William F Pokorny <ano### [at] anonymousorg> wrote:
> On 12/27/23 18:44, Tor Olav Kristensen wrote:
> > I'm sorry Bill, but you have to provide some more information for us about
> > what you are doing here.

https://arxiv.org/pdf/1511.04224.pdf

I was working on figuring out Stephen Marschner's procedural wood texture, and
part of the paper uses triangular waves and rectangular waves with specific
properties, as he states:

6.1.3 Seasonal growth
We turn the r coordinate volume into a time volume by scal-
ing its value and adding a smoothed triangular wave w (r)
to it. Each cycle of the smoothed triangle wave consists of
two linear segments connected by quadratic segments so as
to make the wave C1 continuous. The parameters are the
lengths of the two linear segments and the two quadratic
segments.
We scale the triangle wave so that when added to the radius,
half of the time the wood grows faster than the mean and
half of the time the wood grows more slowly. Then we add
1D noise n to generate variation in growth rate. All in all,
we have
tpre = r + w (r) (23)
t = tpre + n (tpre) (24)
This gives us the time at which any point in the wood was
laid down.
6.1.4 Growth rings
We can then create growth rings from the time volume. By
using a smoothed rectangular wave g = w (t), we can vary
the absorption of the wood according to the season. Simi-
larly to the triangle wave used to determine the growth rate,
each cycle of the smoothed rectangular wave consists of two
constant segments and two cubic segements so as to make
the wave C2 continuous, and the parameters are the relative
lengths of the two linear segments and the two quadratic
segments, plus the minimum and maximum values.

- BW

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