Tiling perlin noise seamlessly, but without repeating to generate an infinite 3D world

Question

I have been working on a 3D game in java using LWJGL for a while now. I am trying to make procedurally generated infinite 3D terrain that is generated around the player.

So far I have:

• 3D terrain chunks that are loaded and unloaded when the player moves. These chunks are made up of triangles not quads, and are 128x128 vertices.
• A Perlin noise class that can successfully generate Perlin noise. (I think it is actually something called value noise, but it works)
• A world class that handles loading and unloading of chunks, and applying the height maps to the chunks.

All of this works as it is coded to do, but not how I want it to. I don't know how to tile the noise seamlessly.

How would I make the noise tile, and furthermore, how would I generate large structures such as mountains that occupy probably up to hundreds of chunks.

Here is what is currently happening with the chunks and noise not tiling:

Here is my Perlin noise code:

private float[][] perlinNoise(int width, int height, int octave, float[][] whiteNoise)
{
    float[][] result = new float[width][height];

    int samplePeriod = 1 << octave;
    float sampleFrequency = 1.0f / samplePeriod;

    for (int i = 0; i < width; i++)
    {
        int x1 = (i / samplePeriod) * samplePeriod;
        int x2 = (x1 + samplePeriod) % width;
        float xBlend = (i - x1) * sampleFrequency;

        for (int j = 0; j < height; j++)
        {
            int y1 = (j / samplePeriod) * samplePeriod;
            int y2 = (y1 + samplePeriod) % height;
            float yBlend = (j - y1) * sampleFrequency;

            float top = (float) MathHelper.interpolateLinear(whiteNoise[x1][y1], whiteNoise[x2][y1], xBlend);

            float bottom = (float) MathHelper.interpolateLinear(whiteNoise[x1][y2], whiteNoise[x2][y2], xBlend);

            result[i][j] = (float) MathHelper.interpolateLinear(top, bottom, yBlend);
        }
    }
    return result;
}

public float[][] generatePerlinNoise(int width, int height, Random random, int octaveCount)
{
    float[][] whiteNoise = new float[width][height];
    float[][][] totalNoise = new float[octaveCount][][];
    float[][] perlinNoise = new float[width][height];
    float amplitude = 1.0f;
    float totalAmplitude = 0.0f;
    float persistance = 0.5f;

    for (int i = 0; i < width; i++)
    {
        for (int j = 0; j < height; j++)
        {
            whiteNoise[i][j] = random.nextFloat() % 1;
        }
    }
    for (int i = 0; i < octaveCount; i++)
    {
        totalNoise[i] = perlinNoise(width, height, i, whiteNoise);
    }
    for (int o = octaveCount - 1; o >= 0; o--)
    {
        amplitude *= persistance;
        totalAmplitude += amplitude;

        for (int i = 0; i < width; i++)
        {
            for (int j = 0; j < height; j++)
            {
                perlinNoise[i][j] += totalNoise[o][i][j] * amplitude;
            }
        }
    }
    for (int i = 0; i < width; i++)
    {
        for (int j = 0; j < height; j++)
        {
            perlinNoise[i][j] /= totalAmplitude;
        }
    }
    return perlinNoise;
}

I think it would also be worth mentioning that I have asked about this on StackOverflow as well.

Answer 1

Given credit to Alan Wolfe for what he said on "INFINITELY tile". A 2d perlin noise (or a 2d simple noise) will have no seam problem as far as you stay away from noise borders (defined by floatin point dimenision) Referencing the image:

and said that you have chunks with 128X128 vertex, in chunk i,j you compute each vertex as :

for x : 0 .. 128-1
 for y : 0 .. 128-1
  PerlinNoise2d.getValue(i*128 + x, j*128 + y)

this , will grant seamless between chunks.

If you want to simulate a infinite world regardless of noise borders , you may use a 3d noise and consider the values on the surface of a sphere.. but this is another story.

Answer 2

I know this is super old, but the underlying implementations of both perlin noise and value noise are just grids that interpolate value fields between cells, so there are two possible options for fixes.

Given a system where you are trying to tile arbitrarily seeded Perlin maps, keep track of the values at the edge nodes for each octave of seeding and run an interpolation pass on a cell the size of the largest octave using the values at the edges of the two divergent maps (for all the smaller octaves excepting the largest you will have to generate all the intermediary values aside from the edge node values)

The alternative system is one where the address of the node informs the seeding (for example, when calculating my random numbers to populate the values for the node, I seed the random generator with something like NodeSeed = GlobalSeed + x + ", " + y In that case every node given the same x, and y will produce the same random value every time. With such a system I can calculate the interpolation overlap with my neighboring node given infinite possible values of x and y. So when I do my interpolation pass I calculate one row/column past the actual value I need for every octave and use that to calculate the interpolated values that will be accurate to the edges of the next cell when I get around to generating it.