# (MATH) For "Retina" tag next macbook pro must pack with 202 ppi display

Discussion in 'MacBook Pro' started by Amethyst, May 14, 2012.

1. ### Amethyst macrumors 6502a

Joined:
Aug 8, 2006
#1
According from apple equation.

a = 2 tan-1 (h/2d)
It can revert to
h = 2d * tan ( a / 2 ) <----(a)

If you want retina display give a = 0.00029

d is distance from your eye to display that around 1.3x of display size
for most case so
d of 11 = 13.3 , 13 = 17.3 , 15 = 19.5 , 17=22.1 , 21 = 27.3 , 27 = 35.5

For some case d is not 1.3x so i assume new d
11 = 15 , 13 = 17 , 15 = 18 , 17=20 , 21 = 24 , 27 = 26

From (a) we ill get h = 2(d)tan(0.00029/2)
11 = 0.00435 , 13 = 0.00493 , 15 = 0.00522 , 17=0.0058 , 21 = 0.00696 , 27 = 0.00754

So ppi = 1/h
11 = 230, 13 = 202, 15 = 192, 17 = 173, 21 = 144, 27 = 133

2. ### Amethyst thread starter macrumors 6502a

Joined:
Aug 8, 2006
#2
So i guess

11" and 13" must use 2048x1536 display res that pack 232 and 196.92 ppi.

15" and 17" can use same 2560x1440 display res because it will pack 196 ppi and 173 ppi that pass retina quality.

So 22" imac must use 2560x1440 display res that pack 140 ppi

And the last big thing 27" will use 3840x2160 with 163ppi

3. ### prism macrumors 6502a

Joined:
Dec 6, 2006
#3
And I would predict that all this, if true, will kill any significant performance gains from the GPU with games played in native rez!

4. ### jsnuff1 macrumors 6502a

Joined:
Oct 4, 2003
Location:
NY
#4
I don't even think there are games that can even support these resolutions.

5. ### Amethyst thread starter macrumors 6502a

Joined:
Aug 8, 2006
#5
I think game will not run on native resolution on these display.

6. ### theSeb macrumors 604

Joined:
Aug 10, 2010
Location:
Poole, England
#6
Even old games like crysis can run at 5760x1200. You need SLI or a a dual GPU for that though.

Joined:
Oct 29, 2011
8. May 15, 2012
Last edited: May 15, 2012

### DrJohnZoidberg macrumors member

Joined:
Mar 16, 2012
#8
The rest of your math appears to be correct, but I don't think the assumptions of viewing-distances are right. I'm writing this on an 11" notebook* and I'm about 20" from the screen (rather than the the 15" you assume).

Viewing distances for notebooks tend to be dictated more by the distance between the user and the keyboard, which is not dependent on screen size, but rather on the user's arm length.

Being short-of-stature, and using the smallest practical screen-size (11"*), I doubt you will find many who view a notebook screen closer than I (~20"), but people with longer arms will probably have viewing-distances closer to 24". I would guess that assuming a viewing distance of 21" (for all notebooks, irrespective of screen-size) would ensure the 'Retina' threshold was exceeded for most people.

At a viewing-distance of 21" my math (not same as yours, but appears to be the same as this guy) says a ppi of 164 would be needed to qualify as 'Retina' (for all notebooks).

I could be wrong, but I think the only standard resolution that would achieve this (for a 15" MBP at the present 16:10 aspect-ratio) is WQXGA (which is 2560×1600). The 13" MBP would need a WUXGA (1920×1200) screen to exceed the 164 ppi threshold.

Obviously this is all conjecture, and it actually comes down to what Apple decide is the normal viewing-distance. It'll be interesting to come back to this thread in a month and compare our guesses with what Apple actually release.

* Edit: I'm suffering from brain-fade. I'm using a 12.5" notebook, not an 11" as I previously wrote.

9. ### Sarmiento macrumors member

Joined:
Mar 31, 2011
#9
Guess if this is true then you have it...