Dear Manu,
this is an interesting search and I am glad your pursuing your own idea.
However let me just give you a quick hint :
1. Speed and size of the con are of utmost importance here regarding distance at witch you can spot a bandit.
In the diag above, you show us that the cone of visual lock (let's call it
CoVL) is of a complex shape : widely expended and then narrowing itself when the distance is increased to a point that it is only a narrow pencil.
At first I wld like to make a remark. Tunnel of vision is what a fighter pilot experience flying low at high speed in a jet. The vision in neat only in the far distance in front of the pilot and the surrounding area is blurred.
Rapidly, without demonstration man can understand that the time available for the retina to "print" an object is the leading factor for the neat vision. If you turn your head 30° out of your axis of view, the object on focus will travel beside you at V/sin30 speed (=2*V). The time for the "retina print" (let's call it
RP) will be divided per two. Compared to an object directly in front of you, teh time for your brain to act in reconnaissance/analysis mode will be divided per 8 if we consider that it's a volume print (both eyes are simultaneously focusing on the same points).
You see now why it's so difficult to distinguish a rapid object even if he is traveling right nearby.
Now that we hve introduced the volume factor leading to a full recognition, let's hve a look of the variable ctrling an identification of a shape (the leading cause to the "there is something there" sentence)
In order to get a (positive) identification (let's call it PI), you hve only to see that a point (unreal : there is no point in mother nature) or a surface is right where you are looking at. Looking at the RP factor and the difference in speed in the above example, we see that the time required for the reconnaissance is 4 time superior at 30 deg than at 0deg.
And there is where the nasty camo plays its part.
Remember that we are talking here with surface and that this surface is nothing else that the averaged contrast with the background. If I am flyiong above a forest and look at a bright orange triangle, the time the brain has with a given RP depend only to it's size and shape. Imagine now, that the surface is painted with a finely tuned pattern of color that blend quite well with the background. Here the averaged contrast ratio is perturbed by the difficulty to make an identification of what is the surrounding background and was is not in that very specifically part of the image. This add time that hev to be subtracted from the available RP to get a PI.This can be summed in a blend factor (
BF) analytically like :
If Cammo : RP:=RP/k with k being the BF
All the above is fairly basic for you and just an other way to say what you hve alrdy explained to all of us in your excellent post.
Now let's take the problem upside down.
Now we are not flying extremely fast low but at WWII patrol speed that said 1/3rd to 1/4th of the speed we were talking in the above.
Time is a function of distance and speed with
t=d/v and reciprocally distance is a function of time and speed
d= v*t
without looking at anything less and focusing ONLY on the above eq. we can understand that
RP= f(d/v) | eq. (i)
PI= f{(v*t)*(v*t)} | eq. (ii)
Then we we can say that at a given time (and same RP) traveling at
4v while sighting at
d is "like" traveling at
v and sighting at
4d.... (Wew what a big step ! I hope you are still there - but remember, don't look at the significance of the value, just at the variable and the way they interact each others)
In the above conditions the PI at v (let's say
PI(v)) would be "reached" 16 time faster.
What does is says is that your sensor (eyeball) scanned zone for a given surface would be insistently 16 time bigger in volume than at 4 time the speed. We hve seen (or more honestly admitted or even more made the hypothesis) that the axis vision is not imparted by the speed at witch your pilot travel giving is head is contently up and his eyes are focused right on his vector of motion. Hence the corresponding volume is 4 time bigger at the base - the volume of a cone being a function of PIr² the circular base and 1/3 of h its height.
So when traveling at 1/4teh the speed, your PI planar zone for a given RP depending of the time available for the scan is 4 time bigger.
In your picture, the 100% "look zone" wld be 4 time bigger.
Now the hardest part (I 'll let those that hve read the above lines so far solve the volumetric case):
What abt the scanning distance that obviously impart the shape of the CoVL with target being acquired sooner than an other one just right beside her?
Saying that we give the answer. hehe
There is one thing that we are all aware of is the target aspect ratio. We know that teh bigger the shape present a target the more probable our canon will score a hit. Hence size matter.
Regarding the visual acquisition things are similar. The biggest the apparent shape, the earlier it will be spotted.
But let's see what is that apparent shape about.
We saw earlier that de-cluttering the background is what ease the brain for a given RP. Let's imagine a bright orange surface traveling at 30° offset at a speed v. The "de-cluttered" surface is of a size function of it's shape (aspect ratio) and the distance traveled for a given RP. Let's say now that the same surface in the same geo condition is traveling 4 time faster, the de-cluttered surface wld be more than 4 time bigger ("more" and not equal as there is the trapeze effect well known of any artist - but the diff is negligible).
Hence my PI with a target traveling 4 time faster is 1/4th of a time.
Hummm not weird... In the above we concluded that the faster we are moving the less RP we hve hence the decreased PI [huge case of sneaky editing - sry]
In fact in both conditions the speed is the relative speed of both our pilot and his target. Let's say that I am flying slower and slightly above of my target. For a given time
t the corresponding RP will be "'bigger" due to the de-cluttered shape swept by the faster move of the target. Hence a lowered PI time
Now let's see what happens if while still flying slightly above my target, I am flying now much faster than the potential contact. As I am travelling faster than him regarding the de-cluttered zone will be smaller and the target shape will evolve more in a volumetric manner - what we hve seen takes averagely more time to be interpreted (8x).
We can admit that it's a matter of balance averaged by a typical Gaussian curve (the rounded mountain like curve).
This is where Manu, your dispersiveness in target acquisition came from ; the relative speed of the observer and the target.
We can analytically summed this with the generalized form of equations :
PI(t) = f(RP, k, q) with k alrdy defined above and q(v) a factor for the Gaussian effect.
Please that note that k and q are kfor a give pilot a given days in given meteorological condition (ok ok you know that just wanted to add some sophisticated word to my rather simplistic demo
)
My guess would be something like PI = k/q*RP (t) with q like 1/v²1 - 1/v²2 and v1 and v2 the relative speed of the pilot and the target.
SO what about the CoVL : That where I thing my demo has some points of interest in the fact that the CoVL is the integrand in time of the PI with the time being the actual time of scanning. Obviously the instantaneous time disappear with the (i) form of the RP like
CoVL = Int.[k/q*RP] from -15° to 15° in a second = Int.1
hence
CoVL= Int.[Int.1]in distance and speed (=Int.2)
or using IntVol [div f] = IntSurf[f] and some mixing magics
we've got something like IntVol = RP (instantaneous)/(ScanedVol in 1 sec)
with RP (inst) = k/q*(d/v) with v the speed of the pilot and d the decreasing dist btw them
and ScannedVol being calculated with the scanned surface and the distance traveled per sec and a cumulative factor.
The cumulative factor hving been discussed somehow by you earlier and translate the persistence of the target in the brain being correlated with it's actual position with its estimated trajectory.
Something like Cf =c*{1-(TAR(t0)-TAR(t))} * PI(t0)/{(t-t0) *R(Ttrj)}
with TAR being the Target Aspect Ratio at a given time
t0 being the time of the initial scan in the zone of the target to correlate
c reflecting the pilot consciousness
R(Ttr) is the rate of change of target trajectory
2. What the hell is the interest to add so much new variables (my demo lack some and prob not in negligible number) ?
At first, let's remind that a sim world is a world where there is no hazard and everything is known and dully characterized.
Secondly let's remind that using the random hard fction consume time.
In your demonstration 6S.Manu, the target acquisition range is supported by a series of calls to the random fction at each frame that will invariably impact the FPS IMHO.
As we know each plane position, the TAR, the speed and all the value needed, it cld be more profitable to use something in the form of the (very long - sry) demonstration.
Once a PI is scored a target reconnaissance process can begin that as I hve alrdy advocated cld be some form of image dilution from blur to neat (a pre-processed sprite ?). But I know certainly nothing on that relatively to our prof devs.
Only my 2 cents !
~S!