I’ve been working on generating Perlin noise for a map generator of mine. The problem I’ve run into is that the random noise is not distributed normally, and is more likely a normal distribution of kinds.
Given two integers X and Y, and a seed value, I do the following:
- Use MurmurHash2 to generate a random number (-1,1). This is uniformly distributed.
- Interpolate points between integer values with cubic interpolation. Values now fall in the range (-2.25, 2.25) because the interpolation can extrapolate higher points (by 1.5 in every dimension) between similar values, and the distribution is no longer uniform.
- Generate these interpolated points, summing them together while halving the amplitudes (See: Perling noise) As the number of sums approaches infinity, the limit of the range now approaches twice the previous values, or (-4.5, 4.5) and is now even less uniform.
This obviously doesn’t work when I want a range from (-1, 1), so I divide all final values by 4.5. Actually, I divide them along the way (by 1.5 after interpolating each dimension, then by 2 after summing the noise.)
After the division, I’m left with a theoretical range of (-1, 1). However, the vast majority of the values are (-0.2,0.2). This doesn’t work well when generating my maps, since I need to determine the percentage of the map filled. I also cannot use histograms to determine what threshold to use, since I’m generating the squares on demand, and not the entire map.
I need to make my distribution uniform at two points – after the interpolation, and after the summing of the noise functions. I’m not sure how to go about this, tho.
My distribution looks like this:
I need it to look like this:
(Both images from Wikipedia.)
Any solutions are appreciated, but I’m writing in C#, so code snippets would be extremely helpful.
Combine the resulting sample with the CDF for the gaussian, which is 0.5*erf(x) + 1 (erf = error function).
Note that in virtue of the Central Limit Theorem, whenever you make sums of random variables, you get gaussian laws.