algorithm - Finding out which tile a mouse click landed in

I am working on an isometric grid based game and im having an issue trying to link a mouse click from the user to a tile. I have been able to split the problem into 2 parts :

• Finding a rectangle that surrounds a tile (which I have been able to do)


• Figuring out from the rectangle which tile the click landed in (has got me stumped)

Here is an example of a rectangle with tiles on the inside:

The rectangle is 70px long and 30px high so if i use an input of say 30x(top)/20y(left) how would I go about determining which tile this fell into?

Answer

For each step you make in x direction you will move 35px left and -15px up to your canvas;

For each step you make in y direction you will move -35px left and -15px up to your canvas;

This means that you can convert your tile coordinate system easely in pixel:

(x,y) => (35·x,-15·x) + (-35·y, -15·y) = (35·x - 35·y, -15·x - 15·y) = (Xpx,Ypx)

You have to resolve the inverse problem you know Xpx and Ypx and you want to know x and y (in tile coordinate).

Xpx = 35·x - 35·y ;

Ypx = -15·x - 15·y ;

can you solve this?it should be:

x = 1/70·Xpx - 1/30·Ypx

y = -1/70·Xpx - 1/30·Ypx

Obviously you will have non integer values in general case: taking the ceil of both x and y will gives you the coordinate of the whole tile.