Rotate it 180 degrees, to find the opposite point on the ellipse.
Run conic again, at negative rho, using the opposite point as the through point, to create the whole ellipse.

(rho is also a measure from 0 to 1 of the angle of a plane through a right cone.)

To find the focus, and eccentricity, create a line the length of half the major axis, and rotate it
to the major axis. (from the minor vertex). Eccentricity = f/a.

(So MoI indirectly determines the eccentricity and focus.)

EDITED: 7 Jan 2012 by BEMFARMER

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 From:  Michael Gibson
4835.15 In reply to 4835.14 
Hi Brian, great notes there - just one clarification on this part:

> rho is rounded off, in MoI, to two decimals.

It's really just the display in the edit field that is rounded to 2 decimals - you can type in a number into that field with as many decimal places as you want and whatever you type will get set as the actual rho value for constructing the conic.

You can also adjust how many decimal places are displayed in edit fields by the setting under Options > General > "Decimal display" , but again that only controls what is displayed, if you type in more decimals than that it will use what you type in any edit field.

- Michael
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 From:  Unknown user
4835.16 
thanks brian,

that information allowed me to create a whole ellipse which was one of my goals. i used the conic tool to make the first arc as usual. then i mirrored/rotated the arc. then based on what you said i found you could use the conic tool to draw the remaining arc by simply using the ends of the first arc, the tan/tan point of the first arc, and the apex of the mirrored/rotated arc. i didn't need to enter a rho value to do that step. so two simple additional steps to get a full ellipse. you can then confirm the ellipse by using the center width and height.

the only thing i still can't figure out is what information one would need to duplicate the ellipse manually. without any nice computer tools like an ellipse button or a conic section button. i have the center, width, height, and i calculated the foci, and calculate the rho value. but none of that really helped me duplicate the ellipse manually. i keep trying stevens' method but can't get the same ellipse with that method. i guess i'm just curious that if i was a naca engineer back in the day, what info would i need to recreate an elliptical leading edge. i'm also puzzled as to why they define the leading edge with a circle if they were putting ellipses in there (i'll probably never know the answer to that question).

i guess i'm wondering if i could add some sort of simple information into the naca definition that could be used to put an ellipse in manually. i know we don't need it for your script. but i'm just wondering about it in general.

update; i found some equations that could be used. that would satisfy my question about how you could define this, in the old days, without too much difficulty. now the only thing i'm curious about is if i can somehow re-create the ellipse, in moi, without using the ellipse or conic section tool. mainly out of morbid curiosity.
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 From:  Michael Gibson
4835.17 In reply to 4835.16 
Hi Anthony,

> now the only thing i'm curious about is if i can somehow
> re-create the ellipse, in moi, without using the ellipse or
> conic section tool. mainly out of morbid curiosity.

Which tools would you want to use instead?

For a NURBS curve to represent an exact conic section curve involves having not just control point positions of the curve set but also particular weight values for each control point set as well, which the ellipse and conic commands will do.

You can't get a conic section (other than a parabola) by just placing curve x,y,z control points without having weights also set.

If you only want an approximated ellipse rather than an 100% mathematically precise one then that's another matter.

See here for more information on the properties of NURBS curves:
http://en.wikipedia.org/wiki/Non-uniform_rational_B-spline
http://www.mactech.com/articles/develop/issue_25/schneider.html

See the parts that describe what a "rational" curve for more information on weights and what NURBS configurations can yield different conic section curves.

- Michael
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 From:  BurrMan
4835.18 In reply to 4835.16 
If you could start with a simple arc and know the minor axis of the ellipse, you could just rotate the arc by a distance of the minor axis in an opposing plane, then the ellipse would appear in plane... Also, a 1d scale of the arc would produce the same. (The rotated arc would need to be flattened to the desired plane.
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 From:  Michael Gibson
4835.19 In reply to 4835.18 
Hi Burr, yup a circle is a conic section curve too, and doing a one directional scale of the circle does produce an ellipse from that.

I'm not sure if drawing a circle was allowed for what Anthony had in mind or not, I'm not really quite sure what he was looking for in creating an ellipse without using the ellipse or conic tools, I thought maybe he meant by making a curve by just placing control points directly?

Anthony - maybe instead of saying which tools you don't want to use to make an ellipse, maybe you could describe which other tools you did want to use to create it?

But of course it's by far the easiest to use the ellipse commands to build an ellipse, that's what they are there for... So I am kind of puzzled by what you're trying to accomplish there.

- Michael
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 From:  Unknown user
4835.20 In reply to 4835.19 
hey michael,

i replied to your post this morning but i notice its not here now. i was saying that i'm trying to find a definition of an ellipse that works equally well in real life and moi. nothing is wrong with moi, i love the program and the tools to make a conic section and ellipse work great. i'm just curious about defining the ellipse for both real life and moi. the reason being the airfoil i'm working with has the leading edge defined with a circle. however, it seems an ellipse is really what is in there (at least for the data set i am referencing right now). so it made me wonder, if i wanted to define an ellipse, how would i go about that. i recently found something that might help. you can define concentric circles about each foci and where they intersect is the points on the ellipse. this would fit in with the rest of the airfoil definition, which consists of points that you run a spline through. so if you add some points at the leading edge, you could run a spline through those as well. which i believe is what you were talking about before.

i was trying to use the stevens' method, however, haven't had luck with that. the premise there would be to use the line and arc tools to draw the ellipse. i'm open to how to define it. any tool would be fine, so long as you can duplicate the method in real life. back when these airfoils were created, it was done on drafting tables with slide rules and things. no calculators or computers.

hope that clears up any confusion i caused you. her are some links to interesting info about the topic:

http://demonstrations.wolfram.com/CirclesAndEllipses/ - interesting way to graphically find x,y points along the ellipse

http://en.wikipedia.org/wiki/Hypotrochoid - interesting and simple way to draw an ellipse, also simple equations to use

http://en.wikipedia.org/wiki/Ellipse - has some equations you can use to calculate points easily, i like the polar coordinates in particular
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