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fi, Phi, fo, fum...

May 31, 2014, 06:22
Post: #1
fi, Phi, fo, fum...
Okay, here's the problem:

After doing whatever I'm going to do to a photo, I normally crop the final image to a 4x5 proportion or ratio or whatever it is. This allows me to order either 8x10 or 16x20 prints, which are both standard paper sizes, without further cropping. Lately I've been messing around with adding a white border to the prints, so I shrink the photo area--which increases the pixel density--to fit with a nice border around it. I've been using a 3/4inch border on 8x10s and it looks okay. Here's an example:

[Image: Y3NTPw1l.jpg]

Now I want to print this but at 16x20:

[Image: fSNfAjJl.jpg]

So, what I did, I used a 1.5" border. But I'm not satisfied with the ratio of border to print in either of them. I want to try to use that Golden Mean or Golden Ratio or Golden Shower or whatever it is, that Phi ratio--1.618. But, I can't figure out how to do the math, how to back up from the 16x20 paper size to get the correct width of the border. If I divide 16 or 20 by 1.618 I get a crazy number I can't relate to anything. If I multiply it, it's even worse. Plus, whatever I get I have to either half it or double it because I have two borders, one on each side. See where I'm going with this, it's confusing.

Now, before you start rolling your eyes and smirking, please remember that I was an ENGLISH major and that was back when it meant something besides knowing how to conjugate the verb "to supersize" and wearing a paper hat and a name tag.

Plus, I'm am not totally unacquainted with the higher maths. I know my times tables all the way up to the sevens and I remember something or other about a Quadrangle Equation with all those square root things or something. Well, I know how to look it up anyway.

So, what do I want to do to find a width for the white border that approaches that Golden whatever? Multiply or divide and by what: 1.618, .618, half of one or the other, twice one or the other, half or twice the difference of one or the other subtracted from the original? Plus, I think I want to be able to do it to pixels per inch because each image has a different ppi after I get done with it. I might crop some really tightly and others hardly at all. Aa-a-a-agh!
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May 31, 2014, 07:00
Post: #2
RE: fi, Phi, fo, fum...
Complexing indeed lol, cool effect to the border, it gives it an artsy look!

printing in Gimp is funky imo. Best to do a small scale black & white (draft) print test with half the size you want.

Divide the final dimensions you want in half, so 16x20 will become 4 x 2 (divided twice)

You want to test small so you don't waste ink if your printing or testing from home.
Then measure the print-out & make adjustments as needed.

Btw, why is this in chit-chat & why didn't you state the problem in the title??? "fi phi fo fum..." lol

"In order to succeed, your desire for success should be greater than fear of failure." BC
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May 31, 2014, 07:27
Post: #3
RE: fi, Phi, fo, fum...
here is an online-calculator:

http://www.kostelijk.nl/thegoldenratioca.../index.php

please visit Gimp-Science-Labs Blog
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May 31, 2014, 07:55
Post: #4
RE: fi, Phi, fo, fum...
Wipes smirk from face...
Not a lot more I can think to add other than suggesting having the final print laminated to avoid any splash damage due to the golden showers Wink

PS I really enjoyed the images you posted...you are a very talented photographer.
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May 31, 2014, 09:23 (This post was last modified: May 31, 2014 09:24 by ofnuts.)
Post: #5
RE: fi, Phi, fo, fum...
The golden ratio is really about Height/Width.

So one question you can ask is whether, within a 5:4 rectangle you can have a constant margin of a given width and come up with an inner rectangle that is 1.618:1 and the answer is yes:

Reasoning only with ratios: if K is your initial aspect ratio (one side is K, the other one is 1), then the aspect ration of the inner rectangle with a margin "x" is:

A=(K-2x)/(1-2x)

Solving for X:

x=1/2*(A-K)/(A-1)

(incidentally this formula shows that the aspect ratio increases when you add margin because A must be greater than K to have a positive margin.

In other words, starting with an aspect ratio of 5:4 (K=1.25) and ending with the Golden Ration (A=1.618):

x=1/2*(1.618-1.25)/(1.618-1)
x=.2977

So, if your complete picture (margins included) is 2500*2000, you need a margin of 2000*.2977=595 pixels to create a Golden Rectangle inside. Quite a waste...

Now answering your questions on
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May 31, 2014, 09:42 (This post was last modified: May 31, 2014 09:49 by rich2005.)
Post: #6
RE: fi, Phi, fo, fum...
All sorts of permutations on this but Gimp will do the arithmetic for you.

Set up your canvas for the photo print size, here 8x10 @ 300 ppi = 2400x3000
If you need to use inches as the units fair-enuf.

[Image: mlOU8Sw.jpg]

Add some 50% guides to mark the center of the canvas.
The borders while symetrical will not be equal so choose either horizontal or vertical. Here I set a one inch guide at the top.
In the view menu check snap to guides is on.
Now you can use the rectangular select tool (1) set to Expand from center (2) Fixed aspect ratio 1:1.618 (3) and portrait/landscape (4)
Draw your selection in from center to snap to the guide. What is left over are symmetrical borders.

A stage further
Turn the guides off. Image -> Guides menu. While there make new guides 'Guides from selection' Kill selection. Save this as a template.

[Image: HDhGvQv.jpg]

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Jun 1, 2014, 01:21
Post: #7
RE: fi, Phi, fo, fum...
Very nice, thanks--BIG help.
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