# How would I translate screen coordinates to Isometric coordinates?

I have a function isoToScreen(x, y) that converts Isometric coordinates to Screen coordinates.

var tileW = 16;
var tileH = 16;

var isoToScreen = function(x, y) {
var posX = (x - y) * tileW;
var posY = (x + y) * tileH / 2;

return [posX, posY];
};


But how would I make a function that converts screen coordinates back to Isometric coordinates?

var pos = screenToIso(16, 8);
pos = 1; // Iso X
pos = 0; // Iso Y

• I don't understand how this function works... I mean, if you input 0,0, you get 0,0 out, and that's clearly not screen coordinates for any isometric view I understand. Dec 17, 2012 at 4:15

var screenToIso = function(screenX, screenY)
{
var isoX = screenY / tileH + screenX / (2*tileW)
var isoY = screenY / tileH - screenX / (2*tileW)

return [isoX, isoY];
}


To get this function you need to rewrite the original math

screenX = (isoX - isoY) * tileW
screenY = (isoX + isoY) * tileH / 2


Starting with the first line you get the following:

screenX = (isoX - isoY) * tileW
screenX / tileW = isoX - isoY
screenX / tileW + isoY = isoX


The second line:

screenY = (isoX + isoY) * tileH / 2
2*screenY = (isoX + isoY) * tileH
2*screenY / tileH = isoX + isoY
2*screenY / tileH - isoX = isoY


Now the two lines look as follows:

A) isoX = screenX / tileW + isoY
B) isoY = 2*screenY / tileH - isoX


Then substitute isoY in the line A, with the formula derived from line B:

isoX = screenX / tileW + 2*screenY/tileH - isoX
isoX+isoX = screenX / tileW + 2*screenY/tileH
2*isoX = screenX / tileW + 2*screenY/tileH
isoX = screenX / (2*tileW) + screenY/tileH
isoX = screenY/tileH + screenX / (2*tileW)


And finally, substitute isoX in line B, with the formula derived from line A:

isoY = 2*screenY / tileH - screenX / tileW - isoY
2*isoY = 2*screenY / tileH - screenX / tileW
isoY = screenY / tileH - screenX / (2*tileW)


Solving linear equations comes very much in handy for a lot of programming, especially graphics or game related programming. Pick up a book on Algebra or read some online tutorials, you will thank yourself later.

• I know I am not good in math, and this page clearly proof it! Great! Dec 17, 2013 at 14:10

Just reverse the order of operations:

var tileW = 16;
var tileH = 16;

function screenToIso(x, y)
{
var posX = ((y * 2 / tileH) + (x / tileW))/2;
var posY = (y * 2 / tileH) - posX;

return [posX, posY];
}

• Thanks for reply and code! I am try this code, but... isoToScreen(10, 0); -> 160, 80. screenToIso(160, 80) -> 90, -150; :( Jun 14, 2012 at 2:31
• Whoops, you're right. Fixed Jun 14, 2012 at 3:04