Merge pull request #21 from SilentSpike/perlin

Improve Perlin noise implementation
2025-01-18 03:21:47 +02:00 · 2017-07-24 11:07:52 +02:00 · 2017-07-24 11:07:52 +02:00 · 9fe48b4adf
commit 9fe48b4adf
parent 5114955d1b ddddd79928
1 changed files with 110 additions and 57 deletions
--- a/locale/gen_shared/perlin_noise.lua
+++ b/locale/gen_shared/perlin_noise.lua
@ -1,74 +1,127 @@
-- original code by Ken Perlin: http://mrl.nyu.edu/~perlin/noise/
+--[[
+    Implemented as described here:
+    http://flafla2.github.io/2014/08/09/perlinnoise.html
+]]--

 perlin = {}
 perlin.p = {}
-perlin.permutation = { 151,160,137,91,90,15,
-   131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
-   190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
-   88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
-   77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
-   102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
-   135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
-   5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
-   223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
-   129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
-   251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
-   49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
-   138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180
-}
-perlin.size = 256
-perlin.gx = {}
-perlin.gy = {}
-perlin.randMax = 256

-function perlin:load(  )
-    for i=1,self.size do
-        self.p[i] = self.permutation[i]
-        self.p[256+i] = self.p[i]
-    end
+-- Hash lookup table as defined by Ken Perlin
+-- This is a randomly arranged array of all numbers from 0-255 inclusive
+local permutation = {151,160,137,91,90,15,
+  131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
+  190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
+  88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
+  77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
+  102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
+  135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
+  5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
+  223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
+  129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
+  251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
+  49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
+  138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180
+}
+
+-- p is used to hash unit cube coordinates to [0, 255]
+for i=0,255 do
+    -- Convert to 0 based index table
+    perlin.p[i] = permutation[i+1]
+    -- Repeat the array to avoid buffer overflow in hash function
+    perlin.p[i+256] = permutation[i+1]
 end

-function perlin:noise( x, y, z )
-    local X = math.floor(x) % 256
-    local Y = math.floor(y) % 256
-    local Z = math.floor(z) % 256
+-- Return range: [-1, 1]
+function perlin:noise(x, y, z)
+    y = y or 0
+    z = z or 0
+
+    -- Calculate the "unit cube" that the point asked will be located in
+    local xi = bit32.band(math.floor(x),255)
+    local yi = bit32.band(math.floor(y),255)
+    local zi = bit32.band(math.floor(z),255)
+
+    -- Next we calculate the location (from 0 to 1) in that cube
    x = x - math.floor(x)
    y = y - math.floor(y)
    z = z - math.floor(z)
-    local u = fade(x)
-    local v = fade(y)
-    local w = fade(z)
-    local A  = self.p[X+1]+Y
-    local AA = self.p[A+1]+Z
-    local AB = self.p[A+2]+Z
-    local B  = self.p[X+2]+Y
-    local BA = self.p[B+1]+Z
-    local BB = self.p[B+2]+Z

-    return lerp(w, lerp(v, lerp(u, grad(self.p[AA+1], x  , y  , z  ),
-                                   grad(self.p[BA+1], x-1, y  , z  )),
-                           lerp(u, grad(self.p[AB+1], x  , y-1, z  ),
-                                   grad(self.p[BB+1], x-1, y-1, z  ))),
-                   lerp(v, lerp(u, grad(self.p[AB+2], x  , y  , z-1),
-                                   grad(self.p[BA+2], x-1, y  , z-1)),
-                           lerp(u, grad(self.p[AB+2], x  , y-1, z-1),
-                                   grad(self.p[BB+2], x-1, y-1, z-1))))
+    -- We also fade the location to smooth the result
+    local u = self.fade(x)
+    local v = self.fade(y)
+    local w = self.fade(z)
+
+    -- Hash all 8 unit cube coordinates surrounding input coordinate
+    local p = self.p
+    local A, AA, AB, AAA, ABA, AAB, ABB, B, BA, BB, BAA, BBA, BAB, BBB
+    A   = p[xi  ] + yi
+    AA  = p[A   ] + zi
+    AB  = p[A+1 ] + zi
+    AAA = p[ AA ]
+    ABA = p[ AB ]
+    AAB = p[ AA+1 ]
+    ABB = p[ AB+1 ]
+
+    B   = p[xi+1] + yi
+    BA  = p[B   ] + zi
+    BB  = p[B+1 ] + zi
+    BAA = p[ BA ]
+    BBA = p[ BB ]
+    BAB = p[ BA+1 ]
+    BBB = p[ BB+1 ]
+
+    -- Take the weighted average between all 8 unit cube coordinates
+    return self.lerp(w,
+        self.lerp(v,
+            self.lerp(u,
+                self:grad(AAA,x,y,z),
+                self:grad(BAA,x-1,y,z)
+            ),
+            self.lerp(u,
+                self:grad(ABA,x,y-1,z),
+                self:grad(BBA,x-1,y-1,z)
+            )
+        ),
+        self.lerp(v,
+            self.lerp(u,
+                self:grad(AAB,x,y,z-1), self:grad(BAB,x-1,y,z-1)
+            ),
+            self.lerp(u,
+                self:grad(ABB,x,y-1,z-1), self:grad(BBB,x-1,y-1,z-1)
+            )
+        )
+    )
 end

-function fade( t )
+-- Gradient function finds dot product between pseudorandom gradient vector
+-- and the vector from input coordinate to a unit cube vertex
+perlin.dot_product = {
+    [0x0]=function(x,y,z) return  x + y end,
+    [0x1]=function(x,y,z) return -x + y end,
+    [0x2]=function(x,y,z) return  x - y end,
+    [0x3]=function(x,y,z) return -x - y end,
+    [0x4]=function(x,y,z) return  x + z end,
+    [0x5]=function(x,y,z) return -x + z end,
+    [0x6]=function(x,y,z) return  x - z end,
+    [0x7]=function(x,y,z) return -x - z end,
+    [0x8]=function(x,y,z) return  y + z end,
+    [0x9]=function(x,y,z) return -y + z end,
+    [0xA]=function(x,y,z) return  y - z end,
+    [0xB]=function(x,y,z) return -y - z end,
+    [0xC]=function(x,y,z) return  y + x end,
+    [0xD]=function(x,y,z) return -y + z end,
+    [0xE]=function(x,y,z) return  y - x end,
+    [0xF]=function(x,y,z) return -y - z end
+}
+function perlin:grad(hash, x, y, z)
+    return self.dot_product[bit32.band(hash,0xF)](x,y,z)
+end
+
+-- Fade function is used to smooth final output
+function perlin.fade(t)
    return t * t * t * (t * (t * 6 - 15) + 10)
 end

-function lerp( t, a, b )
+function perlin.lerp(t, a, b)
    return a + t * (b - a)
 end
-
-function grad( hash, x, y, z )
-    local h = hash % 16
-    local u = h < 8 and x or y
-    local v = h < 4 and y or ((h == 12 or h == 14) and x or z)
-    return ((h % 2) == 0 and u or -u) + ((h % 3) == 0 and v or -v)
-end
-
-
-perlin:load(  )