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我正在为类似 MineCraft 的世界开发地形生成算法。目前,我正在使用基于论文'Simplex Noise Demystified' [PDF]中的实现的单纯形噪声,因为单纯形噪声应该比 Perlin 噪声更快并且具有更少的伪影。这看起来相当不错(见图),但到目前为止它也很慢。

在此处输入图像描述

运行噪声函数 10 次(我需要不同波长的噪声来处理地形高度、温度、树木位置等),每个块(16x16x128 块)的噪声为 3 个八度音程,或调用约 100 万次噪声函数总共需要大约 700-800 毫秒。尽管算法中没有明显的昂贵操作(至少对我而言),但对于以任何不错的速度生成地形来说,这至少是一个数量级太慢了。只是地板,模,一些数组查找和基本算术。下面列出了算法(用 Haskell 编写)。SCC 评论用于分析。我省略了 2D 噪声函数,因为它们的工作方式相同。

g3 :: (Floating a, RealFrac a) => a
g3 = 1/6

{-# INLINE int #-}
int :: (Integral a, Num b) => a -> b
int = fromIntegral

grad3 :: (Floating a, RealFrac a) => V.Vector (a,a,a)
grad3 = V.fromList $ [(1,1,0),(-1, 1,0),(1,-1, 0),(-1,-1, 0),
                     (1,0,1),(-1, 0,1),(1, 0,-1),(-1, 0,-1),
                     (0,1,1),( 0,-1,1),(0, 1,-1),( 0,-1,-1)]

{-# INLINE dot3 #-}
dot3 :: Num a => (a, a, a) -> a -> a -> a -> a
dot3 (a,b,c) x y z = a * x + b * y + c * z

{-# INLINE fastFloor #-}
fastFloor :: RealFrac a => a -> Int
fastFloor x = truncate (if x > 0 then x else x - 1)

--Generate a random permutation for use in the noise functions
perm :: Int -> Permutation
perm seed = V.fromList . concat . replicate 2 . shuffle' [0..255] 256 $ mkStdGen seed

--Generate 3D noise between -0.5 and 0.5
simplex3D :: (Floating a, RealFrac a) => Permutation -> a -> a -> a -> a
simplex3D p x y z = {-# SCC "out" #-} 16 * (n gi0 (x0,y0,z0) + n gi1 xyz1 + n gi2 xyz2 + n gi3 xyz3) where
    (i,j,k) = {-# SCC "ijk" #-} (s x, s y, s z) where s a = fastFloor (a + (x + y + z) / 3)
    (x0,y0,z0) = {-# SCC "x0-z0" #-} (x - int i + t, y - int j + t, z - int k + t) where t = int (i + j + k) * g3
    (i1,j1,k1,i2,j2,k2) = {-# SCC "i1-k2" #-} if x0 >= y0
        then if y0 >= z0 then (1,0,0,1,1,0) else
             if x0 >= z0 then (1,0,0,1,0,1) else (0,0,1,1,0,1)
        else if y0 <  z0 then (0,0,1,0,1,1) else
             if x0 <  z0 then (0,1,0,0,1,1) else (0,1,0,1,1,0)
    xyz1 = {-# SCC "xyz1" #-} (x0 - int i1 +   g3, y0 - int j1 +   g3, z0 - int k1 +   g3)
    xyz2 = {-# SCC "xyz2" #-} (x0 - int i2 + 2*g3, y0 - int j2 + 2*g3, z0 - int k2 + 2*g3)
    xyz3 = {-# SCC "xyz3" #-} (x0 - 1      + 3*g3, y0 - 1      + 3*g3, z0 - 1      + 3*g3)
    (ii,jj,kk) = {-# SCC "iijjkk" #-} (i .&. 255, j .&. 255, k .&. 255)
    gi0 = {-# SCC "gi0" #-} mod (p V.! (ii +      p V.! (jj +      p V.!  kk      ))) 12
    gi1 = {-# SCC "gi1" #-} mod (p V.! (ii + i1 + p V.! (jj + j1 + p V.! (kk + k1)))) 12
    gi2 = {-# SCC "gi2" #-} mod (p V.! (ii + i2 + p V.! (jj + j2 + p V.! (kk + k2)))) 12
    gi3 = {-# SCC "gi3" #-} mod (p V.! (ii + 1  + p V.! (jj + 1  + p V.! (kk + 1 )))) 12
    {-# INLINE n #-}
    n gi (x',y',z') = {-# SCC "n" #-} (\a -> if a < 0 then 0 else
        a*a*a*a*dot3 (grad3 V.! gi) x' y' z') $ 0.6 - x'*x' - y'*y' - z'*z'

harmonic :: (Num a, Fractional a) => Int -> (a -> a) -> a
harmonic octaves noise = f octaves / (2 - 1 / int (2 ^ (octaves - 1))) where
    f 0 = 0
    f o = let r = int $ 2 ^ (o - 1) in noise r / r + f (o - 1)

--Generate harmonic 3D noise between -0.5 and 0.5
harmonicNoise3D :: (RealFrac a, Floating a) => Permutation -> Int -> a -> a -> a -> a -> a
harmonicNoise3D p octaves l x y z = harmonic octaves
    (\f -> simplex3D p (x * f / l) (y * f / l) (z * f / l))

对于分析,我使用了以下代码,

q _ = let p = perm 0 in
      sum [harmonicNoise3D p 3 l x y z :: Float | l <- [1..10], y <- [0..127], x <- [0..15], z <- [0..15]]

main = do start <- getCurrentTime
          print $ q ()
          end <- getCurrentTime
          print $ diffUTCTime end start

这会产生以下信息:

COST CENTRE                    MODULE               %time %alloc

simplex3D                      Main                  18.8   21.0
n                              Main                  18.0   19.6
out                            Main                  10.1    9.2
harmonicNoise3D                Main                   9.8    4.5
harmonic                       Main                   6.4    5.8
int                            Main                   4.0    2.9
gi3                            Main                   4.0    3.0
xyz2                           Main                   3.5    5.9
gi1                            Main                   3.4    3.4
gi0                            Main                   3.4    2.7
fastFloor                      Main                   3.2    0.6
xyz1                           Main                   2.9    5.9
ijk                            Main                   2.7    3.5
gi2                            Main                   2.7    3.3
xyz3                           Main                   2.6    4.1
iijjkk                         Main                   1.6    2.5
dot3                           Main                   1.6    0.7

为了比较,我还将算法移植到 C#。那里的性能快了大约 3 到 4 倍,所以我想我一定是做错了什么。但即便如此,它也没有我想要的那么快。所以我的问题是:谁能告诉我是否有任何方法可以加快我的实现和/或一般算法,或者是否有人知道具有更好性能特征但外观相似的不同噪声算法?

更新:

遵循下面提供的一些建议后,代码现在如下所示:

module Noise ( Permutation, perm
             , noise3D, simplex3D
             ) where

import Data.Bits
import qualified Data.Vector.Unboxed as UV
import System.Random
import System.Random.Shuffle

type Permutation = UV.Vector Int

g3 :: Double
g3 = 1/6

{-# INLINE int #-}
int :: Int -> Double
int = fromIntegral

grad3 :: UV.Vector (Double, Double, Double)
grad3 = UV.fromList $ [(1,1,0),(-1, 1,0),(1,-1, 0),(-1,-1, 0),
                     (1,0,1),(-1, 0,1),(1, 0,-1),(-1, 0,-1),
                     (0,1,1),( 0,-1,1),(0, 1,-1),( 0,-1,-1)]

{-# INLINE dot3 #-}
dot3 :: (Double, Double, Double) -> Double -> Double -> Double -> Double
dot3 (a,b,c) x y z = a * x + b * y + c * z

{-# INLINE fastFloor #-}
fastFloor :: Double -> Int
fastFloor x = truncate (if x > 0 then x else x - 1)

--Generate a random permutation for use in the noise functions
perm :: Int -> Permutation
perm seed = UV.fromList . concat . replicate 2 . shuffle' [0..255] 256 $ mkStdGen seed

--Generate 3D noise between -0.5 and 0.5
noise3D :: Permutation -> Double -> Double -> Double -> Double
noise3D p x y z = 16 * (n gi0 (x0,y0,z0) + n gi1 xyz1 + n gi2 xyz2 + n gi3 xyz3) where
    (i,j,k) = (s x, s y, s z) where s a = fastFloor (a + (x + y + z) / 3)
    (x0,y0,z0) = (x - int i + t, y - int j + t, z - int k + t) where t = int (i + j + k) * g3
    (i1,j1,k1,i2,j2,k2) = if x0 >= y0
        then if y0 >= z0 then (1,0,0,1,1,0) else
             if x0 >= z0 then (1,0,0,1,0,1) else (0,0,1,1,0,1)
        else if y0 <  z0 then (0,0,1,0,1,1) else
             if x0 <  z0 then (0,1,0,0,1,1) else (0,1,0,1,1,0)
    xyz1 = (x0 - int i1 +   g3, y0 - int j1 +   g3, z0 - int k1 +   g3)
    xyz2 = (x0 - int i2 + 2*g3, y0 - int j2 + 2*g3, z0 - int k2 + 2*g3)
    xyz3 = (x0 - 1      + 3*g3, y0 - 1      + 3*g3, z0 - 1      + 3*g3)
    (ii,jj,kk) = (i .&. 255, j .&. 255, k .&. 255)
    gi0 = rem (UV.unsafeIndex p (ii +      UV.unsafeIndex p (jj +      UV.unsafeIndex p  kk      ))) 12
    gi1 = rem (UV.unsafeIndex p (ii + i1 + UV.unsafeIndex p (jj + j1 + UV.unsafeIndex p (kk + k1)))) 12
    gi2 = rem (UV.unsafeIndex p (ii + i2 + UV.unsafeIndex p (jj + j2 + UV.unsafeIndex p (kk + k2)))) 12
    gi3 = rem (UV.unsafeIndex p (ii + 1  + UV.unsafeIndex p (jj + 1  + UV.unsafeIndex p (kk + 1 )))) 12
    {-# INLINE n #-}
    n gi (x',y',z') = (\a -> if a < 0 then 0 else
        a*a*a*a*dot3 (UV.unsafeIndex grad3 gi) x' y' z') $ 0.6 - x'*x' - y'*y' - z'*z'

harmonic :: Int -> (Double -> Double) -> Double
harmonic octaves noise = f octaves / (2 - 1 / int (2 ^ (octaves - 1))) where
    f 0 = 0
    f o = let r = 2 ^^ (o - 1) in noise r / r + f (o - 1)

--3D simplex noise
--syntax: simplex3D permutation number_of_octaves wavelength x y z
simplex3D :: Permutation -> Int -> Double -> Double -> Double -> Double -> Double
simplex3D p octaves l x y z = harmonic octaves
    (\f -> noise3D p (x * f / l) (y * f / l) (z * f / l))

连同将我的块大小减少到 8x8x128,生成新的地形块现在以大约 10-20 fps 的速度发生,这意味着现在四处移动几乎不像以前那样成问题。当然,仍然欢迎任何其他性能改进。

4

1 回答 1

28

最初突出的是您的代码是高度多态的。您应该将您的浮点类型统一专门化为Double,因此 GHC(和 LLVM)有机会应用更积极的优化。

请注意,对于那些试图复制的人,此代码将导入:

import qualified Data.Vector as V
import Data.Bits
import Data.Time.Clock
import System.Random
import System.Random.Shuffle

type Permutation = V.Vector Int

行。您可以尝试很多方法来改进此代码。

改进

数据表示

  • 专门用于具体的浮点类型,而不是多态浮点函数
  • (a,a,a)用未装箱的三元组替换元组T !Double !Double !Double
  • 从 切换Data.ArrayData.Array.UnboxedforPermutations
  • 用包中的多维未装箱数组替换使用三元组的装箱repa数组

编译器标志

  • 编译-O2 -fvia-C -optc-O3 -fexcess-precision -optc-march=native(或等效-fllvm
  • 增加规格约束阈值——-fspec-constr-count=16

更高效的库函数

  • 使用 mersenne-random 而不是 StdGen 生成随机数
  • 替换modrem
  • 用未经检查的索引替换V.!索引VU.unsafeIndex(移动到Data.Vector.Unboxed

运行时设置

  • 增加默认分配区域:-A20M-H

此外,请检查您的算法是否与 C# 相同,并且您使用的是相同的数据结构。

于 2011-04-18T18:45:09.817 回答