Hi Michael, thanks for responding..

The angles are these:



So the coned part is a 30 degree cone and the scallops are cut out at 25 degrees.

We did it with cylinders of radius .5, rotated at 25 degrees, which produced perfect conics down at the base area, though it left the cones slope (the 30 degree angle) "curved, or malformed" as a result.




The conics had me thinking it should be cut with a cone, which produces perfect edges and intersections. I just couldnt figure out how to size the cutting cone to get the resulting numbers? It could be just a big trig calculation that is beyond me. I just wasnt sure if I was missing something, or chose the wrong path.



Here is a result he acheived so far. Note how at the base of the cone there is some surface left from the different angles.. I could only acheive this using cylinders, and then patch rebulding the 30 degree cone with new straight lines and sweeping the conics up to a point.


I wondered if figuring out how to do it with the cone (I think this is more proper) was possible. (Cant figure out the size and height of the cone to use as a cutter to get the angle right)

Hi Burr, so if I understand ok now you are talking about angles measured on the scallop itself, right? [EDIT: didn't see your reply until after my post, but it turned out this was the right measurement so I think this will work for you]


So how about something like this - start by drawing in a line at a 30 degree angle like this - it doesn't matter how long this starting line is except make it big enough that it will stick a ways out past the side of the base cylinder that you are going to be cutting the cones out from:




Now you want to create a second line for the midpoint of the scallop. I think this is the one you want at 25 degrees, right? So the key thing is that this second line must be of the same length as the first one so either use the same numeric length for each of them or just make the second one by copying the first one and rotating it. To do the copy/rotate method, select it and then run Transform > Rotate, check the "make copies" button and type in -5 degrees as the rotation angle, using the top end as the rotation origin.

So now you've got 2 lines of the same length, one at 30 degrees and one at 25 degrees like so:



Now take the outer line and go to the top view and make a copy of it rotated at 45 degrees in the top view.

Then rotate the inner line by 22.5 degrees in the top view.

Now that those are rotated in the top view you've got 3 lines all the same length positioned like this:



These 3 equal length lines are now enough information to create a cone - first make the base of the cone by using Draw curve > Circle > 3 pts to make a circle that goes through the bottom ends of those lines like this:



Now you can draw a cone and snap the base point of the cone on to the center of the circle, place the radius snapped on to the circle, and the top point at the end - here I've spun around to the other side so you can see those 3 lines are right on the surface of the cone:



Hope that's what you are looking for!

- Michael

Basically short version of the above - if you create any 3 lines that run exactly down the side of a cone (the lines must all be the same length and come to the same endpoint on one side), then you can create the cone from that by making the base by circle through 3 points, the center of that circle is the base point for the cone and the other 2 points are snapped on to the lines.

- Michael

Yes, deriving that cone was my issue.. I'll play with that a bit. Thanks for the time Michael!

Where is the glitch?




http://moiscript.weebly.com/uploads/3/9/3/8/3938813/conics.3dm the file format 3dm

Hi Frenchy,
If you use a cylinder to do the boolean cut that is depicted with the cone, then that lower edge is a conic created that can be exactly duplicated with the conic tool. But the other edges are not constructed properly by the intersection of the cylinders in the other planes..

If you cut the surface with a cone, then there is no conic there.

Is this what you meant?

So if you use a cylinder as the cutting object, you will find conics




If you use a cone as the cutting object, there will be no conic

Yeah usually the definition of a conic section is a curve formed by the intersection of a cone and a plane, with different angles of the plane making different types of conic curves.

If you are intersecting things other than a cone and a plane then you may not generate a conic section curve as output, although they still might be generated if you have things arranged in particular ways.

Does that all answer your question Pilou?

- Michael

Nice model.
Google search came up with "Intersection of quadrics"
There is a QI program and 4 research papers. http://hal.inria.fr/docs/00/18/60/89/PDF/JSC1.pdf
(Google each of the 4 research paper titles to find them.)

The little "parabolic" looking curve is not an ellipse, not a conic, and is not planar... it is a "second order curve...."

Thanks, that is more clear now! :)

Ah Bemfarmer,
You are the man!



My conic = 0.4653, 0.4652, 0.4333 My curve = 0.4652, 0.4653, .4332

The "non-planar" was the givaway!

It Was a mistake, though it lead me to my solution! I wonder how many of these have created solutions in the past!!!

Thanks for chiming in. :)

You have made my last hairs losted! :)
A conic curve is always "flat" :)

Frenchy,

a conic curve is derived from running a plane through a cone at some angle. It will be planar. I suppose a conic who's "view" is planar, but curves out of plane, becomes somthing else.. Maybe bem can be specific.