我已经实现了改进的Perlin算法：

#include "lodepng/lodepng.h"

#include <glm/glm.hpp>

#include <vector>
#include <numeric>
#include <iostream>
#include <random>
#include <ctime>

float lerp(float a, float b, float x)
{
    return a + x * (b - a);
}

float fade(float x)
{
    return x * x * x * (x * (6 * x - 15) + 10);
}

float gradient(glm::vec2 point, unsigned char seed)
{
    glm::vec2 randomVectors[] = {
        { -1.0f, -1.0f },
        { -1.0f, 1.0f },
        { 1.0f, -1.0f },
        { 1.0f, 1.0f }
    };

    return glm::dot(point, randomVectors[seed % 4]);
}

float perlinNoiseLayer(const std::vector<unsigned char>& permutations, glm::vec2 point)
{
    glm::vec2 gridCoords = glm::ivec2(point);
    glm::vec2 pointCoords = point - gridCoords;
    glm::vec2 distanceCoords = { fade(pointCoords.x), fade(pointCoords.y) };

    return (lerp(
        lerp(
            gradient(pointCoords, permutations[permutations[gridCoords.x] + gridCoords.y]),
            gradient({ pointCoords.x - 1, pointCoords.y }, permutations[permutations[gridCoords.x + 1] + gridCoords.y]),
            distanceCoords.x
        ),
        lerp(
            gradient({ pointCoords.x, pointCoords.y - 1 }, permutations[permutations[gridCoords.x] + gridCoords.y + 1]),
            gradient({ pointCoords.x - 1, pointCoords.y - 1 }, permutations[permutations[gridCoords.x + 1] + gridCoords.y + 1]),
            distanceCoords.x
        ),
        distanceCoords.y
    ) + 1) / 2;
}

float perlinNoise(const std::vector<unsigned char>& permutations, glm::vec2 point, float frequency, int octavesCount, float persistence, float lacunarity)
{
    float value = 0.0f;
    float maxValue = 0.0f;

    float amplitude = 1.0f;

    for (int i = 0; i < octavesCount; i++)
    {
        value += amplitude * perlinNoiseLayer(permutations, point * frequency);
        maxValue += amplitude;

        amplitude *= persistence;
        frequency *= lacunarity;
    }

    return value / maxValue;
}

bool validatePerlinNoiseParams(glm::ivec2 size, float frequency, int octavesCount, float lacunarity)
{
    glm::vec2 resultVec = glm::dvec2(size - 1) * (frequency * std::pow(lacunarity, octavesCount));
    return resultVec.x < 256 && resultVec.y < 256;
}

std::vector<unsigned char> generatePermutations(std::mt19937& randomEngine)
{
    std::vector<unsigned char> permutations(256);
    std::iota(permutations.begin(), permutations.end(), 0);

    std::shuffle(permutations.begin(), permutations.end(), randomEngine);

    permutations.resize(512);
    std::copy_n(permutations.begin(), 256, permutations.begin() + 256);

    return permutations;
}

int main()
{
    glm::ivec2 size = { 512, 512 };

    float frequency = 1.0f;
    int octavesCount = 1;
    float persistence = 0.65f;
    float lacunarity = 2.0f;
    std::string resultFileName = "noise.png";

    if (!validatePerlinNoiseParams(size, frequency, octavesCount, lacunarity))
    {
        std::cout << "Error: Incorrect parameters" << '\n';

        return -1;
    }

    std::vector<unsigned char> noiseImage{};
    noiseImage.reserve(size.x * size.y);

    std::mt19937 randomEngine(time(nullptr));
    std::vector<unsigned char> permutations = generatePermutations(randomEngine);

    for (int y = 0; y < size.y; y++)
    {
        for (int x = 0; x < size.x; x++)
        {
            noiseImage.push_back(std::round(255 * perlinNoise(permutations, { x, y }, frequency, octavesCount, persistence, lacunarity)));
        }
    }

    lodepng::encode(resultFileName, noiseImage, size.x, size.y, LodePNGColorType::LCT_GREY);

    std::cout << "Operation has finished successfully" << '\n';

    return 0;
}

但是它看起来像是因为数组的大小而受到限制，数组的大小是512（最大256 + 256）。因此，我以这种方式实现了参数的验证：

bool validatePerlinNoiseParams(glm::ivec2 size, float frequency, int octavesCount, float lacunarity)
{
    glm::vec2 resultVec = glm::dvec2(size - 1) * (frequency * std::pow(lacunarity, octavesCount));
    return resultVec.x < 256 && resultVec.y < 256;
}

代码运行良好，但问题是：我可以增加permutations数组的大小来避免这样的严格限制吗？
编辑：我已经实现了这个函数，它生成了适当大小的permutations数组。算法似乎运行良好。唯一的问题是这个解决方案中有没有隐藏的bug？

std::vector<unsigned char> generatePermutations(std::mt19937& randomEngine, glm::ivec2 size, float frequency, int octavesCount, float lacunarity)
{
    const int initialSize = 256;

    std::vector<unsigned char> permutations(initialSize);
    std::iota(permutations.begin(), permutations.end(), 0);
    std::shuffle(permutations.begin(), permutations.end(), randomEngine);

    glm::ivec2 resultVec = glm::dvec2(size - 1) * (frequency * std::pow(lacunarity, octavesCount));
    int result = std::max(resultVec.x / initialSize, resultVec.y / initialSize);

    permutations.resize((result + 2) * initialSize);
    for (int i = 0; i < result + 1; i++)
    {
        std::copy_n(permutations.begin(), (i + 1) * initialSize, permutations.begin() + initialSize);
    }

    return permutations;
}