Graphics Reference
In-Depth Information
radial falloff. In the real world, the total power observed at distance
r
from a uni-
form spherical emitter whose radius is much smaller than
r
is proportional to 1
r
2
.
We can generalize this by computing a value
M
that involves an inverse quadratic:
/
Φ
(
a
0
r
0
m
2
+
a
1
r
1
m
1
+
a
2
r
2
m
0
)
4
M
=
.
(14.44)
π
If we define
a
and
r
by
a
=(
a
0
m
2
,
a
1
m
1
,
a
2
m
0
)
, and
(14.45)
r
=(
r
0
,
r
1
,
r
2
)
,
(14.46)
then we can rewrite the formula for
M
as
Φ
M
=
.
(14.47)
a
·
r
4
π
This strange expression lets us represent a point emitter that experiences non-
physical falloff to approximate a local area source or distant point source ...or
simply to satisfy an artistic vision. In this context, a directional source can be
parameterized by the attenuation constant
a
=(
1, 0, 0
)
. This source will produce
equal intensity at all points in the scene, and that intensity is comparable to what
a local source with power
Φ
one meter from a surface would produce.
The resulting interface (Listing 14.15) follows the spirit of the OpenGL fixed-
function lighting model, albeit with slightly varying units and border cases. We do
not recommend this model for physically based rendering.
Listing 14.15: A simple unified model for spot, directional,
and omni light sources.
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2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
class
PointLight :
public
Light
{
private
:
/
**
For local lights, this is the total power of the light source.
For directional lights, this is the power of an equivalent
local source 1ˆm from the surface.
*
/
Power3
Phi;
Vector3
axis;
/
**
Center of the light in homogeneous coordinates.
*
/
Vector4
C;
Vector3
aVec;
float
spotHalfAngle;
...
};
Listing 14.16:
PointLight
methods for direct illumination.
1
2
3
4
Vector4
PointLight::randomPoint()
const
{
return
C;
}
