Mesh Generation for 3D Graphing calculator in Unity

gistfile1.txt

// 8-27-24
// This is the code for my youtube video https://youtu.be/Orfc-HsCI_s. It is only for generating the front mesh of the 6 sides.
// I hope you will be able to figure out how to make the rest of the sides.
// (The reason I have not put the rest of the code below is because I am not following DRY, and don't want to refactor the code rn.)
// I don't believe this is a good method for generating the mesh, but I was just unable to think of a better way.
// This is just something simple that returns a passing result. If you know how to, or have any idea, please share with me.
// I'd like of know different ways to create a 3D mesh.
// Furthermore, to solve a 3D equation, in here, because it is for testing, I've provided a hard coded equation.

public int resolution = 100;
    public float size = 5f;

private void GenerateMeshFront()
    {
        Mesh mesh = new Mesh();
        GetComponent<MeshFilter>().mesh = mesh;

        Vector3[] vertices = new Vector3[(resolution) * (resolution)];
        int[] triangles = new int[(resolution - 1) * (resolution - 1) * 6];

        float step = size / resolution;
        int triangleIndex = 0;

        for (int i = 0; i < resolution; i++)
        {
            for (int j = 0; j < resolution; j++)
            {
                float y = -size / 2 + i * step;
                float x = -size / 2 + j * step;
                float z = CalculateZFront(x, y);

                if (z != 0)
                {
                    vertices[i * (resolution) + j] = new Vector3(x, y, z);
                }

                if (i < resolution - 1 && j < resolution - 1)
                {
                    
                    int btmLeft = i * (resolution) + j;
                    int btmRight = btmLeft + 1;
                    int topLeft = (i + 1) * (resolution) + j;
                    int topRight = topLeft + 1;

                    triangles[triangleIndex++] = btmLeft;
                    triangles[triangleIndex++] = topLeft;
                    triangles[triangleIndex++] = topRight;

                    triangles[triangleIndex++] = topRight;
                    triangles[triangleIndex++] = btmRight;
                    triangles[triangleIndex++] = btmLeft;
                }
            }
        }

        mesh.vertices = vertices;
        mesh.triangles = triangles;
        mesh.RecalculateNormals();

        float CalculateZFront(float x, float y)
        {
            // Sphere equation
            //float zSquared = 1 - x * x - y * y;
            
            // Hyperboloid equation
            float zSquared = x * x - y * y;
            
            return -Mathf.Sqrt(Mathf.Max(0, zSquared));
        }
    }