Graphics Reference
In-Depth Information
Traditional
z
-buffer, 24-bit
10
2
2
16-bit integer
z
-buffer
10
2
4
Bad
16-bit warped
z
-buffer
10
2
6
10
2
8
10
2
10
Good
Zfar
= 50 miles
Znear
= 25 feet
10
2
12
10
2
4
10
2
3
10
2
2
10
2
1
10
0
Z
eye
Figure 36.14: Comparison of precision versus depth for various z-buffer representations:
24-bit fixed point (green) is obviously strictly more accurate than 16-bit fixed point (blue);
16-bit floating point is more accurate than 16-bit fixed point when far from the camera (on
the right), but has less precision very near to the camera (on the left). The blue and green
curves are lines in log-log space, but would appear as hyperbolas in a linear plot. The
red floating-point line is jagged because floating-point spacing is uniform within a single
exponent and then jumps at the next exponent; the red curve is a smoothed trendline.
These mappings assign relatively more precision close to the near plane
(where
z
-fighting artifacts may be more visible), have a normalized range that is
appropriate for fixed-point implementation, and are expressible as a matrix multi-
plication followed by a homogeneous division. The amount of precision close to
the near plane is based on the relative distance of the near and far planes from the
center of projection. As the near plane moves closer to the center of projection, all
precision rapidly shifts toward it, giving poor depth resolution deep in the scene.
A
complementary
or
reversed
hyperbolic [LJ99] encoding maps the far plane
to the low end of the range and the near plane to the high end. For a fixed-point
representation this is usually undesirable because nearby objects would receive
higher depth representation errors, but under a floating-point representation this
assigns nearly equal accuracy throughout the scene.
Another advantage of the nonlinear depth range is that it is possible to take
the limit of the mapping as
f
[Bli93]. This allows a representation of depth
within an infinite frustum using finite precision.
→∞
Inline Exercise 36.4:
For
n
=
1m,
f
=
101m, compute the range of
z
-values
within the view frustum that map to
[
0, 0.9
]
under the OpenGL projection
matrix. Repeat the exercise for
n
=
0.1m. How would this inform your choice
of near and far plane locations? What is the drawback of pushing the near plane
farther into the scene?
