# Request for 4-point and 5-point Conics, Super ellipses

Would it be possible to add 4-point and 5-point conic creation to V6 ?

The 4-point conic uses four points and a tangent line at either the first or last point.
The 5-point conic generates a conic through five points, no tangent lines are used. An option for this would be to generate just the curve through the points or to generate the entire ellipse if possible.

I have used both types of conics very extensively in CATIA and it would be nice to have them available in Rhino as well.

A super ellipse generator would be nice as well.

Hi Chris,

Have you tried the Conic command? Does this help?

â€“ Dale

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Dale,
I havenâ€™t been able to find anything other than the traditional 3-point conic.

Chris

Iâ€™ve used the Rhino Conic function a lot, both at home and when I worked for Boeing. The other 2 conic versions can make for some very smooth curves when your input is limited such as coming off of the top of the center window post of an airplane or trying to figure out a flared fender for an antique looking car.

Chris

Hi Chris - if possible, could you post some examples of these curves and the input used?

thanks,

-Pascal

Pascal,
Below are a couple of images I put together to show the inputs:
4-Pt Conic - The input is 4 points and a tangent line at either Pt.1 or Pt.4

5 Point Conic - The input is 5 points. Only three of the points can be co-linear

Not much to the inputs for the Conics.

The super ellipses are very similar to a regular set of ellipses. The initial inputs could be identical to the current Rhino ellipse command. The difference is an additional input that sets the fullness of the curve. Sort of the same idea as a Conic rho value. Please see this link -

http://mathworld.wolfram.com/Superellipse.html

Iâ€™ve used them to create a family of curves for a transition duct that required that each cross section have the same area but the height and width varied within a pre-described volume. The ability to modify the fullness of the curves aided in maintaining the constant area. Painful to do manually so the ability to use a super ellipse command combined with some Python code would be very helpful.

Hope this helps,

Chris

@pascal Any work done on this?

Hi Marc - not by me at least, Iâ€™m afraidâ€¦

-Pascal

Hi Pascal,
I found this topic, Super elipse, please, it has some work-arounds.

Not that I am aware of.

Chris

Hi @Marc,

Writing a script to create a superellipse may not be too difficult.

superellipse.3dm (26.0 KB)

Iâ€™ll see what I can come up with.

â€“ Dale

Itâ€™s nice!

Hi @Marc,

To create a superellipse:

1.) Create an ellipse
2.) Select the ellipse and turn on itâ€™s control points
3.) Select the 4 corner control points
4.) Run the Weight command and adjust accordingly.

Does this help?

â€“ Dale

Interesting, Iâ€™ll have to check this out, thanks.

Chris

Hi @Marc, @ChrisH1:

In doing some research, there is no way to represent a true superellipse in NURBS. What I have demonstrated above is an approximation of a superellispe. Not knowing your requirement, I am wondering if this is sufficient? What is your requirement for a superellispe?

Thanks,

â€“ Dale

Mine are as follow:
-Being able to adjust itâ€™s squareness easily
-Symmetrical along the two axis
-Smooth curvature graph
-A nice extra would be to get a good approximate offset of equal simplicity

Same as Marcâ€™s with the added idea of using code to be able to create a smooth blend through a set of superellipse cross sections. Same idea in setting up a group of conics and adjusting the rho value to get a smooth loft. I have a need to create a transition duct from nearly square to elliptical based on constant area cross sections.

Chris

You could use the â€śfree math pluginâ€ť from http://www.rhino3.de/
with these settings:

n=2.5 is equal to â€śpiet hein superellipsâ€ť

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Will this plugin work with Rhino 6 ?

Never mind. It runs just fine on Rhino 6. Thanks, I can picture myself wasting a lot of time playing with this plugin

Chris