Graphics Reference
In-Depth Information
Figure 2.3
In the radiosity method, each surface patch gets a fraction of the radiant exitance of each
other patch. This interdependence is the essence of global illumination.
reconstruction may also include the addition of ray-traced specular highlights and
mirror reflections.
The radiosity method can produce accurate results, but it is both memory in-
tensive and time consuming. How the surfaces are subdivided into patches has a
significant effect on the final solution. When an object has a lot of detail, its sur-
faces have to be subdivided into very small patches, causing an explosion in the
size of the problem. On top of that, the radiosity method only handles purely dif-
fuse reflection (the finite element method can be used for nondiffuse light transfer,
but it is a lot more complicated).
2.3 Monte Carlo Ray and Path Tracing
The rendering equation in the form given by Equation (2.2), expressed in terms
of all incoming directions above a surface point, is inherently recursive. The
incoming radiance
L
i
(
at
x
from some arbitrary direction ω
is the outgoing
radiance at another surface point
x
. The point
x
, can be found by tracing the ray
from
x
in direction ω
. The outgoing radiance at this secondary point
x
is again
given by Equation (2.2) at
x
. The incoming radiance at
x
from another arbitrary
direction can in turn be found by tracing the ray from
x
in that direction, and
so on.
One approach to approximating Equation (2.2) is to apply a kind of numerical
integration to the incoming radiance sampled at points (directions) on the hemi-
sphere. At each sample point, the ray is traced in the corresponding direction to
find the surface point at which the light originates. The same approximation pro-
cess applies at the secondary point, and so it goes. The total number of samples
therefore increases exponentially with the number of reflections, but this can be
mitigated somewhat by using fewer sample points at deeper depths; in fact, some
fixed approximation can be substituted at a prescribed depth. For example, in
,
ω
)
x
