如何判断两个矩形是否有重叠部分?（某公司校园招聘笔试试题）

         做游戏的公司，自然会关注游戏中物体是否碰撞的问题。我们知道：判断两个圆是否有重叠很简单，当且仅当 r1 + r2 <= d 时，两个圆有重叠部分，矩形可以看成是特殊的圆，一个矩形存在垂直方向和水平方向两个半径，基于该思路，写出算法代码如下：（矩形不会倾斜）

#include
#include
using namespace std;

typedef struct rectangle
{
	float centerX;
	float centerY;
	float width;
	float height;
}Rectangle;

bool areTwoRectsOverlapped(Rectangle rect1, Rectangle rect2)
{
	float verticalDistance;    //垂直距离
	float horizontalDistance;  //水平距离
	verticalDistance = fabs(rect1.centerX - rect2.centerX);
	horizontalDistance = fabs(rect1.centerY - rect2.centerY);

	float verticalThreshold;   //两矩形分离的垂直临界值
	float horizontalThreshold; //两矩形分离的水平临界值
	verticalThreshold = (rect1.height + rect2.height)/2;
	horizontalThreshold = (rect1.width + rect2.height)/2;

	if(verticalDistance > verticalThreshold || horizontalDistance > horizontalThreshold)
		return false;

	return true;
}

int main()
{
	Rectangle rect1 = {0.0, 0.0, 20.0, 10};
	Rectangle rect2 = {6.0, 6.0, 2.1, 1.9};

	if(areTwoRectsOverlapped(rect1, rect2))
		cout << "overlapped" << endl;
	else
	    cout << "not overlapped" << endl;

	return 0;
}