Christopher James Huff wrote:
> In article <3DA99C87.2980A601@dcs.gla.ac.uk>,
>  John Williamson <wil### [at] dcsglaacuk> wrote:
>
>>> Ken Perlin recently updated his perlin noise algorithm with a new
>>> polynomial S-curve function that eliminated second-derivative
>>> discontinuities, maybe that could be of some use as a bounded
>>> function...
>>
>> Do you have any details of this? Sounds quite interesting...
>
> The new polynomial is "1 - r*r*(3 - 2*r)".

That's the "old" function, often referred to as "smoothstep function".
That function has a derivative of 6-12*t.
The new function is
  6*t^5 - 15*t^4 + 10*t^3
or
  t*t*t*(10+t*(6*t-15))
This function has zero first and second derivatives at t=0 and t=1
Details can be found in Ken Perlin's paper at
  http://mrl.nyu.edu/~perlin/paper445.pdf

--
Alessandro Falappa
web: http://www.falappa.net/alessandro

Post a reply to this message