Graphics Reference
In-Depth Information
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float
area()
const
{
return
2
*
PI
*
r
*
r;
}
Power3
power()
const
{
return
Phi;
}
Biradiance3
biradiance(
Vector4
Q,
Vector3
P)
const
{
assert(Q.w == 1 && Q.xyz().length() == r);
const
Vector3
& m = -Q.xyz().direction();
const
Vector3
& w_i = (Q.xyz() - P).direction();
return
Phi
*
max(-m.dot(w_i), 0.0f) /
(PI
*
(P - Q.xyz()).squaredLength());
}
};
An
omnidirectional point light
(
omni-light
or [ambiguously]
point light
)isa
luminaire that emits energy equally in all directions and is sufficiently small that
it has negligible bounding radius compared to the distance between the source and
nearby scene locations. A true point light would have to have a surface that was
infinitely bright to produce measurable emission from zero surface area, and so
could not exist. However, there are many luminaires whose volume is negligible
compared to the scale of the scenes in which they are encountered, such as the
bulb in a flashlight or the LED lights on the dashboard of a car. It is also common
to approximate a larger light source with an omni-light at its center, and some
surrounding proxy geometry that appears to the viewer to be the luminaire but
does not actually emit light in the lighting simulation. For example, a campfire
might be modeled by a flickering omni-light floating in the midst of the flames,
which were themselves rendered by a particle system.
An omni-light is typically modeled by its total power emission in all direc-
tions,
Φ
. This is a scalar measured in watts; it can be represented as a 3-tuple
to express power at the red-green-blue frequencies. Real-life experience provides
good estimates for the power of omni-lights in our scene, since lightbulbs are
labeled in watts of power consumed. As we said earlier, the emitted light from a
100W bulb is about 4W. A fluorescent bulb is about six times more efficient, so
a bulb labeled “equivalent to a 100W incandescent bulb” also emits about 4W of
visible light, but it consumes less electric power in doing so.
Let
Q
be the center of an omni-light. The radiance at
P
directly from the lumi-
naire must arrive
from
direction
v
i
points to the light,
from the surface. It is known as the
light vector
and is sometimes also denoted
L
(although we avoid that notation because it is confusingly similar to the radiance
function notation
L
(
v
i
=
S
(
Q
−
P
)
. That is,
)
).
The omni-light is an abstraction of a very small spherical source. We can esti-
mate the radiant emittance due to an omni-light by estimating the effect of ever-
smaller spherical sources. The only way that the size of a source enters our formula
is in the surface area term
A
in Equation 14.37. However, that term appears both
in numerator and denominator, so it cancels and the end result is independent of
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