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# Notes+Questions on Perlin noise and its derivatives

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### #1RenHoek  Members

Posted 24 February 2012 - 04:09 AM

Hi all

I'm currently doing a lot of work with GPU procedural noise in GLSL.
Here are a few questions + notes regarding this.

1) Noise Derivatives
One area I'm working on right now is calculating analytical derivatives for various noises.

Inigo Quilez posted some notes on how to calculate the derivatives of value noise. ( although he incorrectly calls it perlin noise )
=> http://www.iquilezles.org/www/articles/morenoise/morenoise.htm
( This noise derivative is extremely easy and fast to implement in GLSL. More so that what Inigo has posted in his CPU version. Let me know if you want it and I can post )

Inigos approach does not work for Perlin noise. Some people have incorrectly implemented it thinking that it does.
=> https://github.com/cinder/Cinder/blob/master/src/cinder/Perlin.cpp [ NOTE: INCORRECT! ]

I have only seen one correct implementation of perlin noise with derivatives. Although it is only in 2D.
=> http://www.decarpentier.nl/scape-procedural-extensions

Perlins Simplex noise allows for a easy derivative calculation, as kindly demonstrated by Stefan Gustavson here...
=> http://webstaff.itn.liu.se/~stegu/aqsis/flownoisedemo/

So my question / request is if anyone has implemented Classic Perlin Noise with Analytical derivatives in 3D? Or do they know of any implementations? Thanks!

2) Normalizing Classic Perlin noise to -1.0->1.0
I've noticed a few threads on the internet of guys trying to figure out how to normalize perlin noise to a -1.0->1.0 range.
This particular thread goes on for a _very_ long time. It boggles my brain how much time they put into this thred. Sorry if they finally got the answer, or that I maybe missed the point of the thread, but I didn't have time to read it all.

For me it was a very easy thing to solve so I'll post my answer here for anyone who is interested.

The way to do it is to imagine the maximum possible value which could be generated by the perlin noise algorithm.
In 2D this would be having all 4 ( normalized ) gradient vectors pointing to the very center of the square, and the sample being taken from the center of that square. This generates a value of sqrt( 0.5 ) = 0.70710678.....
So the normalization value to scale the noise to a -1.0->1.0 range is 1.0/sqrt(0.5)
In 3D it is 1.0/sqrt(0.75)

Easy!

Ok. Thanks all
Ren Hoek

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