darcshadow

Distortion Correction on Cup

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I know how to account for the cone shape of a cup to get the image to go straight, my question is does anyone have a formula that accounts for how the image looks  on the vertical curve. For example, if you place a square on a cylinder and then look at it straight on, depending on the radius of the cylinder and the size of the square, it will look like a rectangle. It will appear to be taller than wide. Anyone have a calculation to compensate for this?

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After a bit more thinking I don't think this is as complicated as I thought it might be. Dusting off my high school geometry I think the following will give the width you'd need to stretch an image to get it to appear at the correct aspect ratio.

Stretch Width = arcsin(image width/Diameter of cylinder)

Need to experiment, but I believe if I stretch the image as specified by the equation and then run it through the cone correction tool when applied to a glass it should be straight and have the desired appearance.

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I generally just wrap a piece of copy paper around the thing and then draw a line where I want it to be straight. Unwrap and voila you have something you can scan in and use to warp/bend your text or graphic to meet the curve. sometimes takes some tweaking if there are compound curves. Every cup is different it seems. 

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Getting is straight isn't my problem, The pattern along path in Inkscape takes care of that for me. The problem is say a 3" square when applied to a cylinder will not appear to be 3" wide anymore because of the curve, it'll appear to be slightly less. So you either have to make the image shorter or wider to keep the original aspect ratio. This is not usually an issue for most designs but I have one that is, at least it is to me, because I have noticed it, and now every time I look at it I see it.

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Wildgoose, I don't think we're talking about the same thing. Here's a diagram. In order to get the red square to appear square on the cylinder, it will need to be stretched to the size of the blue rectangle.

Capture.JPG

 

Go-C, after doing the math, 10% is pretty close to what the match comes back with. It'll vary some depending on size of cup/cylinder and size of image but 10% is a good ballpark.

After some more thinking I think I decided I want to shrink the height rather than change to width so here is my new equation.

H = h/w*D*sin(w/D)

  • h - height of image
  • w - width of image
  • D - diameter of cup
  • H - new height for image
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Wild guess here.

Blue minus red = a

blue plus a = what you want.

Just a wild guess like I said. If it works, let me know.

 

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That'll get you close, but not exact, and there's the question of not knowing both blue and red, you only know one or the other. I edited my previous post so you might have missed my equation that I came up with.

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A string and straight edge would work. Lay the straight edge across the top of the cup and set it for the width of your image, then take the string and wrap it around the cup to get the length of the arc. Then just stretch the image out to the length of the arc. That should work, I like knowing the math as well.

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It may actually be twice the difference. Not sure.

Draw on paper, cut it out and have a look.

if blue = a

red =b

difference =c

a-b=d

c x 2 + a   should be the answer. Unless it is not   d x 2. then just c + a.

Stretch proportionately to keep size.

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This only accounts for the cone shape and getting the design to be straight, does not account for the perceived width verses actual width of the image.

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Come to think about it, there is a lot more involved.

Not only does it look out of square, but it is also going to look shorter at the end of the square. Top to bottom. Not much, but it is there.

Now I got ya thinking.

I don't know if there is any math that can cover that part.

How about a strait on pic and use vertical lines to measure the difference for the height and the other stuff for the width?

 

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