How to distort artwork for printing on a cup?

Question

I need to print using my regular office printer a design I have already made to wrap around to the shown here under mug.

As you may notice that the circumference of the top part is wider than the lower part. which mean That I need a sort of deformation or cone projection to do the job.

So please how can I do that doing Illustrator or Photoshop.

ps. There is a post discussing the process designing and printing for mugs here and it is not my case, it discuss the mug printing production itself, but my case is just a regular printing to warp a the printed paper around the mug.

using the wrap command is the solution but actually I don't know the exact amount that I have to adjust the distortion to get my design wrapped exactly over the mug. also I need to know how to determine the dimensions I marked "?" below.

Answer 1

Find a cup template for the production company you are going to use.

Little Trick in Illustrator:

You can apply a warp effect to a layer. This way anything on the layer will be warped. Figure out warp settings which mimic the arc of the template. Then apply that effect to a layer.

Then simply draw or copy/paste artwork to that layer. You can then adjust and see the warp which is happening. If you wish to see flat art, simply toggle the visibility for the Warp effect to off for the layer.

When you're done, remove the warp effect entirely.

All this is somewhat irrelevant. The design should be designed flat, without any consideration for the warp which occurs in printing. The printing distortion is specifically designed to counteract the natural distortion due to the substrate. The warp should only be used to distort the final artwork for self-printing.