Given the grid, starting from the center and the spiral, and the position, what is the identifier?

Question

Grid:

+---------------+---------------+---------------+---------------+---------------+
| id:  20       | id:  19       | id:  18       | id:  17       | id:  16       |
| pos: (-2, -2) | pos: (-1, -2) | pos: (0, -2)  | pos: (1, -2)  | pos: (2, -2)  |
+---------------+---------------+---------------+---------------+---------------+
| id:  21       | id:  6        | id:  5        | id:  4        | id:  15       |
| pos: (-2, -1) | pos: (-1, -1) | pos: (0, -1)  | pos: (1, -1)  | pos: (2, -1)  |
+---------------+---------------+---------------+---------------+---------------+
| id:  22       | id:  7        | id:  0        | id:  3        | id:  14       |
| pos: (-2, 0)  | pos: (-1, 0)  | pos: (0, 0)   | pos: (1, 0)   | pos: (2, 0)   |
+---------------+---------------+---------------+---------------+---------------+
| id:  23       | id:  8        | id:  1        | id:  2        | id:  13       |
| pos: (-2, 1)  | pos: (-1, 1)  | pos: (0, 1)   | pos: (1, 1)   | pos: (2, 1)   |
+---------------+---------------+---------------+---------------+---------------+
| id:  24       | id:  9        | id:  10       | id:  11       | id:  12       |
| pos: (-2, 2)  | pos: (-1, 2)  | pos: (0, 2)   | pos: (1, 2)   | pos: (2, 2)   |
+---------------+---------------+---------------+---------------+---------------+

The code:

public static int IDFromPos(int sectionX, int sectionY) {
    int sectionId = 0;
    if (sectionX < 0 && Mathf.Abs (sectionX) >= Mathf.Abs (sectionY)) {
        sectionId = (int)Mathf.Pow (((-2 * sectionX) + 1), 2) - 1 - (-sectionX - sectionY);
    } else if (sectionX > 0 && Mathf.Abs (sectionX) >= Mathf.Abs (sectionY)) {
        sectionId = (int)Mathf.Pow (((2 * sectionX) + 1), 2) - 1 - (4 * sectionX) - (-sectionX - sectionY);
    } else if (sectionY < 0) {
        sectionId = (int)Mathf.Pow (((-2 * sectionY) + 1), 2) - 1 - (2 * sectionY) - (-sectionY + sectionX);
    } else {
        sectionId = (int)Mathf.Pow ((2 * (sectionY - 1) + 1), 2) + (sectionY - 1 + sectionX);
    }

    return sectionId;
}

Test

IDFromPos(-2, -2) = 20
IDFromPos(-2, -1) = 21
IDFromPos(-2, 0) = 22
IDFromPos(-2, 1) = 23
IDFromPos(-2, 2) = 24
IDFromPos(-1, -2) = 27 (should be 19)
IDFromPos(-1, -1) = 6
IDFromPos(-1, 0) = 7
IDFromPos(0, 0) = 0
IDFromPos(0, 1) = 1
IDFromPos(0, 2) = 10
IDFromPos(1, 0) = 5  (should be 3)
IDFromPos(1, 1) = 6  (should be 2)
IDFromPos(1, 2) = 11
IDFromPos(2, 0) = 18 (should be 14)
IDFromPos(2, 1) = 19 (should be 13)
IDFromPos(2, 2) = 20 (should be 12)

I've been looking at this for so long. I do not see my error (s). Given the position (x,y), what is id? What is wrong with this feature?

The grid positions are not normal, so please look carefully. -, - top left, +, + bottom right.

Answer 1

The calculations inside the second and third else ifare incorrect. In the second case, the last subtraction should actually be an addition. In the third case, the average subtraction should be an addition.

// ...
} else if(sectionX > 0 && Mathf.Abs(sectionX) >= Mathf.Abs(sectionY)) {
    sectionId = (int)Mathf.Pow(((2 * sectionX) + 1), 2) - 1 - (4 * sectionX) + (-sectionX - sectionY);
} else if(sectionY < 0) {
    sectionId = (int)Mathf.Pow(((-2 * sectionY) + 1), 2) - 1 + (2 * sectionY) - (-sectionY + sectionX);
}
// ...

This fixes all your tests.

Answer 2

:

x * x >= y * y, x >= 0:
   id = 4 * x * x - x - y
x * x >= y * y, x < 0:
   id = 4 * x * x - 3 * x + y
y * y < x * x, y >= 0:
   id = 4 * y * y - 3 * y + x
y * y < x * x, y < 0:
   id = 4 * y * y - y - x

id(2,1) = 16 - 2 - 1 = 12
id(2,-1) = 16 - 2 + 1 = 15
id(-2,1) = 16 + 6 + 1= 23
id(-1, -2) = 16 + 2 + 1= 19
id(-1, 2) = 16  - 6 - 1= 9