How to draw a plane intersecting a cylinder at a "compound angle"

[bor]

TL;DR Summary

geometry hand drawing

Hello.

For a project I am working on I need to draw a template of a "curve of intersection" of a plane (B) intersecting a cylinder at a "compound angle"..
I do not know the correct terminology so I added a sketch of what I wish to achieve.
If it is not understandable please say so and I will try to clarify it better.

I have found a method for drawing a curve of intersection of a cylinder with the plane A in my sketch..

But I can not find a method for drawing a curve of intersection of a cylinder and plane B as shown in my sketch.

So I kindly ask If someone could show me a method for hand drawing this shape or point me to some tutorials, examples,... explaining such a method.

Thank you for your help.

Bor

 

[fresh_42]

The shape is an ellipse. So I'd say start with the ellipse. (e.g. https://en.wikipedia.org/wiki/Ellipse)

 

[bor]

Hello.

Thanks. I do realize the shape created is an ellipse but I do not know how to draw that particular ellipse.. so I am looking for a method of drawing a "curve of intersection" of a plane and a cylinder under a compound angle (double angle?)..

Something similar to this method (picture below) I found for drawing (plotting?) a curve of intersection when the angle is not compound (a single, simple angle?)

Please forgive my ignorance. English is not my first language in addition to that I am a mathematically challenged person with next to no education (all those formulas and "math language" on the linked wiki page looks like hieroglyphs to me) who would like to cut a hole in a (double 45 degree) angled ceiling so I can install through it a cylindrical pillar with a diameter of 300 mm.

I am sure I could find the exact shape I am looking for with the aid of 3d CAD software but unfortunately I come from a paper and pencil era, so I am digitally challenged aswell.

The only method I came up with is to actually cut a piece of smaller round stock (30mm lets say, only because my band saw can not accommodate the actual diameter of 300 mm which is needed).. Then measure the length and width of the ellipse produced.. then increase this dimensions by a factor of ten.. and then proceed to draw the bigger jet similar ellipse with the ""rectangle method"..

But I am sure there exists a more elegant and simpler method of drawing this particular ellipse..

So if anyone is aware of such a method, please share it. Thank you.

Bor

 

[fresh_42]

I would start with an empty sheet of paper, rotate it by 45°, then draw a horizontal ellipse, either with a ruler that has ellipses for drawings, or with two pins and a string. Then rotate it back and draw all the rest.

Or draw it separately, cut it out, and use it as a pattern.

Or calculate the equation and draw it point by point. With a dozen of points distributed all around you should have a good skeleton to draw the entire curve.

 

[Lnewqban]

Welcome, @bor !

The diameter of your column is 30 centimeters.
Could you explain why your band saw can't cut that 30 centimeters hole into the ceiling material?
Would that cut be done in one flat piece to be split, or in two halves of ceiling?
If in two halves, what the orientation of the half ellipse would be respect to the ceiling flat half?

How thick is the material of your ceiling?
Will the cut be done perpendicular to that material or following the angle of contact with the column?

Why the double 45 degrees?
Thank you.

 

[bor]

Hello.

I do appreciate the time and effort made to help out a complete stranger.. so thank you.
Jet I must sadly admit that after reading your (fresh_42) last answer several times and despite my best
efforts to comprehend it I failed to do so. I am afraid that I am just lacking too much of elementary/basic level knowledge on the topic.. and as I find it far easier to understand pictures than worded descriptions, a sketch of your solution might be more useful.. for example, with the picture in my second post, I it find easy to comprehend what was done and how the ellipse was generated.

Lnewqban.. Thank you for your interest in my topic... Regarding the band saw I think there has come to a misunderstanding... I was trying to describe how I could generate the exact shape needed (albeit proportionally smaller), by cutting cylindrical material (a pipe, lets say) under the correct angle with the band saw.. The ceiling itself I will be cutting with a reciprocating saw.. the material is wood and is 20 mm thick, I will be cutting it so that the cut follows the the angle of contact with the column. And the cut-out will be done on the existing and installed ceiling, overhead.. "in situ" so to speak.. as for the angles.. that is just what I am working with.. the house is already built. The accuracy need not be exceptional but I would like to keep the cut within the tolerance of 10 mm or so..

Any way, I have since came up with a new/better solution that I will be utilizing. It involves zero math and one laser (pointer). I will place a wooden template disc of appropriate diameter on the floor in the exact location of where the column will be later placed. Then I will guide the laser pointer (pointing vertically to the ceiling) along and around the perimeter of the template disc and (along the way) marking a sufficient number of points on the ceiling .. that will then allow me to connect them and generate the shape needed.

Even though I have now found a simple and inexpensive solution that I am pleased with..
I am still bothered and frustrated that I was so far unable to find a method of (geometrically?) drawing a curve of intersection for a given example... Especially since I have previously been able to easily find methods for drawing more complex (in my opinion) curves of intersection.. between two cylinder at various angles for instance.. something I utilize when "mitering" pipes.. So I am still very much interested in a method of drawing the curve of intersection produced when a plane cuts a cylinder at a "compound" angle.. Any solution is most welcome. Thank you.

Bor

 

[A.T.]

For a project I am working on I need to draw
....

So I kindly ask If someone could show me a method for hand drawing this shape

If this is for a project, and not for fun, why does it have to be hand drawn? There is surely some free software that can do this, like:
https://www.geogebra.org/3d

 

[Lnewqban]

...
Lnewqban.. Thank you for your interest in my topic... Regarding the band saw I think there has come to a misunderstanding... I was trying to describe how I could generate the exact shape needed (albeit proportionally smaller), by cutting cylindrical material (a pipe, lets say) under the correct angle with the band saw.. The ceiling itself I will be cutting with a reciprocating saw.. the material is wood and is 20 mm thick, I will be cutting it so that the cut follows the the angle of contact with the column. And the cut-out will be done on the existing and installed ceiling, overhead.. "in situ" so to speak.. as for the angles.. that is just what I am working with.. the house is already built. The accuracy need not be exceptional but I would like to keep the cut within the tolerance of 10 mm or so..

Thank you, bor.

Why the double 45 degrees?

If I understand correctly, you will cut the ceiling and then, insert a pipe-column through the elliptical hole, then anchor top and bottom of that column to floor and beam.

Consider that any irregularity of lack of flatness of the floor will magnify any deviations from a perfectly vertical and round 300 mm diameter cylinder of light.
Perhaps using a flat glass or marble on the floor could help.
I would use a plumb hanged from several of the laser marked points just to verify.
"Measure twice, cut once".

Please, see attachment:

 

[fresh_42]

If this is for a project, and not for fun, why does it have to be hand drawn? There is surely some free software that can do this, like:
https://www.geogebra.org/3d

Here is another one if you don't mind the language:
https://www.mathegrafix.de/download/index.htm
(I somehow managed to start a version in English but I have no idea how. )

Maybe
https://www.physicsforums.com/threa...h-physics-earth-and-other-curiosities.970262/
has a useful link (search for "graphic"). If you find another useful link that's on the list then please tell me!