From: ROBIN HOLLANDS Subject: TECH: HMD quality Date: Tue, 3 Oct 1995 17:29:14 +0100 From: ROBIN HOLLANDS There has been much discussion both on the newsgroup and via email about Marc Bernatchez's measure of quality of HMDs. Whilst I agree that HMD choice is subjective and therefore qualitative discussion cannot really be disproved since its simply a matter of choice, Marc has chosen instead to put numbers to everything. The measure of quality is simply a cost function, similar to cost functions used to optimise industrial and other processes. As a veteran of industrial simulation and automatic optimisation, I know that these things can be very temperamental to the weighting (i.e. the 'importance') given to each parameter. The only way to see what the implications are of your decisions is to look at the entire mathematical surface resulting. If you don't like numbers move on now! Marc's costing is as follows: > Taken from my web page... > > har = 0 --> 100% to har = 20 --> 0% > > FOV = 180 --> 100% to FOV = 10 --> 0% > > Price = 0$US --> 100% to Price = 1M $US --> 0% (nb: the price as been > evaluated on an > exponential basis, i.e.: 100 $US = 66.6% , 1000 $US = 50% , 10 000 $US = > 33.3% , ... ) > > The way I have done it is, to my opinion, ensuring that the weighting is > only dependent of the human factors for the two first parameters. Take the > har (horizontal angular resolution). An infinite resolution gives 100% for > this variable. I chose a 20 arc minutes per pixel to be the bare minimum (at > this point you're less than legally blind). Same thing for the FOV. At 180 > degrees of field of view, which is about the limit of the human field, I > fixed a 100% rank. And then again I chose an arbitrary 10 degrees of FOV as > the minimum (which is half the required 20 degrees of FOV for human stereo > overlap region). Finally, for the price, I just used the actual price range > for HMDs on the market. Since quality improvement versus price shows to be > exponential, so I did for this variable. > > So the ranks will still be valid in five years from here (hopefully) with > these weighting. I.e.: You should never see ranking higher that 100% even > ten years from here. The first thing to realise is that a cost function should be based in *independant* variables. Field of view and acuity are linked via the number of pixels on the display, and are therefore not independant. A better choice is to start with physical display resolution and field of view (FOV), from which the angular resolution naturally follows. To simplify matters, also ignore the price weighting for now, since price is determined primarily by market forces, and also has an affect on the constraints applied to both possible screen resolution (the best screen you can get for the price), and FOV (what optics can you afford). Using Marc's numbers above, you get the following: Angular resolution=Field of View/Number of Pixels AR=FOV/N Quality = (FOV-10)*(1/170) + (0.3-AR)*(1/0.3) {FOV Quality} + {AR Quality} Q=(FOV-10)*(1/170)+(0.3-(FOV/N))*(1/0.3) working through gives... Q = FOV * (0.0059 - 3.33/N) + 0.941 For a given display resolution, quality changes linearly with FOV. On the assumption that you get the best display resolution that your final budget will allow (e.g. most consumer HMDs use more or less the same physical resolution screen), what value should you use to maximise Marc's level of quality? Because the quality measure is linear, the maximum value will always be at one end of the line or the other, never a happy medium. In fact, examining the maths shows that for any display resolution less than 564 pixels, you must reduce the Field of View to a minimum to maximise quality (i.e. the best consumer HMD would have a 1 degree field of view - check the maths!). Over 564 pixels you maximise quality simply by getting the widest field of view you can. At around 564 pixel resolution, you can choose whatever field of view you feel like, because the quality will always be around 94% Even if you stop the quality factor from angular resolution going negative greater than 0.2 degrees per pixel, you simply end up with a kink in the centre of the line where the FOV causes the angular resolution to be less than 0.2 degrees a pixel. Whilst this does mean that between 40 pixels to 564 pixels you can either maximise quality by either reducing the FOV to a minimum or making it really big, the most practical solution would still most often be to reduce the FOV to near 0. Check the numbers out for yourselves, and you'll see my original concerns shown in the maths. Marc had chosen 'common sense' numbers for his measure of quality, but as you see from above, 'common sense' is always correct. Marc had also given me the opportunity to work with him to create a better measure, but I'm firmly of the opinion that we know so little about the human factors of HMD design that any discussion now is simply philosophical, and certainly nowhere near a mathematical structure. Cheers, Robin P.S. I estimate that the Nintendo VirtualBoy has a quality rating of over 95% compared with 50% to 70% value of other consumer HMDs. And I hate it! Robin***************************************************************** * Dr Robin Hollands : * * Reply to: : e-mail: * * s-mail: : R.Hollands@Sheffield.ac.uk * * AC&SE Dept. :---------------------------------* * Sheffield University : 'Just because something doesn't * * Mappin Street : do what you planned it to do * * Sheffield S1 4DU -- UK -- : doesn't mean it's useless.' * * voice +44 (0)114 2335622/2825186 : - T.Edison * * fax +44 (0)114 2731729 : * **********************************************************************