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  1. #1

    Default Creating labels for curved surfaces

    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
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    Last edited by Xhris; 19 February 2009 at 07:41 PM. Reason: changed letters to avoid potential miscalculations
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  2. #2
    Join Date
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    Surrey, BC, Canada
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    Default Re: Creating labels for curved surfaces

    Hi,
    Great work and thanks for the formula.
    Jim
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  3. #3

    Default Re: Creating labels for curved surfaces

    Great formula but need to measure and work out, have a look at attached file, looks a bit complected but is quite simple, have tried to get it layed out on a single sheet, just mark out and draw, not to good with the maths so with trianglation not needed.
    Have a good day all
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  4. #4

    Default Re: Creating labels for curved surfaces

    Hi jeffb, I didn't quite follow your instructions; I think this kind of thing is best shown in a video. Edit: Oh wait, now I think I get the basics of it. Does this really work for all cup sizes?

    You did make me realise that some people may struggle a bit with the maths, so I wrote a replacement tutorial with an example of how to solve the equations step-by-step. Hope it makes things easier for people.

    Xhris
    Attached Files Attached Files
    Last edited by Xhris; 20 February 2009 at 06:54 PM.
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  5. #5

    Default Re: Creating labels for curved surfaces

    OK Xhris
    Believe me this will work for anything, I was doing this after 5year apprentaship 40 years or so ago, have used it from small to big and when I say big would a ships funnel do!!
    Yes the basic isvery sound practice and just needs adapting for other things, but as I say the basics are long proved
    IP

  6. #6
    Join Date
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    Default Re: Creating labels for curved surfaces

    Jeffb, your method is approximate. It is not precise. In your illustration it's quite clearly visible that the perimeter of the wide end of the cup is longer than the long side of your label.
    Although all other dimensions are correct (curvature of the label sides and width).
    John.
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  7. #7

    Default Re: Creating labels for curved surfaces

    Well, that's two tutorials for people depending on approach. I'm sure people will find them useful. Thanks jeffb.
    IP

  8. #8
    Join Date
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    Default Re: Creating labels for curved surfaces

    I did this once years ago when I needed to create a label for a tapered container. Not being good with math, I wrapped a piece of paper around the surface like a cone. Then I drew a vertical line at both ends.

    I unfolded the cone, placed the paper on a large piece of illustration board and extended the lines outward until the crossed. At the intersection of the two lines, I fashioned a large compass to draw curved lines on the area of the paper that would be the label, and added my text to that curve (manually cutting apart type set text).

    Your method is probably easier.
    IP

  9. #9

    Default Re: Creating labels for curved surfaces

    That's what I thought about doing for a minute when I first started...then I remembered I had a maths background . I'll make a video as well in a bit. Probably not including the calculations (that's boring and self-explanatory now with the new xar file I attached before), but about drawing the scale diagram. It's really easy. Actually, I've got a good idea for a video...
    Last edited by Xhris; 20 February 2009 at 10:32 PM.
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  10. #10
    Join Date
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    Default Re: Creating labels for curved surfaces

    I think the bast way is to combine these two methods. The first part form jeffb is simpler. But we still need some math for label length.
    Here how this can be done.
    Attached Files Attached Files
    Last edited by gwpriester; 21 February 2009 at 03:30 PM.
    John.
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