Hmm…lol
According to that website 103 horizonal and vertical = 145deg:
So… if they calculated it that way then it would match up with the claim. Then a separate weird calculation maybe to get the 120 horizontal?
Who knows haha. I’d love to see this be addressed anyway, just to get clarity.
So then they calculated incorrectly. You can’t use pythagoras for FoV calculations, that’s a n00b beginner mistake like @jojon pointed out LOL
Hopefully the reality is that the FOV is larger then the numbers we got here, but who knows. I will say I was happy with what I saw, so I at least know I would be happy with the Crystal, but had I not tried it myself then these numbers would have turned me off.
Diagonal FoV is a horrible way to measure any VR headset anyway. Horizontal/Vertical always makes vastly more sense.
And, yes, Risa’s tool does grab the rendered FoV the headset itself reports.
Your quiry would best to ask @risa2000 if that is from his hmdq program. As he can explain how it calculates.
The math is correct, or is in the right ballpark. The tool you used to calculate the FOV, does not do just the geometrical calculation, but also takes into account the HAM (hidden area mask) which may limit a diagonal FOV.
If you have a look at the HMDGDB database at, for example, Pimax 5k Plus page (Pimax 5K Plus (Normal FOV, Parallel Projection ON, 90Hz) | HMD Geometry Database), you can notice in the FOV visualization render that diagonal FOV is limited by the HAM in the peripheral corners and does not even reach the theoretical value the perfect frustum would have.
Just a note: The different FOVs (angles) are marked by triangles of different colors: yellow - vertical, red - overlap, magenta - peripheral, and cyan - diagonal.
Now coming back to the calculation for simple FOV of the shape of perfect frustum - i.e. one which does not have a HAM.
If I take your example, with vertical and horizontal FOVs being the same (i.e. 103°) and the frustum being symmetric, i.e. having the “left”, “right”, “top” and “bottom” FOVs being the same (i.e. 51.5°), calculating the diagonal FOV can be done relatively easily this way (I am using Python console to demonstrate the arithmetic operations):
IPython 8.4.0 -- An enhanced Interactive Python. Type '?' for help.
In [1]: from math import *
In [2]: hor_fov = radians(103)
In [3]: ver_fov = radians(103)
In [4]: half_tan_hor = tan(hor_fov/2)
In [5]: half_tan_ver = tan(ver_fov/2)
In [6]: half_tan_diag = sqrt(half_tan_hor**2 + half_tan_ver**2)
In [7]: half_diag = atan(half_tan_diag)
In [8]: diag_fov = 2 * half_diag
In [9]: degrees(diag_fov)
Out[9]: 121.28813765330132
Just to check the intermediate values:
In [10]: hor_fov, ver_fov, half_tan_hor, half_tan_ver, half_tan_diag, half_diag, diag_fov
Out[10]:
(1.7976891295541595,
1.7976891295541595,
1.2571722989189547,
1.2571722989189547,
1.7779101153709482,
1.0584386728311084,
2.1168773456622167)
You may notice that I am also using Pythagoras theorem in my calculation, but I am using it on tangent values (to get another tangent), and I can use it only because the frustum is symmetric and the diagonal “crosses” the frustum axis.
For non symmetric frustum the calculation is done purely in 3D Euclidean algebra by using vectors and operations on them.
Heh… These are early reported numbers, so maybe we’ll see others, come future drivers and ocular tests, but the thought still strikes me to wonder how close to reality one might end up, were one to take the proportional difference between advertised and so-far reported actual FOV for the Crystal, and applying it to the advertised one for the 12k… :7
Thank you guys ! Good lesson again as always !
Non-Euclidean geometry meets PC-Gamers 
Actually it is perfectly Euclidean geometry, just in 3D 
.
Ah, yes, but is it hyperbolic or spherical?
But again: I’m not sure the lens-types aren’t to blame. None of the above accounts for the lenses. Comparing the aspherical profile of the Crystal to the 8KX may be altogether invalid.
Wonder if this guy could give us an HMDQ for the PP mode off…
Well, I think the cope is over, not looking like it’s the wrong profile. The tester posted the SteamVR resolution at 100% with PP both on and off.
4352 x 5100 on, 4248*5100 off
This tracks with what Pimax posted a while back of the Crystal’s resolution(Keep in mind slight variance for IPD, he said he used software tweaks)
Here. Somebody also reported 3856x4560 at 80% SS in EU roadshows. Which tracks with these numbers. They’re also somebody who was very insistent the FoV was bigger than the Index.
It’s uh, yeah. Looking like that 103 FoV is all correct here. That’s… Yeah ow.
@PimaxUSA @hammerhead_gal @SweViver @PimaxQuorra
Can we get some official word on this? These FOV results are a massive difference from what the crystal spec sheet claims.
Months ago I asked why no one had done the ROV test. All those Roadshows not one FOV result.
Weeks ago I PM’d Kevin asking how the lenses were identified, I got no answer.
A week or too ago I PM’d Pimax recommending they send final retail boxes to the testers. Thus eliminating any mixups. No answer.
Is it a lens mix up? Is it the added Millimetres to the lens spacing? Is it wrong measurements? Answers on a postcard.
I mean it has to be. If the FoV would really be 80 degrees for the 35 PPD lens then people would have said things during the roadshows. No way anyone would think that would be a good FoV, that’s just a horrible FoV. Also the ROV numbers line up pretty well with the Risa tool numbers for the 42 PPD lens.
Then it begs the question, how hard is it to identify these lenses? Why is Pimax not bringing their own ROV results to the table? How many more mixups is Pimax going to make? Who’s in charge of all this?
Maybe Pimax is taking your advice and staying quiet on promises and delivery dates.
But FOV?
I just tried my Pico4 and get maxed 110 degrees horizontal in ROV.
