Parabolic Curve

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Luiz FPP
MCAD Lurker

Parabolic Curve

Postby Luiz FPP » Wed Apr 20, 2005 7:36 pm

How can I make a parabolic curve in sketch?

How many ways can it's been makes?

sorry my english! :loco:

Thanks!
Luiz
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SeanDotson
Forum Admin

Postby SeanDotson » Wed Apr 20, 2005 7:50 pm

Extrude a cone then cut it with a plane. Project the cut edges.
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Luiz FPP
MCAD Lurker

Postby Luiz FPP » Wed Apr 20, 2005 7:52 pm

Thanks man.
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Luiz FPP
MCAD Lurker

Postby Luiz FPP » Wed Apr 20, 2005 8:15 pm

Another way:

I think thats is more precise to insert parameters.

Using SPLINE in 3 points... look the other 2 points confirm that spline meke a parabolic curve, or i'm wrong?

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SeanDotson
Forum Admin

Postby SeanDotson » Wed Apr 20, 2005 8:57 pm

Nope, you look right to me. Many ways to skin the cat.
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ziggykd
MCAD Lurker

Postby ziggykd » Thu Apr 21, 2005 1:03 am

Don't forget, you can also use ImportCoord.
David Sediles
Design Engineer
Applied Fiber Manufacturing
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Jeff Howard

Postby Jeff Howard » Thu Apr 21, 2005 5:17 am

Luiz FPP wrote:Using SPLINE in 3 points... look the other 2 points confirm that spline meke a parabolic curve, or i'm wrong?


I think the three point spline will usually be pretty close, but not exact (if it matters). A conic (parabola is a conic with rho = 0.5) is a degree 2 curve with three control vertices. The "three point" spline is a (probably, by default) degree 3 with five control vertices. The default control vertice positions and weights won't be correct to exactly duplicate the conic (if it's possible to get it "exact"). The deviation on your 2 x 1 curve will be about 0.013

You can get an associative curve by using a 3D sketch, Intersect vs the non-assoicative Project Cut Edges.
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Quinn Zander
Content Manager

Postby Quinn Zander » Thu Apr 21, 2005 5:37 am

Is there a way to define the conic section from the Parabola's equation?

Or, is there a way to define the cut plane on a cone so that it's angle of intersection (and cone taper) gives a resultant Parabola defined by a certain equation?
QBZ
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Russ Walker
MCAD Contributer

Postby Russ Walker » Thu Apr 21, 2005 4:44 pm

There is a very clever way to sketch a Parabola using the fact that the distance from any point on the curve to the focal point is identical to the distance from that same point to the directrix (sp?).

Charles Bliss has posted this a couple of times - take a look at this thread:

http://discussion.autodesk.com/thread.j ... ID=4501374
-Russ
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Tuko
MCAD Lurker

Postby Tuko » Sat Apr 23, 2005 4:21 pm

A couple of things about these curves.
1.- Cut a cone with a horizontall plane (parallel to the base). You will get a circle
2.- Cut a cone with a inclined plane. You will get a ellipse
3.- Cut a cone with a plane parallel to generatrix curve (side face of cone). You will get a parabola
4.- Cut a cone with a plane parallel to axis. You will get a hyperbola
This method provides you with the mathematically exact curves.
Using a spline gives you a proper solution, but not the exact one.
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Jeff Howard

Postby Jeff Howard » Sun Apr 24, 2005 3:53 pm

Jeff Howard wrote:I think the three point spline will usually be pretty close, but ....


I take it all back. Started out just trying to find a good way to create parametric construction geometry to do an intersection curve, but went on to look at created splines, deviations, etc. The results are very interesting. Going on what I've seen so far (would need to verify repeatability for any given situation, but would guess they will be) it appears that a three point spline is a very good way to go. The attachment is an IV6 part. Read the notes attached to various sketches.

Somewhere up the way it's said that a hyperbolic curve is the intersection of a cone and plane parallel to cone's axis (?). Looking at a description of conics on mathworld it says "intersects both nappes" which doesn't restrict the plane to being parallel to axis. Anyone know for sure?
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TGPE
MCAD Contributer

Postby TGPE » Tue Apr 26, 2005 9:01 pm

Jeff,

A hyperbola does intersect on both sides of the axis. If you look at a cone as being the surface generated by a line NOT parallel to an axis, and rotated about a point on that axis, you will see that the cone has a surface above and below the axis point. A plane parallel to the axis will cut the cone in both halves, and generate the classic dual-curve hyperbola.

These are the old, original definitions of geometric shapes from the Egyptians and Greeks, long before Newton started trying to define the whole world in calculas.

Tom
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Jeff Howard

Postby Jeff Howard » Wed Apr 27, 2005 3:06 am

TGPE wrote:... A plane parallel to the axis will cut the cone in both halves, and generate the classic dual-curve hyperbola.

These are the old, original definitions of geometric shapes from the Egyptians and Greeks, long before Newton started trying to define the whole world in calculas.


Thanks, Tom.

Can you tell me; is the curve created by a plane that is not parallel to the axis, but still intersects both nappes considered to be a hyperbola?

I'm still trying to catch up with the Egyptians and Greeks. I'm gonna have to leave Newton for the next life, I believe. :)

Addendum: Finally found a reference that seems to show the answer to my question.

http://xahlee.org/SpecialPlaneCurves_di ... tions.html

Y'all have a good 'un.
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TGPE
MCAD Contributer

Postby TGPE » Wed Apr 27, 2005 1:26 pm

Well, that'll teach me to shoot off my mouth. I'm glad you found your answer. That's a good site, with a lot more information than I had stored away in my high school memories. (That was in a previous MILLINNIUM!)

Is any of this helping you design your thing-a-ma-bob?

Tom
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Jeff Howard

Postby Jeff Howard » Wed Apr 27, 2005 11:22 pm

Uh, huh. Plotting orbits. 8~)

Actually, believe it or don't; I had never quite figured out how to constrain the geometry to create a cone to create a given parabola. Digging into that lead to other questions, ... , and now I'm more confused than ever.

:)

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