feat(core): add Perlin noise generator for terrain shaping

core/include/vf/Noise.h

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+#pragma once
+
+#include <array>
+#include <cstdint>
+
+namespace vf {
+
+// Improved Perlin noise (Ken Perlin, 2002) over a seeded permutation table.
+// Output of noise2D/noise3D is in the range [-1, 1].
+class PerlinNoise {
+public:
+    explicit PerlinNoise(uint32_t seed = 1337u) { reseed(seed); }
+
+    void reseed(uint32_t seed);
+
+    float noise2D(float x, float y) const;
+    float noise3D(float x, float y, float z) const;
+
+    // Fractal Brownian motion: sum of `octaves` scaled noise layers.
+    // Result normalised to roughly [-1, 1].
+    float fbm2D(float x, float y, int octaves, float lacunarity, float gain) const;
+
+private:
+    std::array<int, 512> perm;
+};
+
+} // namespace vf

core/src/Noise.cpp

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+#include "vf/Noise.h"
+
+#include <cmath>
+#include <numeric>
+
+namespace vf {
+
+namespace {
+
+inline float fade(float t) { return t * t * t * (t * (t * 6.0f - 15.0f) + 10.0f); }
+
+inline float lerp(float a, float b, float t) { return a + t * (b - a); }
+
+inline float grad(int hash, float x, float y, float z) {
+    int h = hash & 15;
+    float u = h < 8 ? x : y;
+    float v = h < 4 ? y : (h == 12 || h == 14 ? x : z);
+    return ((h & 1) == 0 ? u : -u) + ((h & 2) == 0 ? v : -v);
+}
+
+} // namespace
+
+void PerlinNoise::reseed(uint32_t seed) {
+    std::array<int, 256> base;
+    std::iota(base.begin(), base.end(), 0);
+
+    // xorshift32 permutation shuffle, fully determined by the seed.
+    uint32_t state = seed ? seed : 0x9e3779b9u;
+    auto next = [&state]() {
+        state ^= state << 13;
+        state ^= state >> 17;
+        state ^= state << 5;
+        return state;
+    };
+
+    for (int i = 255; i > 0; --i) {
+        int j = static_cast<int>(next() % static_cast<uint32_t>(i + 1));
+        std::swap(base[i], base[j]);
+    }
+    for (int i = 0; i < 512; ++i) perm[i] = base[i & 255];
+}
+
+float PerlinNoise::noise3D(float x, float y, float z) const {
+    int xi = static_cast<int>(std::floor(x)) & 255;
+    int yi = static_cast<int>(std::floor(y)) & 255;
+    int zi = static_cast<int>(std::floor(z)) & 255;
+
+    float xf = x - std::floor(x);
+    float yf = y - std::floor(y);
+    float zf = z - std::floor(z);
+
+    float u = fade(xf);
+    float v = fade(yf);
+    float w = fade(zf);
+
+    int a = perm[xi] + yi;
+    int aa = perm[a] + zi;
+    int ab = perm[a + 1] + zi;
+    int b = perm[xi + 1] + yi;
+    int ba = perm[b] + zi;
+    int bb = perm[b + 1] + zi;
+
+    float x1 = lerp(grad(perm[aa], xf, yf, zf), grad(perm[ba], xf - 1, yf, zf), u);
+    float x2 = lerp(grad(perm[ab], xf, yf - 1, zf), grad(perm[bb], xf - 1, yf - 1, zf), u);
+    float y1 = lerp(x1, x2, v);
+
+    float x3 = lerp(grad(perm[aa + 1], xf, yf, zf - 1), grad(perm[ba + 1], xf - 1, yf, zf - 1), u);
+    float x4 = lerp(grad(perm[ab + 1], xf, yf - 1, zf - 1), grad(perm[bb + 1], xf - 1, yf - 1, zf - 1), u);
+    float y2 = lerp(x3, x4, v);
+
+    return lerp(y1, y2, w);
+}
+
+float PerlinNoise::noise2D(float x, float y) const { return noise3D(x, y, 0.0f); }
+
+float PerlinNoise::fbm2D(float x, float y, int octaves, float lacunarity, float gain) const {
+    float sum = 0.0f;
+    float amplitude = 1.0f;
+    float frequency = 1.0f;
+    float totalAmplitude = 0.0f;
+    for (int i = 0; i < octaves; ++i) {
+        sum += amplitude * noise2D(x * frequency, y * frequency);
+        totalAmplitude += amplitude;
+        amplitude *= gain;
+        frequency *= lacunarity;
+    }
+    return totalAmplitude > 0.0f ? sum / totalAmplitude : 0.0f;
+}
+
+} // namespace vf