Isometric coords to cartesian coords

Question

I'm new to the tilemap feature of Unity, and I'm having a hard time with all those coords.

I created a new project, added an isometric tilemap and left all values to their default. In the Unity Editor (and in-game at runtime as well), the coordinates of the cells are like this:

This is pretty disturbing to me and it will be to most players (not programmers) too I guess.

I would like something like this:

However, I can't figure out how to do the transformation.

I tried this:

Vector3 currentWorldPos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
Vector3Int currentCellPos = _grid.WorldToCell(currentWorldPos); // This gives the coordinates as in the Unity Editor except for z
currentCellPos.z = 0; // Set z to 0 so the coordinates of the cell are exactly as in the Unity Editor
Vector3 cartesianCellPos = new Vector3((2 * currentCellPos.y + currentCellPos.x) / 2, (2 * currentCellPos.y - currentCellPos.x) / 2, 0); // Try to transform the Unity coordinates into cartesian coordinates: WRONG RESULT

But this calculation gives weird results, not what I expect at all.

Do you know how I could transform the Unity coordinates shown in the first screenshot into the coordinates shown in the second screenshot?

Answer 1

The coordinate system you've chosen is not a Cartesian plane. The axis x=0 forms a zig-zag instead of a straight vertical line, because you've shifted the start point of alternating rows.

Vector2Int ToJaggedRow(Vector3Int isometric) {
    int row = isometric.x + isometric.y;
    int column = isometric.x - isometric.y;

    // Shift alternating rows by one.
    if((Mathf.Abs(row) & 1) == 1)
        column++;

    // All column numbers are now even numbers.
    // Divide by 2 to get them into consecutive integers.
    column /= 2;

    return new Vector2Int(column, row);
}