 # Truncated Cone

Is there a way to lay out a truncated cone of known dimensions using simple shapes–basically, circles, rectangles, and lines? I want to make a lampshade-shaped dealio in a basic vector drawing program, but using a height and diameters of my choosing. Let’s just say it will be 6 inches tall, 4" at the large end, and 2" at the small end.

Note: I will want to do this multiple times with different dimensions, so I need a method rather than a solution.

Note again: Math > me. Please speak s l o w l y and use the idiot glossary. Thanks in advance.

You mean from a certain angle, like a perspective drawing? It might be easier to model it in 3D using something free and simple like Google Sketchup (truncated cone methods one or two).

Otherwise, if mathematical precision isn’t important, couldn’t you just draw two ovals and two lines?

It’s actually going to be a cutting file for a 3D paper project. SketchUp would be a great answer if I could “unroll” the model to a 2D drawing.

Y’know, I just realized i can…in a way. Take one segment of the cone and copy/rotate it the required number of times. It should be way easier than working out the angles, anyway. Thanks for the inspiration!

Draw concentric 360 * (D - d) / SQRT[(D-d)^2 + 4 h^2] degree arcs with radii of D * SQRT[(D-d)^2 + 4 h^2] / (2 * (D - d)) and d * SQRT[(D-d)^2 + 4 h^2] / (2 * (D - d)). Where D is the larger diameter, d is the smaller diameter, and h is the height.

E.g. For the example you gave 2" diameter top, 4" diameter bottom, and 6" height. Use D = 4, d = 2, and h = 6 to find that you need to draw concentric 59.18 degree arcs with radii of 6.08" and 12.17".

I drew a picture which should help you make sense of the above.

Thanks; that should be just what I need. Bonus points for you that I (mostly) understood it! I can’t actually measure degrees of arc in this program, but i should be able to fake it close enough for the intended purpose.

That won’t work for what the OP wants: Concentric circles will make the truncation the same height everywhere. I think what the OP wants is for the cone to be truncated by a non-horizontal plane.

I haven’t worked out the math completely yet. Using the dimensions stipulated, my attempt at a spreadsheet to figure it returned a result of 29 degrees rather than 59. That resulted in mathy confusion and headache. However, the shape shown in the drawing Lance Turbo included is about right.

I’m glad you didn’t get frustrumated.