Formula for Proportional Enlargement

[Mike Guilbault]

I've got a small program to calculate gallery wraps.  It adds the width and depth of the stretcher bar to the 'face' dimension of the finished wrap (ie. the front) so that I can calculate the image area I need to print and canvas size I need to print on.  This is for a straight wrap, not mirrored, and often odd sizes.  However, I'm finding that when I add the stretcher depth/width to the width of the image, for example, that the height of the image isn't proportionally the same using the same added extra.  Does anyone know the formula for proportionally expanding the height to an increase in the width, or vice-versa?

[PeterAit]

That's exactly what you want! Adding a 2" stretcher margin all around to a 16 x 24 photo gives you a 20 x 28 print, not the same proportions. But, you still need that extra 2" all around. If you did it proportionally you would add more to the long dimension, to no purpose.

[Mike Guilbault]

So then I will be cropping a portion of the length?  For some reason I can't get my mind wrapped around this.

[dgberg]

Mike,
You even have me a little confused.
You are printing anything on the sides or not?
Canvas stretcher depth?
If you are only printing on the face lets say 18 x 24" and your bars are 1 1/2" deep and you are stapling on the back( ?) then I would just add 6" per side for a canvas size of 24" x 30"
You have the image area or face you do not have to calculate it.
Maybe explain it one more time.

[jrsforums]

Mike, these actions by Ernst Dinkla may help you.

http://www.pigment-print.com/dinklacanvaswraps/six-canvas-wrap-actions.htm

[Mike Guilbault]

Mike,
You even have me a little confused.
You are printing anything on the sides or not?
Canvas stretcher depth?
If you are only printing on the face lets say 18 x 24" and your bars are 1 1/2" deep and you are stapling on the back( ?) then I would just add 6" per side for a canvas size of 24" x 30"
You have the image area or face you do not have to calculate it.
Maybe explain it one more time.

I'm probably complicating it more than need be.

The image itself is wrapped around the sides. The stretcher depth may vary depending on the finished size of the piece, but typically 1.5 or 1.75".

I think part of the trouble I was having was that LR Print module handles a single image print and custom print a little differently.

I had an image that I was going to print to a finished size of 44x29" - so the 'face' was just that.  The wrap depth is 1.5" and the stretcher bar is 1.25" thick.  I use the Stretch Relief pliers which need 3/4" to grab past the inside of the back of the stretcher bar, so 1.5" sides and then across the back of the stretcher another 1.25" plus the extra 3/4" for the pliers to grab.  So that's a total of an extra 7" width which brings my canvas required to 36" - fit perfectly on a 36" roll - which is why I'm going with 29" rather than 30".

Now, for the image though, I need the face width of 29" plus the wrap depth of 1.5" plus I add an extra 1/4" for safety to make sure it wraps all around - so 1.75" of 'wrapped' image added to each side of the 29" for a total image width of 32.5".  Applying the same additions to the length gives me 47.5" from the 44" face I started with.

However, when I 'enlarge' the image for printing to 32.5", the length is now 49" - not 47.5".  Proportionally the length has grown longer so now I have to crop the image to make it fit the 47.5" that was calculated by just adding the same inches to the length as the width.  But if I want to use the full image, without cropping it, I now have 49".  I'm looking for the formula that calculates the 49". 

I have a proportional calculator that does this, but I'm trying to build it into a small app so I don't have to jump back and forth between two or three apps.

[hugowolf]

I am not sure where you are getting the 49 inches from. Surely if you are using a 3:2 aspect ratio, you should be getting 48.75 inches, no?

And if it is actually 48.75 inches, then this is just 1.5 times the short side. Or am I missing something?

Brian A

[Schewe]

I have a proportional calculator that does this, but I'm trying to build it into a small app so I don't have to jump back and forth between two or three apps.

Your fundamental problem is the failure to understand adding a specific amount to dimensions are not a proportional calculation...you need to add a SPECIFIC amount to the ends and sides, not a proportional amount. If you need to add 1.75, then you need to add 1.75 + 1.75 to the ends and sides...(same deal if you are expecting to view the cropped image after deducting the 2x 1.75).

If you think about it, you'll understand that you can't add a proportional amount to an existing dimension because the proportions would be wrong.

[enduser]

Perfect Photo Suite offers an excellent routine to do this automatically for you.  Enst's excellent actions also do it well.  In addition, Qimage will do it automatically for you too.

But look at it this way: you've made a 16" x 24" image, which is a ratio of 1.5 to 1.

You want a 2" margin all round for the wrap, which makes the image 20" x 28".

This is a ratio of 1.4 to 1.  That's it. The ratio changes, and is supposed to.

(On the other hand it's surprising how many customers give me an equal sided square file and ask for a panorama print without any cropping )

[darlingm]

Hoping I'm understanding what you're looking for and that this is helpful…

Schewe is dead on.  Take an absurd and extreme example of a 10 foot by 1 inch face.  Adding the same amount of inches to each dimension is going to make the piece less elongated.  (Still very elongated, but less.)

Reading between the lines, I'm thinking something useful to you might be if you want the small dimension to be 29", so you max out our 36" wide canvas, what should the long dimension be?

In that case…..

Let's say you have a 2:3 aspect ratio image, which is what it sounds like you have.

I personally like multiples and percentages better than ratios, so I think of everything in terms of 1:X.  What everyone else calls a 2:3 aspect ratio, I think of as a 1:1.5 ratio.  Well, I actually ignore the whole idea of a ratio and just look at the pixel count.  If it's a 3418x5127 pixel image, I know the long dimension is exactly 1.5 times the short one.  This way, it really makes no difference if you wind up with a long side of a cropped image being something weird like 1.358 times the short edge - you aren't trying to figure out what ratio that is.

If you want the short dimension on the front of the canvas to be 29", you're adding 1.5" and 0.25" to each side, or a total of 3.5", bringing you to the 32.5" you calculated for the inked area of the short dimension.

To find the inked area long dimension (not face size) that fits proportionally, that would be 1.5 times 32.5, or 48.75.

From there, you'd subtract the 3.5" that is on the sides and back, arriving with a proportional long dimension on the front of the canvas being 45.25".

You asked for a formula…

ProportionalLongDimensionOfFace = (ImageLongDimension / ImageShortDimension) * (DesiredShortDimensionOfFace + 2 * (DepthOfBar + SafetyMargin))

IF you have the case of a 2:3 (or as I call it 1:1.5) photograph, and you're using 1.5" deep bars, and want a 0.25" margin, that formula reduces down to:

ProportionalLongDimensionOfFace = 1.5 * DesiredShortDimensionOfFace + 5.25

Feel free to use any unit of measurement in the (ImageLongDimension / ImageShortDimension) part -- as long as it's the same unit on both.  In cases like this, I always use the pixel dimensions and ignore the ratio or document size.

As another side note, I've found it's extremely difficult to notice a small non-proportional enlargement.  (Unless you have a very similar sized proportional enlargement side by side.)  I'd be happy to make the face 45" or 46", and wouldn't think twice about it.  In Photoshop, you can uncheck constraint proportions.  Even making it 46" is a whopping 1.6% distortion (46/45.25.)  I haven't found anyone noticing distortion under 5%.

[Ernst Dinkla]

Your fundamental problem is the failure to understand adding a specific amount to dimensions are not a proportional calculation...you need to add a SPECIFIC amount to the ends and sides, not a proportional amount. If you need to add 1.75, then you need to add 1.75 + 1.75 to the ends and sides...(same deal if you are expecting to view the cropped image after deducting the 2x 1.75).

If you think about it, you'll understand that you can't add a proportional amount to an existing dimension because the proportions would be wrong.

Correct. And it is essentially the same when you add borders or a matte to a print when the print is framed. The matte, the frame both get another aspect ratio than the image itself has, the aspect ratio's of the matte and the frame differ as well. Take a framed print, put the ruler diagonally on the corners of the image and the ruler will not be in line with the corners of the frame. One exception; the square image if every enlargement of border, matte, frame, around the image is equally wide all around. Then the 1:1 aspect ratio, the 45 degr diagonal is fitting with the 1:1 enlargement, the 45 degr edge cut of the frame bars.

--
Met vriendelijke groet, Ernst

http://www.pigment-print.com/spectralplots/spectrumviz_1.htm
July 2013, 500+ inkjet media white spectral plots.

[Mike Guilbault]

I am not sure where you are getting the 49 inches from. Surely if you are using a 3:2 aspect ratio, you should be getting 48.75 inches, no?

And if it is actually 48.75 inches, then this is just 1.5 times the short side. Or am I missing something?

Brian A

You are correct Brian... I just noticed that I had rounding turned on with my proportion calculator  when I turned that off, I indeed got 48.75.  That may have been my whole problem.  I was typing these numbers into LR Print Module and they weren't matching up. 

Thanks for the other explanations too everyone.  That did clear it up in my mind.  I never was, nor claimed to be a math wiz and appreciate the clarification.