## Introduction: Distorting Artwork for Glass Chemical Etching and Sandblasting

If you’re using a laser to etch glass, you can use your regular artwork without any problem. However, if you are using a vinyl cutter or adhesive paper to make a mask for chemical etchant (like this or this) you will want to manipulate the artwork for it to look better on the conical glass shape.

This instructable discusses how to manipulate artwork in Illustrator for use with a vinyl cutter for glass etching. It also applies to any 2D artwork you might want to wrap around a conical glass. You will need a calculator with trigonometric functions, or you can use this calculation page I made.

The last step shows numbers you’ll want to use, but you can also scroll through for derivation (especially helpful in case I got something wrong).

## Step 1: What Do We Want?

We want to distort artwork to fit around a conical glass. If we could 'cut' down the side of the glass and 'unwrap' the outside, we would see that it looks like an arc, not like a rectangle. We want to map our rectangular artwork onto this arc.

Put more pointedly: what are the critical dimensions of the cup, and what are the critical dimensions in illustrator? And, how can we go from the first set of measurements to the second?

## Step 2: Converting Glass Parameters to Illustrator Parameters

The following calculations assume radians, not degrees. Photos at the top follow the derivation.

We have three parameters for the conical glasses - top and bottom diameters (d2, d1 respectively), and the distance along the glass between these measurements (h). Please only measure for conical sections.

We want the parameters necessary to make an arc - inside and outside radii (r1 and r2 for inverted cone glasses), and the angle this arc subtends (theta).

We have three unknowns and we can write three independent and simultaneous equations, and because we are very good at math, we can massage these equations into forms that let us directly calculate r1, r2, and theta.

In illustrator, the window for an arc mesh lets you choose between -100% and 100% Bend, where 100% represents a full 180 degree arc. We can multiply the theta by 100/pi to get Bend %. If you did your calculations using degrees, multiply by 5/9.

We still need to set up the rectangle of artwork. Even if your artwork does not wrap around the glass, you need your artwork to be inside a rectangle that would wrap your entire glass. Then, once everything has been distorted, you can choose how much to cut out for your mask. Because you measured the height along the glass, that height should be the height of your rectangle (which becomes distance between the two arcs in Illustrator). The width of your rectangle should become the smaller circumference when arc-ed.

In Illustrator, the smaller arc shares endpoints with edge of the rectangle (lower edge for a positive bend radius, upper edge for a negative bend radius.

Please note that this image is for a conical glass whose top is larger than the bottom. The *smaller radius* should be used for this calculation (r1 for a glass those top radius is smaller than the bottom radius). We can draw a close up image of the arc image to understand r1 relates to the width of the artwork rectangle. Then, thanks to the law of sines, we can calculate the width.

Now we have all parameters necessary for Illustrator! Last image is a summary of these values.

## Step 3: A Note About Text

There are two ways to handle text with this method

1. You can create text in your rectangular design, then distort it with the arc mesh with all other components.
2. You can create baselines for the text, distort those, then write using the 'type on a path' tool

The choice is entirely yours, and the difference is often small. Here are two considerations for which method to choose:
a. If your text is very tall, then method 1 will distort it a lot. If your text is short, then method 1 won't look much different from method 2.
b. Method 2 does not work well for blocks of text, which would need separate baselines for each line in the block

if you have other thoughts on handling text, please write them in the comments!

## Step 4: Summary

To distort images for wrapping around a conical glass...