Graphics Reference
In-Depth Information
y
A light source
x
n
2
z
z
v
o
v
i
Camera
(or eye)
P
A triangle
Figure 15.1: A specific surface location P that is visible to the camera, incident light at
P from various directions
{
v
i
}
, and the exitant direction
v
o
toward the camera.
To keep things simple, we assume a pinhole camera with a virtual image plane
in front
of the center of projection, and an instantaneous exposure. This means
that there will be no blur in the image due to defocus or motion. Of course, an
image with a truly zero-area aperture and zero-time exposure would capture zero
photons, so we take the common graphics approximation of estimating the result
of a
small
aperture and exposure from the limiting case, which is conveniently
possible in simulation, albeit not in reality.
We also assume that the virtual sensor pixels form a regular square grid and
estimate the value that an individual pixel would measure using a single sample at
the center of that pixel's square footprint. Under these assumptions, our sampling
rays are the ones with origins at the center of projection (i.e., the pinhole) and
directions through each of the sensor-pixel centers.
1
Finally, to keep things simple we chose a coordinate frame in which the center
of projection is at the origin and the camera is looking along the negative
z
-axis.
We'll also refer to the center of projection as the eye. See Section 15.3.3 for a
formal description and Figure 15.1 for a diagram of this configuration.
The light that arrived at a specific sensor pixel from a scene point
P
came
from some direction. For example, the direction from the brightest light source
in the scene provided a lot of light. But not all light arrived from the brightest
source. There may have been other light sources in the scene that were dimmer.
There was also probably a lot of light that previously scattered at other points
and arrived at
P
indirectly. This tells us two things. First, we ultimately have to
consider all possible directions from which light may have arrived at
P
to generate
a correct image. Second, if we are willing to accept some sampling error, then we
can select a finite number of discrete directions to sample. Furthermore, we can
1. For the advanced reader, we acknowledge Alvy Ray Smith's “a pixel is not a little
square”—that is, no sample is useful without its reconstruction filter—but contend that
Smith was so successful at clarifying this issue that today “sample” now is properly
used to describe the point-sample data to which Smith referred, and “pixel” now is
used to refer to a “little square area” of a display or sensor, whose value may be esti-
mated from samples. We'll generally use “sensor pixel” or “display pixel” to mean the
physical entity and “pixel” for the rectangular area on the image plane.
