Graphics Reference
In-Depth Information
our
L
αL
.(In
practice, this means evaluating both tiles, then interpolating values from
both onto one master grid.) If
α
is an irrational number, the sum of the
two is nonperiodic. You can see if
α
is rational, it's not hard to prove the
sum
is
periodic, in fact if
α
=
r/s
for integers
r
and
s
then the period
is
L
times the least common multiple of
r
and
s
, divided by
s
. f
α
is
irrational but very close to a rational number
r/s
with small integers
r
and
s
, the sum will not be exactly periodic but look very close to it, which still
might appear objectionable. One of the best choices then is the golden
×
L
repeating ocean tile another one of dimension
αL
×
ratio (
√
5+1)
/
2=1
.
61803
...
which (in a sense we will not cover in this
topic) is as far as possible from small integer fractions.
Other possible techniques involve layering in further effects based on
nonperiodic noise. For example, combinations of upwelling currents in the
sea and wind gusts above often give the ocean a patchy look, where in
some regions there are lots of small ripples to reflect light but in others the
surface is much smoother. This can be modeled procedurally, but here we
stop as it lies outside the realm of simulation.
