# How to project an image into a cone?

I have a circular image that I want to print over a cone. That is, over a circle with a wedge cut out, and then assembled into a cone.

However, if I just print my image and then cut the wedge, not only that part will be removed, but also the proportions will be messed up, and straight lines become curved.

I would like to do some processing to my image so when printed and assembled, the image will look as designed, when looked straight from the front (the tip of the cone pointing at the observer). Optimally, the processing should wrap the image in the wedge so I can have some freedom when assembling the cone.

Are there any tools that do this for me? or any processing I can do to achieve this effect?

I actually want to do this over a shallow cone (the wedge cut goes around some 5 degrees), but knowing a general solution for sharper cones would be optimal.

(I have no idea how to tag this, so please feel free to retag this question)

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Just to clarify because your question reads "into" instead of "onto" - are you trying to print the image on the inside of the cone or on the outside of the cone? – Ryan Jan 23 '13 at 11:15
@Ryan: Outside, but no matter how I see it, it should be the same. – Panda Pajama Jan 23 '13 at 16:00
I don't know the answer, but I believe the process is called 'anamorphic projection': en.wikipedia.org/wiki/Anamorphosis – e100 Jan 23 '13 at 17:29
Not an actual answer, but a good reference for cone perspectives if you are gonna try it yourself are birthday hats (thewarehouse.co.nz/is-bin/intershop.static/WFS/TWL-B2C-Site/…) – Yisela Jan 23 '13 at 19:55
The thing is that I'm not designing it so it can be projected onto a cone. I have an existing design, and I want to convert it to the conical projection. The math for this is trivial, so maybe I'm going to have to roll my own program for doing this? – Panda Pajama Jan 23 '13 at 20:08

Well, I solved it.

Let's consider my avatar as the original image. I make sure it is cropped into a circle.

Then in photoshop, I do Filter->Distort->Polar coordinates->Polar to rectangular:

Then, I resize the contents (but not the container [e.g. select all, edit->transform->scale]) of the image horizontally. The percentage I reduce is the percentage of degrees I will remove:

Finally, I go back to polar coordinates, and retrim as a circle:

Wrapping the image around the removed wedge is an exercise left to the reader.

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