I'm working on an isometric tile rendering engine and I need to reverse a function I used to translate the Cartesian coordinates into isometric coordinates. I've already written a function for this, but I've been getting a strange logical error and I think it must be somewhere in my code for translating from isometric coordinates back into Cartesian. Anyways, here's the code for translating Cartesian->Isometric

    private Vector2 cartToIso(Vector2 init){
        Vector2 iso = new Vector2();
        iso.x = (((init.x - init.y) * TILE_WIDTH_HALF))+X_OFFSET;
        iso.y = MAP_HEIGHT-TILE_HEIGHT-((init.x + init.y) * TILE_HEIGHT_HALF);  
        return iso;  
    }

Any suggestions would be appreciated. Also if anyone was wondering, what I'm trying to do right now is create an algorithm for tile picking in my engine. The API(LibGDX) is a little strange in the sense that it uses a bottom-up Y coordinate system but with any of the input(ie, clicks) it uses a top-down Y coordinate system. I can post the code I have for tile picking later if anyone thinks they can help me more, but I'll save it for now since it's pretty long.

I'm working on an isometric tile rendering engine and I need to reverse a function I used to translate the Cartesian coordinates into isometric coordinates. I've already written a function for this, but I've been getting a strange logical error and I think it must be somewhere in my code for translating from isometric coordinates back into Cartesian. Anyways, here's the code for translating Cartesian->Isometric

    private Vector2 cartToIso(Vector2 init){
        Vector2 iso = new Vector2();
        iso.x = (((init.x - init.y) * TILE_WIDTH_HALF))+X_OFFSET;
        iso.y = MAP_HEIGHT-TILE_HEIGHT-((init.x + init.y) * TILE_HEIGHT_HALF);  
        return iso;  
    }

Any suggestions would be appreciated. Also if anyone was wondering, what I'm trying to do right now is create an algorithm for tile picking in my engine. The API(LibGDX) is a little strange in the sense that it uses a bottom-up Y coordinate system but with any of the input(ie, clicks) it uses a top-down Y coordinate system. I can post the code I have for tile picking later if anyone thinks they can help me more, but I'll save it for now since it's pretty long.

Edit: This is the method I use to reverse it, and it seems to be giving me the incorrect results. Does this look correct?

    private Vector2 isoToCart(int x, int y){
        Vector2 cart = new Vector2();
        x = x-X_OFFSET;
        y = y-MAP_HEIGHT;
        cart.x = (x / TILE_WIDTH_HALF + (y / TILE_HEIGHT_HALF)) /2;
        cart.y = (y / TILE_HEIGHT_HALF -(x / TILE_WIDTH_HALF)) /2;
        return cart;
    }