Creating labels for curved surfaces

[Xhris]

Hi everyone,

I came across a challenge this morning that I solved and thought people here could benefit from my work. The task was to create a label to put around a cup. Unfortunately the cup was conical in shape which made designing a label more difficult than creating a rectangular strip.

Fortunately the conical cup was rotationally invariant but I realised I’d need to do some mathematics to solve the problem. I considered producing a full walkthrough of the geometric calculations and logic but then decided it was inappropriate for TG and have instead just made a mini-tutorial with the essentials needed to complete the task for simplicity and ease of understanding.

(See figure below). Essentially, you just have to measure the top and bottom circumference of the cup and its height. Then stick the numbers into the equations in the attached xar file and get values of the two radii of curvature and angle between the arcs swept out (making sure you convert to degrees from radians). These last three parameters allow you to draw a scale diagram in Xara to get the arc area region needed. Once you’ve designed the surface logo about a rectangle of similar dimensions to the arc region, you can use the Mould tool to map it accordingly. Any bitmaps may need to be traced to be correctly moulded.

Hope people find it useful at some point.

Xhris