Graphics Reference
In-Depth Information
• Most apparently smooth surfaces, like the surface of a piece of chalk, are
microscopically rough. These behave as if they were made of many tiny,
smooth facets, each following the previous rule; as a result, light hitting
such a surface scatters in many directions (or is absorbed, as in the mirror-
reflection case mentioned in the preceding bulleted item).
• A pinhole in a flat sheet of material admits a bundle of light rays, all of
which pass through or very near to the center of the pinhole.
• A pixel of a camera, or one of the cells in the eye that detects light, sums up
(by integration) all the light that arrives at a small area over a small period
of time. The value of the integral is the sensor response that corresponds to
how much total light, based on the number of incident photons, the pixel
(or cell) “saw.”
• A pixel of a display can be adjusted to emit light of a specified intensity
and color.
That's it! This is enough of a model of light to produce very realistic pictures.
Each of the bulleted items above is only approximately correct, but each is cor-
rect enough for a great many purposes. With them in hand, three big challenges
remain. First, we need some data structures for representing the surfaces, cam-
era, and lights in a scene. Second, we need an algorithm for evaluating all of the
light bounces and integration. Third, and most important, both the data structures
and the algorithm have to be efficient. Nature uses about 10 21 photons per square
meter per second to produce images of scenes lit by the sun; even if computers
were a billion times more powerful than they are today, we still couldn't afford
to write loops or data structures that actually simulate the motion of every single
photon.
1.13.2 Objects and Materials
Our initial assumption about objects is that they are composed of materials that
either reflect or absorb light (or do both, in varying amounts) at their surfaces.
We assume that air does neither—light simply passes through it. And we ignore,
for the time being, materials that transmit light, like water and glass, and to some
degree, materials like skin.
Because we assume that light only interacts with the surfaces of materials,
we represent objects by their surfaces, which are in turn generally represented by
polyhedra with triangular faces. Because the edges between faces have no surface
area, we ignore them and treat all light-object interactions as happening at the
interior of triangles. Each triangular facet T of a polyhedron lies in some plane,
and there's a unit vector n perpendicular to this plane that points away from the
object and into the air (or empty space); we call this the normal vector to the
triangle T . If the polygonal object approximates the original surface well, then
this normal vector approximates (and is often treated as) the surface normal to
the original surface, or a vector perpendicular to the surface at some particular
point (see Figure 1.17).
For a perfectly reflective surface like a mirror (a specular surface), light that
arrives 10
in a direction
and hits the triangle T is reflected in the
n -plane, with
10. There are two possible choices for describing the light arriving at a surface: Either
record the direction of travel of the photons (the transport-centered view), or record
the direction from the surface point to the light (the reflection-centered view). For now,
we'll use for the former; many papers use L for the latter.
 
 
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