Modeling Apollonius conic sections

Ran into this graphic on the web,which I’ve pasted in the model for reference.I thought it would be a good exercise to attempt creating a 3d model with native tools. My model is based on it’s own dimensions. I did not try to copy the jpg. exact dimensions. Creating the sections was the challenge. After a few hours I was pretty much stuck. The required ellipse has stumped me. I got the cone and circle right I believe. Not too sure if the the parabola I drew is accurate though. My method I wrestled out was pretty clunky so I didn’t bother doing the Hyperbola. Would love to see a pro’s approach to it.
I think it would be a good project for a Skill Builder video, but I could not find a way to contact Arron to present the idea. If anyone has his contact possibly you could pass it on to him. ?

Apolonius Conic sections .skp (346.0 KB)

Why don’t you think about it in the same way the graphic implies them? Draw a cone and then draw rectangles that pass through the cone at the various angles. Use Intersect Faces to create the ellipse and the other curves.


Of course the solution would be something simple! :stuck_out_tongue_winking_eye: Makes it WAY easier to determine the angle also. Thankyou for checking it out Dave

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Sorry. I should have made it more difficult using lots of tools. :crazy_face:

Sometimes all it takes it a different look at something.

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That’s just the way I approached it. I believe for the parabola the inclined plane is parallel to the slope of the cone. Being just native tools, you can do it on SU for iPad too.

Yes, it’s been on my list to do a video of.

You’re right. I didn’t draw it that way because I was lazy. You guilted me into fixing it. :smiley:

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Yeah, the first time I tried this for a parabola, my memory was bad and I made a hyperbola instead, but it still looked good enough I didn’t realize it and finished the whole model with it. If you mirror the cone upward tip to tip, you get the other symmetrical side of the hyperbola with the one plane intersecting both cones. The inclined plane parallel to the cone slope won’t ever intersect the upper cone.

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I re-did the model using your method. Worked out nicely. I didn’t know a Parabola face was Para llel to the cone. You taught me a bonus! Now I will have to re-open the model and fix that! Cheers.


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