Page 10 - Developer

WHY WE COULDN’T view space or in NDC (Normalized in the bottom row), and each you still need to pass data through
USE STANDARD Device Coordinates) space. term has equal magnitudes but the GPU twice, which takes time.
STEREOGRAPHIC When projecting for stereo, we opposite signs for each view. The In our case, we were already up
PROJECTION add two additional transformations left view will have negative shear against the 30 fps boundary, so we
to represent the interaxial and and positive translation, while the had very little extra rendering time.
Before looking at our stereo convergence: an xz-shear S right view has positive shear and
reprojection solution, let’s and an x-translation T. Some negative translation.
quickly review how the standard implementations incorporate the So what do we choose for the OUR SOLUTION:
stereographic method works. The translation into the view matrix magnitude of S and T? They need to STEREO REPROJECTION
idea is that we are trying to provide and the shear into the projection be related; otherwise you will end up

to each eye (via shutter glasses, matrix, but I find it more compact with bad convergence and headaches The alternative to rendering
or polarization, anaglyph color, or to add both to the projection for your viewers. Other things that everything twice is to render color
head-mounted display) a view from matrix. The end result can be seen need to be taken into consideration and depth information for a single
that particular eye’s perspective. in Figure 2, showing both standard are your monitor/television size and view, then use the information
There are two pieces here: First, D3D and OpenGL perspective your horizontal field of view. A larger for that view to generate a stereo

each eye is displaced from the projection matrices. monitor implies that you will be pair—rendering the left view and
center by a certain distance, called sitting farther from it, which implies using it to create the right view,
the interocular distance. It’s this that less shear is required. And the for example. Because the original
displacement that allows stereo convergence distance in turn is image will not have the correct

viewing in the first place. Secondly, dependent on the field of view. projection for at least one of the

depending on what we’re focusing The set of equations that we views, we will have to remap the
on, the eyes will toe in or out when used in ALL 4 ONE can be found in color data to match the new view,
we look at a near or far object, Figure 3, partially derived from or perform reprojection. For the
respectively (see Figure 1). Samuel Gateau’s GDC 2009 talk on sake of the rest of the article
The interocular distance is about stereoscopic 3D [see Reference we’ll assume that unless stated
5–8cm, measured from the center 1] and the Sony documentation. As otherwise, we’ll be reprojecting
of each pupil. When working with we can see, S is dependent on the from a left view to a right one.
virtual cameras, we often refer to the interocular distance and monitor We will need to have access
interaxial distance instead. Because width, and T is dependent on S, to the color and depth images to

of toe-in, there will be a plane where convergence distance, and field of do this. If you’re rendering into a
points on that plane will project to view. This is a bit counterintuitive, backbuffer (or don’t have access to
the same screen position in both but it works quite well. a console that lets you just dip into
views. We call this the convergence memory and point a new texture
plane, and the distance to that to it), you’ll need to change your
plane is known as the convergence rendering approach. Fortunately,
distance. Points between the view if you’re using something like
points and the convergence plane FIGURE 2: Standard stereoscopic deferred rendering or deferred
projection matrices.
will have negative parallax (and will lighting, you’ll have already done
appear to stick out of the screen), this and will have textures available
and points behind the convergence Note that the shear and translation with this information. Otherwise,
plane will have positive parallax. have opposite signs (they end up you’ll have to use render targets in
Note that the units for these with the same sign in the OpenGL Direct3D or framebuffer objects in
distances could change, depending projection matrix because the FIGURE 3: Stereoscopic parameters. OpenGL for both color and depth.
on whether you are measuring in shear gets multiplied by the —1 While CRYSIS 2 was the fi rst
The process at this point is quite notable use of stereo reprojection in
simple: Render two views, one for games, it is not a new technology.
each eye, and send each image to Erik Benerdal described a similar
the display. Other than setting up approach on his blog in 2008 [see
the projection matrix, this doesn’t Reference 2]. Other reprojection
take much work, and in fact some approaches have used scatter-
stereo drivers take advantage of based splatting or image warping
this simplicity to automatically using meshes [see Reference
provide stereo for games. However, 3]. The technique I’m presenting
it does have one disadvantage: You here is a gather approach derived
do have to render the scene twice. from parallax occlusion mapping,
We could optimize this a bit, of which takes a color image, a depth
course; we could do all nonrendered image, and uses raycasting to

processing first, cull for the convex create the appearance of geometry
hull of both frustums rather than displacement within a shader.
one at a time, or generate a single A full description of parallax
FIGURE 1:
Stereoscopic 3D pushbuffer and only modify the mapping is outside the purview

frustum setup. projection matrices—but in the end of this article. You can find more
8 GAME DEVELOPER | OCTOBER 2012