Marching Cubes Algorithm using Unity

Marching cubes is a computer graphics algorithm for extracting a polygonal mesh of an isosurface from a three dimensional discrete scalar field.
This is my implementation of this algorithm using Unity.

Generating Values

First, we will need a function that takes in a point in 3D space and gives out a single value, we can use this function to sample points in a particular region of space in regular intervals. I used a function that returns a random value between 0 and 1, a better implementation would be to use a noise function, like Perlin noise or Simplex noise.
We then set a value called Surface Level, the points below the Surface Level will disappear. Those points we can think of them as in empty space and the points above the Surface Level we will think of as on the surface of inside of a certain shape, the goal of the Marching Cubes Algorithm is to construct the surface of that shape from triangles so we can display it as a mesh.

Algorithm

To think about this problem we can simplify it to a single cube, there are 8 corner points, each can be either inside or outside of the shape which gives as 2^8 or 256 possible configurations, we can use a triangulation table to represent these states.

public static class TriangluationTable
{
    private static readonly int[,] triangleConnectionTable = new int[,]
	   {
		{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
		{0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
        
        	...

        	{0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
		{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}
       };
}

So let's take this case for example:

Corner points 0, 1, 2 and 5 are active which we can interpret as configuration 11100100 or configuration 228, this is the code for calculating that index:

// gets the index of this particular cube in the triangulation table
int cubeIndex = 0;
for (int i = 0; i < 8; i++)
{
    if(values[i] > surfaceLevel)
    {
        cubeIndex |= 1 << i;
    }
}

now we can lookup that entry in the triangulation table

{4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1}

this tells me to join edges 4, 11, 7 and 9, 11, 4 and 9, 2, 11 and 9, 1, 2 to form 4 triangles.

All we need to do now is march through the entire space and construct the mesh one cube at a time, Thus, Marching Cubes.

using the FastNoiseLite library from Jordan Peck, we can apply a noise function instead of random values, this can give us a multitude of shapes depending on the noise function used, using Simplex Noise we can generate terrain like meshes.

We can apply a little bit of smoothing on the result to obtain realistic results instead of the blocky look.