Isometric Grid Math

Overview

Every isometric bug eventually traces back to the coordinate transform. This skill gives the exact, tested grid<->screen formulas for a 2:1 projection so placement and picking are pixel-correct.

When to Use

• Tiles render in the wrong place or overlap.
• Mouse clicks select the wrong tile.
• You are starting a renderer and need the core transform.

Process

1. Fix tile width W and height H (2:1 means W = 2*H).
2. grid->screen: screenX = (col - row) * (W/2); screenY = (col + row) * (H/2).
3. Add the world origin offset so (0,0) is where you want it on screen.
4. screen->grid (for picking): invert the transform using W and H.
5. Round screen->grid results to integer tile coords.
6. Validate round-trip: grid -> screen -> grid returns the original tile.
7. Document the anchor (tile top vs tile center) and stay consistent.

const screenX = (col - row) * (W / 2);
const screenY = (col + row) * (H / 2);
// inverse
const col = ((screenX / (W/2)) + (screenY / (H/2))) / 2;
const row = ((screenY / (H/2)) - (screenX / (W/2))) / 2;

Rationalizations (Stop Lying to Yourself)

Excuse	Reality
"I will tweak offsets until it looks right"	Magic offsets break on resize/zoom. Derive the transform.
"Rounding does not matter"	Unrounded screen->grid selects the wrong tile near edges. Round it.

Red Flags - STOP if you catch yourself:

• Hard-coded pixel offsets instead of a derived transform.
• No screen->grid inverse for picking.
• Round-trip grid->screen->grid does not return the same tile.

Verification

You are NOT done until every box is checked:

• grid->screen and screen->grid are both implemented.
• Round-trip conversion is exact for integer tiles.
• Anchor convention is documented and consistent.