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(c) Compute the fast Fourier transform of the resultant array. Does it appear to be
a blue-noise distribution?
(d) Try this process again with various values for
r
. Below what frequency (in
terms of
r
) is there relatively little energy?
(e) Now generate a similar occupancy array using stratified sampling, and com-
pare the frequency spectra of the two processes. Describe any differences you find.
(f) Generalize to 2D.
(g) Implement Mitchell's [Mit87] point diffusion algorithm for generating blue
noise, and compare its results to the others.
Exercise 32.12:
For a rectangular area light, write code to sample a point from
the light uniformly with respect to area. Do the same for a spherical source. For
the sphere, recall that the projection
(
x
,
y
,
z
)
r
)
, where
r
=
√
x
2
+
z
2
is an area-preserving map from the unit-radius cylinder about the
y
-axis, extending
from
y
=
→
(
x
/
r
,
y
,
z
/
−
1to
y
=
1, onto the unit sphere.