perline_noise

This repogitory creates various mountains by using perline noise. Check out this article to understand perline noise in detail.

Related article I wrote

• Create Random 3D Terrain by Using Perline Noise

Algorithm

1. Create random gradient vectors

Each grid point has a gradient vector, which has a random angle.

dirs = [
    (math.cos(a * 2.0 * math.pi / 256), math.sin(a * 2.0 * math.pi / 256))
    for a in range(256)
]

2. Caculate distance vector

The vector from each grid point to the target point is called a distance vector.

3. Calculate the dot product of the gradient vector and distance vector

A grid point that is close to a certain point has a stronger influence. To do this smoothly, use the following fade function.

$$ 6t^5-15t^4+10t^3 $$

def calculate_weighted_dot_product(gridX, gridY, x, y, period, dirs, perm):
    distX, distY = abs(x - gridX), abs(y - gridY)
    # The closer the distance between a point and the grid,
    # the greater the weight of that grid.
    weightX = 1 - 6 * distX**5 + 15 * distX**4 - 10 * distX**3
    weightY = 1 - 6 * distY**5 + 15 * distY**4 - 10 * distY**3
    hashed = perm[perm[int(gridX) % period] + int(gridY) % period]
    dot = (x - gridX) * dirs[hashed][0] + (y - gridY) * dirs[hashed][1]

    return weightX * weightY * dot

4. Merge results in multiple octaves

By merging results in octaves with different frequencies and amplitudes, you can get more natural and detailed results.

def calculate_octave_perline_noise(x, y, period, octs, dirs, perm):
    noise = 0
    # Add noise functions
    for octave in range(octs):
        amplitude = 0.5**octave
        frequency = 2**octave
        noise += amplitude * create_noise(
            x * frequency, y * frequency, period * frequency, dirs, perm
        )

    return noise

Implementation

You can get a 2D random image by running following command.

python3 create_perline_noise.py --size 128 --octs 5 --set_seed

You can get a 3D random mountain by running following command.

python create_3d_terrain.py --size 128 --octs 5 --set_seed

If you want a rough mountain, you should change the number of octs from 5 to 1.

If you want to output a different mountain each time it is executed, do not specify the --set_seed argument.

python create_3d_terrain.py --size 128 --octs 5

References

• How do you generate tileable Perlin noise?
• Understanding Perlin Noise
• Improving Noise
• An Image Synthesizer
• Custom hillshading in a 3D surface plot