marching cubes in csharp

Marching Cubes is a popular algorithm used for generating polygonal meshes from volumetric data, commonly used in 3D graphics and game development. Here's how to implement it in C# using Unity:

Step 1: Create a Voxel Grid

Create a regular grid of voxels to represent your volumetric data. Each voxel should store a density value, which can be calculated using a mathematical function or obtained from another source. In Unity, you can represent a voxel grid using a 3D array:

main.cs
int[,,] voxelGrid = new int[width, height, depth];
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Step 2: Determine the Cube Configuration

For each cube in the voxel grid, determine its configuration by comparing the density values of its eight corners with a threshold value. There are 256 possible configurations, but we can simplify the process by using a lookup table.

main.cs
int cubeIndex = 0;
if (voxelGrid[x, y, z] > threshold) cubeIndex |= 1;
if (voxelGrid[x + 1, y, z] > threshold) cubeIndex |= 2;
if (voxelGrid[x + 1, y, z + 1] > threshold) cubeIndex |= 4;
if (voxelGrid[x, y, z + 1] > threshold) cubeIndex |= 8;
if (voxelGrid[x, y + 1, z] > threshold) cubeIndex |= 16;
if (voxelGrid[x + 1, y + 1, z] > threshold) cubeIndex |= 32;
if (voxelGrid[x + 1, y + 1, z + 1] > threshold) cubeIndex |= 64;
if (voxelGrid[x, y + 1, z + 1] > threshold) cubeIndex |= 128;
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Step 3: Generate Vertices and Triangles

For each cube configuration, generate a set of vertices and triangles using look-up tables. Unity provides a Mesh class for creating and manipulating meshes.

main.cs
Vector3[] vertices = new Vector3[12];
for (int i = 0; i < 12; i++)
{
    int edgeIndex = triangleTable[cubeIndex, i];
    if (edgeIndex == -1) break;
    
    Vector3 vertex1 = voxelPositions[edgeIndexTable[edgeIndex, 0]];
    Vector3 vertex2 = voxelPositions[edgeIndexTable[edgeIndex, 1]];
    
    float value1 = voxelGrid[edgeIndexPositions[edgeIndex, 0]].value;
    float value2 = voxelGrid[edgeIndexPositions[edgeIndex, 1]].value;
    
    vertices[i] = vertex1 + (vertex2 - vertex1) * (threshold - value1) / (value2 - value1);
}

int[] triangles = new int[16];
for (int i = 0; i < 16; i++)
{
    int triangleIndex = triangleTable[cubeIndex, i * 3];
    if (triangleIndex != -1)
    {
        triangles[i] = vertexIndex + triangleIndex;
    }
    else
    {
        break;
    }
}

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The voxelPositions array contains the position of each voxel, the edgeIndexTable and edgeIndexPositions arrays contain information about the edges, and the triangleTable array contains information about the triangles to generate.

Step 4: Create a Mesh

Combine and assign the generated vertices and triangles to a Mesh component of a Unity GameObject.

main.cs
Mesh mesh = new Mesh();
mesh.vertices = vertices;
mesh.triangles = triangles;
gameobject.GetComponent<MeshFilter>().mesh = mesh;
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This will create a polygonal mesh, which can then be rendered by a material in a Unity scene, or exported into a file format like OBJ.

Note that the implementation above only generates the mesh at a single threshold value. To create a smooth changing mesh (such as used in 3D-printing toolpaths) you'll need to loop through a series of threshold values, and then interpolate between their corresponding meshes.