20 oz tumbler wrap template

[Jorbill7]

Hello, I'm trying to adjust/warp the bottom portion of my 20 oz tumbler print template. I have the math needed to do a conical warp, however i'm not sure how to apply that math inside the program to make it work. All i have is the math and my file, please help.
I've used smart objects as to easily transfer the design over to the print. the piece i'm trying to change is labeled BOTTOM SO

Top part - width 25.5 cm - diameter 3.19 cm
bottom - width 23 cm  - diameter 2.88

[Jacob Bugge]

Jorbill,

Reply edited owing to a different interpretation.

What is the height of the label?

It is needed because you can create an infinite number of labels with those widths and diameters with any conical shape possible, and it is needlessly inaccurate to use an approximate height based upon the template, which looks like 6.67 cm based upon the right part of the screenshot; the left part having different proportions.

[Bobby Henderson]

Designing graphics to wrap around a drink cup is not so fun to do unless the person doing the work really loves math. I attached an image from a work file I made back in 2007. A local drive-in burger restaurant needed a great big version of one of their soft drink cups made for a parade float. I had to make identical graphics for this great big cup.

I visually drew out a side view of the cup, recording the diameter of the top and bottom. I drew out a convergence point below the cup. Then I did a bunch of other things to arrive at the right arc shape I need for the graphics to wrap around the cup. I used Illustrator's Arc effect to warp the graphics to fit that shape.