add math.noise

res/modules/internal/extensions/math.lua

@@ -39,3 +39,35 @@ end
 function math.sign(x)
     return (x > 0) and 1 or (x < 0 and -1 or 0)
 end
+
+local noise_period = 3021
+local noise_rands = {}
+
+for i=1,noise_period do
+    table.insert(noise_rands, math.random() * 2.0 - 1.0)
+end
+
+local function smoothstep(t)
+    return t * t * (3 - 2 * t)
+end
+
+local function sample_noise(x)
+    x = x % noise_period
+    local left_cell = math.floor(x)
+    local right_cell = (left_cell + 1) % noise_period
+    local t = smoothstep(x - left_cell)
+    return noise_rands[left_cell + 1] * (1.0 - t)
+        + noise_rands[right_cell + 1] * t
+end
+
+function math.noise(x, octaves)
+    octaves = octaves or 1
+    local value = 0.0
+    local mul = 1.0
+    for i=1,octaves do
+        value = value * (1.0 - mul) + sample_noise(x + 37 * i) * mul
+        x = x * 2.0
+        mul = mul * 0.5
+    end
+    return value
+end