Measuring perceived depth in S3D games
Posted: Wed Mar 23, 2011 12:05 pm
Continued from this post on the thread "My PS3 3D Gaming Experience" : http://www.mtbs3d.com/phpBB/viewtopic.p ... 294#p58294" onclick="window.open(this.href);return false;
I wondered what the perceived depth would be for this Crysis 2 screenshot, so I calculated the depth for each parallax distance I measured, by using the Acer GD245HQ 24'' monitor as a reference (the one used for the screenshot).
I also considered the viewing distance to be 3.1ft (94,48cm) because it's the limit of visual acuity for this display (ie. fully resolved 1080p for 20/20 normal eyes) and a standard eye separation of 6,5cm.
This gives the following formula (thanks to Thales) :
(p / 2) / (s / 2) = D / (D + d) (formula 1)
Where
P = parallax between two points on the screen in cm
s = eye separation (6,5 cm)
d = viewing distance (94,48 cm)
D = depth inside the screen in cm (the value we want to calculate)
Here are the measured values in pixels followed by the value for parallax (1920 - measured distance) :
- green HUD in lower left : 1915 pixels (5 pixels)
- yellow part of the arm : 1893 pixels (27 pixels)
- farthest part of the gun : 1881 pixels (39 pixels)
- white thing on the ground at the left of the hand : 1867 pixels (53 pixels)
- black and yellow frame on the ground in the left : 1864 pixels (56 pixels)
- poster in the bathroom : 1863 pixels (57 pixels)
We need to convert these parallax values in centimeters to obtain p :
p = parallax * screen_width / pixel_width (formula 2)
The pixel width is 1920 and the screen width in centimeters is given by :
screen_width = 16 * diagonal / sqrt(337) = 53,13cm
Using (2) and the real values, we now have this equation for (1) :
(parallax * 53,13) / 3840 / 3,25 = D / (D + 94,48)
Using the free trial of Derive 6.1 to solve the formula for the distance from the screen (d), we obtain the following equation :
D = (4183102 * parallax) / (25 * (416000 - 1771 * parallax))
Here are the results obtained, in cm behind the screen plane :
- screen plane (0 pixels) : 0cm
- green HUD in lower left (5 pixels) : 2,05cm
- yellow part of the arm (27 pixels) : 12,27cm
- farthest part of the gun (39 pixels) : 18,80cm
- white thing on the ground at the left of the hand (53 pixels) : 27,53cm
- black and yellow frame on the ground in the left (56 pixels) : 29,57 cm
- poster in the bathroom (57 pixels) : 30,27cm
I think it better illustrates the depth one is supposed to see with this game on a 24" 1920p 3D monitor. It shows than in this configuration this game looks like it's trapped in a box of dimension 53 x 29 x 30 cm (W x H x P). Way to go for immersion...
I wondered what the perceived depth would be for this Crysis 2 screenshot, so I calculated the depth for each parallax distance I measured, by using the Acer GD245HQ 24'' monitor as a reference (the one used for the screenshot).
I also considered the viewing distance to be 3.1ft (94,48cm) because it's the limit of visual acuity for this display (ie. fully resolved 1080p for 20/20 normal eyes) and a standard eye separation of 6,5cm.
This gives the following formula (thanks to Thales) :
(p / 2) / (s / 2) = D / (D + d) (formula 1)
Where
P = parallax between two points on the screen in cm
s = eye separation (6,5 cm)
d = viewing distance (94,48 cm)
D = depth inside the screen in cm (the value we want to calculate)
Here are the measured values in pixels followed by the value for parallax (1920 - measured distance) :
- green HUD in lower left : 1915 pixels (5 pixels)
- yellow part of the arm : 1893 pixels (27 pixels)
- farthest part of the gun : 1881 pixels (39 pixels)
- white thing on the ground at the left of the hand : 1867 pixels (53 pixels)
- black and yellow frame on the ground in the left : 1864 pixels (56 pixels)
- poster in the bathroom : 1863 pixels (57 pixels)
We need to convert these parallax values in centimeters to obtain p :
p = parallax * screen_width / pixel_width (formula 2)
The pixel width is 1920 and the screen width in centimeters is given by :
screen_width = 16 * diagonal / sqrt(337) = 53,13cm
Using (2) and the real values, we now have this equation for (1) :
(parallax * 53,13) / 3840 / 3,25 = D / (D + 94,48)
Using the free trial of Derive 6.1 to solve the formula for the distance from the screen (d), we obtain the following equation :
D = (4183102 * parallax) / (25 * (416000 - 1771 * parallax))
Here are the results obtained, in cm behind the screen plane :
- screen plane (0 pixels) : 0cm
- green HUD in lower left (5 pixels) : 2,05cm
- yellow part of the arm (27 pixels) : 12,27cm
- farthest part of the gun (39 pixels) : 18,80cm
- white thing on the ground at the left of the hand (53 pixels) : 27,53cm
- black and yellow frame on the ground in the left (56 pixels) : 29,57 cm
- poster in the bathroom (57 pixels) : 30,27cm
I think it better illustrates the depth one is supposed to see with this game on a 24" 1920p 3D monitor. It shows than in this configuration this game looks like it's trapped in a box of dimension 53 x 29 x 30 cm (W x H x P). Way to go for immersion...