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conic sections


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I need some help creating conic section geometry. the circle and the ellipse tool are no problem, the trouble I'm having is in creating parabolic and hyperbolic curves. i think i can draw a parabolic curve by using the polyline tool and selecting the end of the latus rectum, the vertex, and the opposite end of lR. however how would i extend this curve past the lR? Is there a script i can use in which i could enter in the standard equation and get back the parabola/hyperbola/ellipse/circle? like i said really ellipse and circle i could care less about since they are simple, I'm far more interested in hyperbolas and parabolas. Any information would be very appreciated.

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Hello J. Fildes, there was an extensive thread on this (or perhaps a very similar) topic a while back. Have you tried typing "Parabola" or "Ellispe" into the Search box at the upper right of this forum? You might find some useful info. I also concur with Grant that Islandmon is the master at this sort of stuff... P

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I had searched under those topics and they were helpful in constructing a parabola using 3 known points (which i used as the vertex, and end points of the latus rectum) but i was wanting some way to verify that what i've drawn is correct as well as extend the parabola past the latus rectum. it would be great if there was a script in which you could define the equation and achieve the resulting parabola, or give a location for the directrix and the focal point and achieve the resulting parabola.

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A workaround:

If you know your parameters you can draw a cone of proper angle and section it with a plane, then extract the parabolic NURBS curve. If you need 2d, convert to polygon.

The NURBS will be faceted. Draw cone and plane at 100 times (eg) the final curve target size so that the polygon will have enough vertices to appear very smooth when scaled down to final size.

Also to check the polyline curve you drew with Vertex & LR, there are conic section generators in basic math/graphing software. Perhaps the desired curves can be generated externally and imported or pasted (with the x/y axes) into VW.

-B

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  • 2 weeks later...

I ended up doing the parabolas in an old fashioned way by using the directrix and the focus and plotting points then passing a polyline (cubic vertex) through all of the points, the result looked ok, I just wish I could find a script or lean more about scripting to generate the result without spending that much time on it. As for hyperbolas I went back to a manual drafting technique. I drew a circle from the focus to a vertex and drew another circle from the opposite focus to the same vertex. Then i offset each of the circles multiple times by 1 unit (in my case .25"). The point where these circles intersect formed the curve of the hyperbola. Using the polyline with cubic vertex again a very nice looking curve was generated, i then mirrored the result for the opposite curve. I'm attaching the drawing file to show the results for anyone who is interested.

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  • 11 years later...

There isn't a specific tool, but:

 

A little Marionette would probably do the trick, or

Faster would be to simply draw a cone and slice it parallel to its edge and Extract the curve:

 

(ps all other the conic sections Ellipse, Circle, Hyperbola can also be created this way)

Parabola.PNG

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