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PostPosted: Thu Aug 06, 2009 5:39 pm 
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Rusty_Russell wrote:
16:10 is a manipulation of the 5:4 aspect ratio (also visible with tiles).


O.o How do you manage that one? 5 and 4 don't even go into 16 and 10 evenly.

Rusty_Russell wrote:
realXCV, 4:3 is overloaded - it isn't just 4/3 it's 4x by 3y. To treat it as a fraction is to ignore it as a ratio.


Ratios between two things can be treated like a fraction.

With aspect ratios we use x and y (width and height), thus:
4x for every 3y = 4x:3y = 4x/3y = 4/3(x/y) = 1.33 x/y

The "descriptions"/units are left off when talking about aspect ratios because it is understood that they mean the ratio of x to y - x:y (the ratio of width to height - width:height)

More Wikipedia goodness ;)

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PostPosted: Thu Aug 06, 2009 6:06 pm 
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Herohtar, turn the 5 * 4 the other way up. I said this before. 5 * 4 is landscape. Make it portrait and then it does.

I didn't say it couldn't be treated as a fraction. I said that when you treat it as a fraction, remember that it's a ratio of x and y as well.


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PostPosted: Thu Aug 06, 2009 6:19 pm 
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Rusty_Russell wrote:
Herohtar, turn the 5 * 4 the other way up. I said this before. 5 * 4 is landscape. Make it portrait and then it does.

I didn't say it couldn't be treated as a fraction. I said that when you treat it as a fraction, remember that it's a ratio of x and y as well.


Now you're applying rotations as well as uneven transformations. That just doesn't work; if you start doing stuff like that then every aspect ratio is "related", be it 4:3, 16:9, 16:10 or 27:43.

EDIT: Also, once you apply that rotation you no longer have a 5:4 aspect ratio -- it is now 4:5

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Last edited by Herohtar on Thu Aug 06, 2009 6:25 pm, edited 1 time in total.

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PostPosted: Thu Aug 06, 2009 6:23 pm 
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4:3 is (1:1)(4*3)
16: 9 is (2:1)(8*9)
16:10 is (2:2)(8*5)

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PostPosted: Thu Aug 06, 2009 8:31 pm 
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Rusty_Russell wrote:
realXCV, 4:3 is overloaded - it isn't just 4/3 it's 4x by 3y. To treat it as a fraction is to ignore it as a ratio.


Try looking at the back of the box of most movies, generally they are converted to a x:1 ratio. Eg, on the back of Casablanca, which is 4:3, it's labeled as 1.33:1, which is simply 4 divided by 3, rounded to 2 decimal places. On the back of The Dark Knight, it's listed as 1.78:1 for the IMAX scenes, calculated the same way (16 divided by 9). Just because it's converted to a x:1 ratio doesn't mean that it's no longer a ratio, however it's much easier to compare the wideness difference when it's all converted to x:1. For example, with 1.33:1, 1.78:1, and 2.4:1 (rounded to 2 decimal places), it's much easier to see the wideness difference compared to looking at it as 4:3, 16:9, and 12:5. For example, my netbook is 1024x768, which simplifies to 128:75 (1024/8:600/8), or, if converted to x:1, 1.70666...:1. For a 4:3 screen, 1024:768 simplifies to (1024/256):(768/256), 800:600 simplifies to (800/200):(600/200), both of which are 4:3, or 1.33....:1. If you take 1.33....:1 and multiply by 768 to both sides, you'll still get the proper 1024:768 that you'd expect.

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PostPosted: Thu Aug 06, 2009 8:33 pm 
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I understand that. You aren't understanding me though. Seeing 4:3 as only a ratio is just seeing half of the picture. It doesn't recognise the fact that 4:3 is referring to a rectangle 4x by 3y in size.

When you see that as a tile, you'll understand my viewpoint. I'm not contradicting anyone who says that 16:9 isn't 4:3. I know that their ratios are different (hence the stretching when viewing 4:3 on a 16:9 screen).


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PostPosted: Thu Aug 06, 2009 8:51 pm 
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Last time I checked, a 16:9 screen displayed only one picture not 12.

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PostPosted: Thu Aug 06, 2009 8:52 pm 
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Rusty_Russell wrote:
I understand that. You aren't understanding me though. Seeing 4:3 as only a ratio is just seeing half of the picture. It doesn't recognise the fact that 4:3 is referring to a rectangle 4x by 3y in size.


You aren't understanding ratios. Seeing 4:3 as a ratio does exactly what you are saying: that a screen/image/whatever is 4x by 3y, or in other words, the ratio of the dimensions is 4 to 3.

For example, 800x600 is a 4:3 aspect ratio. Why? Because 800/600 reduces to 4/3 -- 800/600 = 200*4/200*3 = (200/200)(4/3) = 4/3.

But in reality, it should be 4x by 3x, because both x and y are always going to be the same number.

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PostPosted: Thu Aug 06, 2009 9:00 pm 
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Herohtar wrote:
But in reality, it should be 4x by 3x, because both x and y are always going to be the same number.


It might be easier to say that x = 4z, y = 3z, or x = 1.33... * z, y = z, or maybe even x = 1.33... * y, take your pick.

Edit: Going a little bit further in the first one, to have fun in the land of algebra.
Code:
x = 4z, y = 3z (or, 3z = y)

Divide by 3 on both sides to solve for z

 3z     y
---- = ---
 3      3

     y
z = ---
     3

Now that we have z, go back to solving for x:
x = 4z

Substitute in what we found z to be, and we get:

     4y
x = ----
     3

And, of course, if we divide 4/3 in this case, then we get:
x = 1.33... * y

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PostPosted: Thu Aug 06, 2009 9:18 pm 
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I do understand ratios. Again, you're missing my point.


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PostPosted: Thu Aug 06, 2009 9:19 pm 
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Rusty_Russell wrote:
I do understand ratios. Again, you're missing my point.


Uh... what exactly is your point again? It seems to have changed along the course of this thread...

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PostPosted: Thu Aug 06, 2009 9:23 pm 
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:D

That's possible. I am no longer saying in any way, shape or form that 4:3 is 16:9.

You can look at 4:3 in two ways - as a function of x and y and as a fraction, same for 16:9. Because the two fractions are different, a 4:3 picture on a 16:9 monitor will be stretched.

I want to leave the fraction part aside altogether though. What I am saying is that 4x by 3y on 4x by 3y will give you 16x by 9y - and 4 * 3 4x by 3y tiles.

I tried using matrices to do a cartesian transform, but I used the wrong tool (hence my comment about wrong shovel earlier).

A rotation is a cartesian transform too, that's why I don't have any trouble building 16x by 10y from 8 rotated 4x by 5y tiles.


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PostPosted: Thu Aug 06, 2009 10:45 pm 
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Rusty_Russell wrote:
You can look at 4:3 in two ways - as a function of x and y and as a fraction, same for 16:9. Because the two fractions are different, a 4:3 picture on a 16:9 monitor will be stretched.


You can, but you'd be wrong. A ratio is not a function; it is an expression of a relationship between two or more values.

However, you can use a ratio in a function. For example, if you wanted to calculate the width or height of a 16:9 image you would create this equation: 16:9 = x:y or 16/9 = x/y. You can then create functions for finding the value of one of the two dimensions by solving for either of the two values. So let's say you have a 16:9 monitor that has a height of 1080... take 16/9 = x/y and solve for x (the width): x = (16/9)y = (16/9)(1080) = 1920. Thus a 16:9 monitor with a height of 1080 has a width of 1920. The same works for finding the value of y -- the equation becomes y = (9/16)x

Now, you can play around with x = (16/9)y or y = (9/16)x all you want, but you can't turn that into x = (4/3)y or y = (3/4)x using any mathematical rules -- the only way to do so is to just "brute force" swap out the ratio in there, making it an entirely different equation.

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PostPosted: Thu Aug 06, 2009 11:09 pm 
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You're taking function more literally than I'm using it. An expression of x and y would have been more correct, I guess.


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PostPosted: Fri Aug 07, 2009 12:51 am 
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Rusty_Russell wrote:
I understand that. You aren't understanding me though. Seeing 4:3 as only a ratio is just seeing half of the picture. It doesn't recognise the fact that 4:3 is referring to a rectangle 4x by 3y in size.
yes... that's what a ratio means...

Quote:
When you see that as a tile, you'll understand my viewpoint. I'm not contradicting anyone who says that 16:9 isn't 4:3. I know that their ratios are different (hence the stretching when viewing 4:3 on a 16:9 screen).

and now you're not making any sense.

Is it just me, or has this guy actually changed his argument from post to post and acted like he's still arguing the same point?[edit]no, it's just me...[/edit]

Rusty_Russell wrote:
You're taking function more literally than I'm using it. An expression of x and y would have been more correct, I guess.

LRN 2 English? If you're using a word wrong, you might want to choose a different word to use. If you're talking math, you'd better be using your terminology as literally as humanly possible, because math people are very literal people.

There's a reason the 2 in
Code:
int i = 2;

is called a Literal.


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