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I have the 3D-coordinates of every vertex of the mesh but that's about it. How would I automatically generate a UV map for this mesh, since this list of vertices will change every time I generate a rock? How do I get all these faces correctly mapped in a (1,1) square?

I have the 3D-coordinates of every vertex of the mesh but that's about it. How would I automatically generate a UV map for this mesh, since this list of vertices will change every time I generate a rock? How do I get all these faces correctly mapped in a (1,1) square?

EDIT 5:

I had to move the code a bit but it finally works now! Like you guys predicted, the seems are not optimal, but I'm happy how it is now. Thanks!

EDIT 4:

Mesh mesh = new Mesh();
mesh.name = "RockMesh";
List<int> Triangles = new List<int>();

var vertices = Vertices.Select(x => new Vertex(x)).ToList();

var result = MIConvexHull.ConvexHull.Create(vertices);
mesh.vertices = result.Points.Select(x => x.ToVec()).ToArray();
var xxx = result.Points.ToList();

foreach(var face in result.Faces)
{
    Triangles.Add(xxx.IndexOf(face.Vertices[0]));
    Triangles.Add(xxx.IndexOf(face.Vertices[1]));
    Triangles.Add(xxx.IndexOf(face.Vertices[2]));
}

mesh.triangles = Triangles.ToArray();

Which gives me the following UV map:

  float scaleFactor = 0.5f;

Vector3[] verts = mesh.vertices;
Vector2[] uvs = new Vector2[verts.Length];

// Iterate over each face (here assuming triangles)
for(int index = 0; index < mesh.triangles.Length; index += 3)
{
    // Get the three vertices bounding this triangle.
    Vector3 v1 = verts[mesh.triangles[index]];
    Vector3 v2 = verts[mesh.triangles[index + 1]];
    Vector3 v3 = verts[mesh.triangles[index + 2]];

    // Compute a vector perpendicular to the face.
    Vector3 normal = Vector3.Cross(v3 - v1, v2 - v1);

    // Form a rotation that points the z+ axis in this perpendicular direction.
    // Multiplying by the inverse will flatten the triangle into an xy plane.
    Quaternion rotation = Quaternion.Inverse(Quaternion.LookRotation(normal));

    // Assign the uvs, applying a scale factor to control the texture tiling.
    uvs[mesh.triangles[index]]     = (Vector2)(rotation * v1) * scaleFactor;
    uvs[mesh.triangles[index + 1]] = (Vector2)(rotation * v2) * scaleFactor;
    uvs[mesh.triangles[index + 2]] = (Vector2)(rotation * v3) * scaleFactor;
}

Which gives me the following UV map: [![enter image description here][2]][2]

  float scaleFactor = 0.5f;

int[] tris = mesh.triangles;

Vector3[] verts = mesh.vertices;
Vector2[] uvs = new Vector2[verts.Length];

// Iterate over each face (here assuming triangles)
for(int index = 0; index < tris.Length; index += 3)
{
    // Get the three vertices bounding this triangle.
    Vector3 v1 = verts[tris[index]];
    Vector3 v2 = verts[tris[index + 1]];
    Vector3 v3 = verts[tris[index + 2]];

    // Compute a vector perpendicular to the face.
    Vector3 normal = Vector3.Cross(v3 - v1, v2 - v1);

        Debug.Log("surface " + index/3 + " : " + (normal*0.5f).magnitude);

    // Form a rotation that points the z+ axis in this perpendicular direction.
    // Multiplying by the inverse will flatten the triangle into an xy plane.
    Quaternion rotation = Quaternion.Inverse(Quaternion.LookRotation(normal));

    // Assign the uvs, applying a scale factor to control the texture tiling.
    uvs[tris[index]]     = (Vector2)(rotation * v1) * scaleFactor;
    uvs[tris[index + 1]] = (Vector2)(rotation * v2) * scaleFactor;
    uvs[tris[index + 2]] = (Vector2)(rotation * v3) * scaleFactor;
}

The red triangle on the left and the dark blue one on the right should be the same shape/size: