Koch 分形，海岸线，雪花

此算法用于生成Koch分形（海岸线，雪花）。速度高速，效果绚丽

//支持的初始直线水平角度为60 的倍数。 交换起点与终点坐标可改变生成方向
void Koch(CDC *pDC, int x1, int y1, int x2, int y2, int n)
{
	if (n > 0)
	{
		double k = 1.0*(y2 - y1) / (x2 - x1);
		int x3 = (x2 - x1) / 3;
		int y3 = (y2 - y1) / 3;

		Koch(pDC, x1, y1, x1 + x3, y1 + y3, n - 1);
		Koch(pDC, x2 - x3, y2 - y3, x2, y2, n - 1);
		if (abs(k) <= 1e-6)
		{
			Koch(pDC, x1 + x3, y1, x1 + x3 + x3 / 2, y1 + sqrt(3.0) / 2 * x3, n - 1);
			Koch(pDC, x1 + x3 + x3 / 2, y1 + sqrt(3.0) / 2 * x3, x2 - x3, y1, n - 1);
		}
		else if (k > 0)
		{
			Koch(pDC, x1, y2 - y3, x2 - x3, y2 - y3, n - 1);
			Koch(pDC, x1 + x3, y1 + y3, x1, y2 - y3, n - 1);
		}
		else
		{
			Koch(pDC, x1 + x3, y1 + y3, x2, y1 + y3, n - 1);
			Koch(pDC, x2, y1 + y3, x2 - x3, y2 - y3, n - 1);
		}
	}
	else
	{
		pDC->MoveTo(x1, y1);
		pDC->LineTo(x2, y2);
	}
}

调用：

int k = 4; //递归的深度
	CPen pen, *oldpen;

	pen.CreatePen(PS_SOLID, 1, RGB(255, 0,0 ));
	oldpen = pDC->SelectObject(&pen);
	Koch(pDC, 800, 150, 440, 150, k);
	pen.DeleteObject();

	pen.CreatePen(PS_SOLID, 1, RGB(0, 255, 0));
	pDC->SelectObject(&pen);
	Koch(pDC, 440, 200, 800, 200, k);
	pen.DeleteObject();

	pen.CreatePen(PS_SOLID, 1, RGB(0, 0, 255));
	pDC->SelectObject(&pen);
	Koch(pDC, 200, 100, 300, 275, k);
	Koch(pDC, 400, 100, 200, 100, k);
	Koch(pDC, 300, 275, 400, 100, k);
	pen.DeleteObject();
	pDC->SelectObject(oldpen);

递归4次的效果图例如以下：