c# - 给定一个网格，从中心开始向外螺旋，还有一个位置 ID 是什么？

Question

网格:

+---------------+---------------+---------------+---------------+---------------+
| 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)   |
+---------------+---------------+---------------+---------------+---------------+

代码:

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;
}

测试

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)

我已经盯着这个看很久了。我看不到我的错误。给定 (x,y) 位置 id 是什么？这个函数有什么问题？

网格位置不正常，请仔细观察。 -,- 是左上角，+,+ 是右下角。

Answer 1

第二个和第三个else if里面的计算是错误的。在第二个中，最后一个减法实际上应该是一个加法。第三，中间的减法应该是加法。

// ...
} 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);
}
// ...

这会修复所有测试。