闪电生成算法

儿时想搞明白的闪电生成算法, 今天终于想起来并且看明白了.

算法很简单.

把起点和终点不断二分, 直到一个极限值, 然后再全部连接.

 1     void drawLightning(HDC hdc, const POINT &start, const POINT &end, float diff)
 2     {
 3         if (diff < s_minDiff)
 4         {
 5             MoveToEx(hdc, start.x, start.y, nullptr);
 6             LineTo(hdc, end.x, end.y);
 7         }
 8         else
 9         {
10             POINT mid = {
11                 (start.x + end.x) / 2,
12                 (start.y + end.y) / 2,
13             };
14             mid.x += LONG((random() - 0.5f) * diff);
15             mid.y += LONG((random() - 0.5f) * diff);
16             drawLightning(hdc, start, mid, diff / 2);
17             drawLightning(hdc, end, mid, diff / 2);
18         }
19     }

第三个参数 diff 控制闪电的曲折程度,

内部变量 s_minDiff 是极限值.

这两个变量决定闪电有多少个关键点.

 

假设 diff == 10, s_minDiff = 5

已知, 每次递归 diff / 2, 因此最终 diff 会小于 s_minDiff, 也就是2.5.

为了方便理解, 可以用二叉树来形象标识.

       0

　0　   0

0   0  0  0

二叉树有3层, 每层都是一次递归.

第一层递归 diff / 2 => 10 / 2.

第二层递归 diff / 2 => 5 / 2.

第三层递归 diff < s_minDiff.

所有节点相加就是总共调用次数.

所有画线的操作, 都在叶子节点中.

 

通过以上, 可以计算以下

递归层数 => diff / s_minDiff + 1

画线次数 => 2 ^ (递归层数 - 1)

调用次数 => 2 ^ (递归层数) - 1

 

demo下载