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Lua - 生成Perlin噪声 - 如何获得条形而不是正方形

luaperlin-noiselove2d
5

我目前正在学习Löve 2d/Lua，并尝试使用Perlin Noise算法生成噪声。

我在此处改编了Ken Perlin的Improved Noise代码：

根据Doug的答案进行修复后编辑的代码

-- original code by Ken Perlin: http://mrl.nyu.edu/~perlin/noise/

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
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
    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))))
end

function fade( t )
    return t * t * t * (t * (t * 6 - 15) + 10)
end

function 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

这是我的 Löve 脚本 main.lua:

需要引入 'noise' 库:

function love.load(  )
    perlin:load()
    -- love.graphics.setBackgroundColor(255, 255, 255)
    love.window.setMode(500, 500)
end

function love.update( dt )

end

function love.draw(  )
    for i=1,500 do
        for j=1,500 do
            local x = perlin:noise(i/10, j/10, 0.3)
            love.graphics.setColor(math.floor(x*255), math.floor(x*255), math.floor(x*255))
            love.graphics.rectangle("fill", 5*(i-1), 5*(j-1), 5, 5)
        end
    end
end

我遇到的问题是，与其得到一些伪随机方块的漂亮图像，我得到了一些像这样的渐变条纹：

noise generated in Löve 2d

我很困惑为什么我没有得到通常的噪声渲染。
编辑：这是正常的渲染！

working rendering of perlin noise

2个回答
6

一个问题：

local X = math.floor(x) and 255
local Y = math.floor(y) and 255
local Z = math.floor(z) and 255

应该是

local X = math.floor(x) & 255
local Y = math.floor(y) & 255
local Z = math.floor(z) & 255

假设您已经拥有了Lua 5.3.x。如果您使用的是早期版本的Lua，则可能会有或者没有适用于Löve的位运算库。在这种情况下，您可以使用：

local X = math.floor(x) % 256
local Y = math.floor(y) % 256
local Z = math.floor(z) % 256

解释：逻辑运算符 and 返回它的第一个参数，如果该值为false或nil；否则，返回它的第二个参数。
谢谢，谢谢！在发帖之前我搜索了 Lua 文档，但没有找到关于位运算的任何信息，所以这篇文章对澄清问题非常有帮助！尤其是因为 Love 使用的是 Lua 5.1，所以即使我想要也无法使用 5.2 或 5.3。 - GHandel
2
您正在使用and替换&（按位与），我已经更新了您的示例（使用Lua - 按位逻辑运算中的BitAND方法），并替换了您使用and的地方，其中包括perlin:load中的初始声明或X、Y、Z以及grad中的h声明。我使用love进行了测试，输出结果看起来是正确的。
-- original code by Ken Perlin: http://mrl.nyu.edu/~perlin/noise/
local function BitAND(a,b)--Bitwise and
    local p,c=1,0
    while a>0 and b>0 do
        local ra,rb=a%2,b%2
        if ra+rb>1 then c=c+p end
        a,b,p=(a-ra)/2,(b-rb)/2,p*2
    end
    return c
end

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[255+i] = self.p[i]
    end
end

function perlin:noise( x, y, z )
    local X = BitAND(math.floor(x), 255) + 1
    local Y = BitAND(math.floor(y), 255) + 1
    local Z = BitAND(math.floor(z), 255) + 1

    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]+Y
    local AA = self.p[A]+Z
    local AB = self.p[A+1]+Z
    local B  = self.p[X+1]+Y
    local BA = self.p[B]+Z
    local BB = self.p[B+1]+Z

    return lerp(w, lerp(v, lerp(u, grad(self.p[AA  ], x  , y  , z  ),
                                   grad(self.p[BA  ], x-1, y  , z  )),
                           lerp(u, grad(self.p[AB  ], x  , y-1, z  ),
                                   grad(self.p[BB  ], x-1, y-1, z  ))),
                   lerp(v, lerp(u, grad(self.p[AA+1], x  , y  , z-1),
                                   grad(self.p[BA+1], x-1, y  , z-1)),
                           lerp(u, grad(self.p[AB+1], x  , y-1, z-1),
                                   grad(self.p[BB+1], x-1, y-1, z-1))))
end


function fade( t )
    return t * t * t * (t * (t * 6 - 15) + 10)
end

function lerp( t, a, b )
    return a + t * (b - a)
end

function grad( hash, x, y, z )
    local h = BitAND(hash, 15)
    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 and 1) == 0 and u or -u) + ((h and 2) == 0 and v or -v)
end
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