[unity] mapping 2D coordinates to ID

        On the plane , Lattice coordinates are usually two-dimensional coordinates （X,Y）, But two-dimensional coordinates have many inconveniences , And if as a key value , Its value taking efficiency is not high . So most of the time , Two dimensional coordinates need to be converted into ID To use （ And can from ID Convert back to coordinates ）.

        The common way is X*N+Y,N For a large enough number . But this way has problems , It can only support all positive numbers or all negative numbers , Once there are positive and negative , Coordinate conversion will fail . Therefore, we need a more convenient algorithm , Can map two-dimensional coordinates into ID, And can transform each other .

1、 sketch

        The basic principle is shown in the figure below ：

          This is it. ID Generation order of , Generate in a spiral shape .

2、 Code

        There is nothing to say about the principle , Pure computation . Go straight to the code ：

        2.1 ： Coordinate conversion ID

        public int ToInt(Vector2Int grid)
        {
            if (grid.x == 0 && grid.y == 0) return 0;

            int k = math.max(math.abs(grid.x), math.abs(grid.y));
            if (grid.x > grid.y)
                return 4 * k * k + 1 + 2 * k + grid.x + grid.y;
            else
                return 4 * k * k + 1 - 2 * k - grid.x - grid.y;
        }

        2.2： ID Convert back to coordinates

        ID Converting back to coordinates is slightly more complicated , The code is as follows ：

        public Vector2Int GetMapGrid(int index)
        {
            if (index == 0) return Vector2Int.zero;
            float sqrtX = math.sqrt(index);
            int k = (int)((sqrtX + 1) / 2);
            if (sqrtX > 2 * k)
            {
                int xAy = index - (4 * k * k + 1) - 2 * k;
                if (xAy < 0)
                {
                    int y = -1 * k;
                    int x = xAy - y;
                    return new Vector2Int(x, y);
                }
                else
                {
                    int x = k;
                    int y = xAy - x;
                    return new Vector2Int(x, y);
                }
            }
            else
            {
                int xAy = (4 * k * k + 1) - index - 2 * k;
                if (xAy < 0)
                {
                    int x = -k;
                    int y = xAy - x;
                    return new Vector2Int(x, y);
                }
                else
                {
                    int y = k;
                    int x = xAy - y;
                    return new Vector2Int(x, y);
                }
            }
        }