均匀分布的随机噪声的产生 [英] Generation of uniformly distributed random noise
问题描述
我一直在努力产生Perlin杂的<一个href="http://stackoverflow.com/questions/3129676/whats-a-good-way-to-generate-random-clusters-and-paths/3131010#3131010">map我的发电机。我碰到的问题是，该随机噪声不是正态分布，并且更可能的种正态分布。
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.
由于两个整数X和Y，和种子值，我做到以下几点：
Given two integers X and Y, and a seed value, I do the following:
- 使用<一个href="http://stackoverflow.com/questions/3134759/how-can-i-best-generate-a-static-array-of-random-number-on-demand/3135446#3135446">MurmurHash2以产生一个随机数（-1,1）。这是均匀分布的。
- 在插值立方插值整数值之间的点。现在值落在相似的价值观之间的范围内（-2.25，2.25），因为插补（在每个维度1.5）推断高点，且分布不再是均匀的。
- 在生成这些插入点，总结在一起，而减半的幅度（参见： Perling噪声的）作为总和的数目接近无穷大，该范围的上限现在接近previous值的两倍，或（-4.5，4.5），现在甚至不太均匀。
- 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.
时，我想的范围为（-1,1），所以我把所有的最终值由4.5这显然是行不通的。其实，我（内各个维度，然后通过2相加后的噪声后1.5。）将它们沿途
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.)
师后，我留下的（-1,1）的理论范围。但是，值绝大多数为（-0.2,0.2）。生成我的地图时，这并不能很好的工作，因为我需要确定填充地图的比例。本人也不能使用直方图来确定要使用的阈值，因为我生成随需应变的平方，而不是整个地图
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.
我需要让我的均匀分布在两个点 - 插值后，和噪音功能求和之后。我不知道如何去这个，寿。
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.
我的分布是这样的：
我需要它看起来是这样的：
I need it to look like this:
（两个图像来自维基百科。）
(Both images from Wikipedia.)
的任何解决方案AP preciated，但我正在写在C＃中，因此code段将是非常有益的。的
推荐答案
结合所产生的样品与CDF为高斯，这是0.5 * ERF（X）+ 1（ERF =误差函数）。
Combine the resulting sample with the CDF for the gaussian, which is 0.5*erf(x) + 1 (erf = error function).
请注意，在凭借中心极限定理，只要你做的随机变量之和的，你得到高斯定律。
Note that in virtue of the Central Limit Theorem, whenever you make sums of random variables, you get gaussian laws.
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