Page 16 - Developer

references
i
t
e
c
o
rix an
d p
t
n m
a
e s
t
l
t
y
e
o
j
r
re
o p
r
h
e l
s u
t
o t
e
w giv
ft vi
e
e
s
c
t
e
o
j
in
t in
o
in
g a p
Using the D3D-style stereo projection matrix and projecting a point into the left view gives us: :
e D3D-
U
h
s
sin
g t
[1] Gateau, Samuel. “The In and
Out: Making Games Play
Right with Stereoscopic 3D
Technologies.” GDC 2009, http://
developer.download.nvidia.com/
presentations/2009/GDC/GDC09-
3DVision-The_In_and_Out.pdf
[2] Benerdal, Erik. “Generating
stereoscopic images with parallax
occlusion mapping,” www.scalari.
net/2008/04/22/generating-
stereoscopic-images-with-
parallax-occlusion-mapping
Aft e r t h e re c ip r oc al divi d e an d c o n si d e rin g o nl y t h e Subtracting these gives the displacement between [3] Didyk, Peter, Tobias Ritschel, Elmar
After the reciprocal divide and considering only the
Subtracting these gives the displacement between
x x x values, we end up with: : the left and right views in NDC space: Eisemann, Karol Myszkowski,
x values, we end up with:
the left and right views in NDC space:
d u
valu
e e
h
, w
s
p wi
n
e
t
and Hans-Peter Seidel. “Adaptive
Image-space Stereo View
Synthesis.” In Vision, Modeling,
and Visualization (2010), Reinhard
Koch, Andreas Kolb, Christof Rezk-
Salama (Eds.)
[4] Brawley, Z., and Tatarchuk, N.
2004. “Parallax Occlusion Mapping:
However, NDC space has a range from -1 to 1.
However, NDC space has a range from -1 to 1. Self-Shadowing, Perspective-
To convert this to a displacement for texture
To convert this to a displacement for texture Correct Bump Mapping Using
coordinates, which range from 0 to 1, we halve the
coordinates, which range from 0 to 1, we halve the Reverse Height Map Tracing.” In
x
x
ul
o
r is t
f n
-
distance, which gives us:
s
s
e re
t
n
n
e
h
e
_c
n
Where x_center is the result of non-stereo projection. . distance, which gives us: ShaderX3: Advanced Rendering
Where x_center is the result of non-stereo projection.
i
t
t o
o
c
re
o p
t
e
j
e
r
o
with DirectX and OpenGL, Engel,
Expanding and simplifying, we end up with: W., Ed., Charles River Media, pp.
Expanding and simplifying, we end up with:
135-154.
[5] van de Hoef, Marries, and Bas
Zalmstra. “Fast Gather-based
Construction of Stereoscopic
Images Using Reprojection.”
Utrecht University, 2011.
S
arl
y t
e
i
w
am
e
a
e s
h
p
c
l
e a
e
, t
f w
h
l
If we replace S with s, this is clearly the same as the
If we replace S with s, this is clearly the same as the
his is c
I
s t
e re
th
wh
equation in Figure 6, so s is just S when reprojecting
o
equation in Figure 6, so s is just S when reprojecting
p
r
j
t
in
n re
c
e
e
g
from a left eye view to a right eye view. Note that for
from a left eye view to a right eye view. Note that for
center reprojection, we would split the difference
center reprojection, we would split the difference
going from center to left and center to right, and so
going from center to left and center to right, and so
halve the displacement.
halve the displacement.
o
t
an
r c
o
r
t fo
his
g t
in
m
p
ut
, si
ain
s are im
gn
Again, signs are important for computing this:
Again, signs are important for computing this: :
g
A
p
x
x
for reprojecting and rendering the left eye, we’d use
(Recall that d is cot(fov/2)). Similarly, for x_right:
(Recall that d is cot(fov/2)). Similarly, for x_right: t : fo r re p r o j e c t in g an d re n d e rin g t h e l e ft e y e , w e ’ d u s e
_ri
gh
for reprojecting and rendering the left eye, we’d use
t t
h
e in
e
h
, w
e
r t
v
–s, +sc/z, –S, and +T. For the right eye, we invert the
r
–s, +sc/z, –S, and +T. For the right eye, we invert the
y
gh
t e
e ri
o
. F
e
signs and so use +s, –sc/z, +S, and -T.
signs and so use +s, –sc/z, +S, and -T.
s
h
e
t
ui
ul
f t
e
t is q
e ni
e g
d re
h
c
et m
n
e e
. W
T
The end result is quite nice. We get most of the
t o
o
s
The end result is quite nice. We get most of the
speed benefits of reprojection, with the good-looking
speed benefi
e
n
e
d b
ts of reprojection, with the good-looking ts of reprojection, with the good-looking

e
fi
s
p
e
alpha of standard stereo, and all it took was a little bit
alpha of standard stereo, and all it took was a little bit
alp h a o f s t an d ar d s t e re o , an d all i t t o o k wa s a li t tl e b i t
of math and some extra setup.
of math and some extra setup.
that the alpha-blended objects will primarily dependent on our DIY 3D code.php. I’m looking forward to
have the correct depth occlusion. convergence plane distance c seeing how you improve upon it in
Secondly, we must compute and our interocular distance i. In That’s the whirlwind tour your future games!
standard stereo projection matrices reprojection we have the same of our implementation of 3D
that will match up with our convergence plane distance, but stereoscopy in RATCHET & CLANK: JIM VAN VERTH has beenworked in the
reprojected result. we have a different value s that ALL 4 ONE. I hope this gives you games industry since 1996, and is
probably bears some relation to some direction in writing your currently a senior engine programmer at
MATCHING STANDARD the interocular distance. However, own version of 3D stereoscopic Insomniac Games. He’s also co-author of
AND REPROJECTION it’s unclear what that would be reprojection, no matter the the book Essential Mathematics for Games
STEREO to match the standard stereo platform. To give you a starting and Interactive Applications. You can email
projection. To determine that, let’s point, I’ve created an OpenGL him at jim@essentialmath.com.
Remember that we have project a point into left and right demo demonstrating the basic
two variables for our standard NDC space and measure the delta techniques, which you can find RATCHET AND CLANK images courtesy/
stereo: S and T, which are between them in the x direction. at http://gdmag.com/resources/ copyright SCEA 2012
14 GAME DEVELOPER | OCTOBER 2012