I have a 2D map, for each element I apply this isometric projection to place my Sprite

 //Element e;
 float[] f= projection(e.getX(), e.getY() ,z);
         // x and y represent Sprite Coordonate (tile_width and height depend of my 
         // camera size and the number of elements in x and in y
 float x =  f[0]*tile_width;
 float y =  f[1]*tile_height;

   public float[] projection(float x, float y, float z)
   {
     return new float[]{  (( x )-(y) ) , ((x/2) + (y/2) - z  )}; 
   }

the sprite for one element :

The result of my projection :

The problem is I need to add an offset of tile_height/2 to the y and tile_width/2 to the x to have something like this (in the red rectangle I drawed with paint what I want) :

Where did I make wrong?

(I found the projection method in How should I sort images in an isometric game so that they appear in the correct order? )