Question

I draw isometric map with tile 64×32:

const Offset = 160;
int X, Y;

for (int a=0; a < 6; a++)
 for (int b=0; b < 6; b++) {
X = a * 32 - b * 32 + Offset;
Y = a * 16 + b * 16;
DrawTile(X, Y, tile);
 }

Image, illustrating this code: https://i.stack.imgur.com/Rc4kD.png

Dear professionals, please, help with a formula of transformation of mouse coordinates in isometric indexes of a cell. Example: (105; 100) -> [1; 4].

Thanks.

P.S. Please excuse my bad English. I’m just learning…

Answer 1

You have two basis vectors p=(32,16) and q=(-32,16). Any vector r is linear combination of p and q:

r = a * p + b * q
components:
rx = a * 32 - b * 32 = (a - b) * 32
ry = a * 16 + b * 16 = (a + b) * 16
so your indexes are:
a = (2 * ry  + rx) div 64
b = (2 * ry  - rx) div 64
(div is integer division)

Added:
Note that I’ve used middle top point as coordinate zero and take into account your offset