How to produce the perfect (tight) bounding box for a game object in Unity relative to a specific camera.

unity_object_bounding_box.cs

    private Rect Get_object_bounding_box(GameObject game_object, Camera cam)
    {
        // This is a relativly intense way as it is looking at each mesh point to calculate the bounding box.
        // but it produces perfect bounding boxes so yolo.

        // get the mesh points
        Vector3[] vertices = game_object.GetComponent<MeshFilter>().mesh.vertices;

        // apply the world transforms (position, rotation, scale) to the mesh points and then get their 2D position
        // relative to the camera
        Vector2[] vertices_2d = new Vector2[vertices.Length];
        for (var i = 0; i < vertices.Length; i++)
        {
            vertices_2d[i] = cam.WorldToScreenPoint(game_object.transform.TransformPoint( vertices[i]));
        }

        // find the min max bounds of the 2D points
        Vector2 min = vertices_2d[0];
        Vector2 max = vertices_2d[0];
        foreach (Vector2 vertex in vertices_2d)
        {
            min = Vector2.Min(min, vertex);
            max = Vector2.Max(max, vertex);
        }

        // thats our perfect bounding box
        return new Rect(min.x, min.y, max.x - min.x, max.y - min.y);
    }