我有一个很简单的解决办法

设x1, y1x2,y2,l1,b1,l2分别为它们的坐标和长、宽

考虑条件((x2 现在，这两个矩形重叠的唯一方式是，如果点(x1,y1)的对角线在另一个矩形内或者类似地，点(x2,y2)的对角线在另一个矩形内。这正是上面的条件所暗示的。

我已经实现了c#版本，它很容易转换为c++。

public bool Intersects ( Rectangle rect )
{
  float ulx = Math.Max ( x, rect.x );
  float uly = Math.Max ( y, rect.y );
  float lrx = Math.Min ( x + width, rect.x + rect.width );
  float lry = Math.Min ( y + height, rect.y + rect.height );

  return ulx <= lrx && uly <= lry;
}

假设你已经像这样定义了矩形的位置和大小:

我的c++实现是这样的:

class Vector2D
{
    public:
        Vector2D(int x, int y) : x(x), y(y) {}
        ~Vector2D(){}
        int x, y;
};

bool DoRectanglesOverlap(   const Vector2D & Pos1,
                            const Vector2D & Size1,
                            const Vector2D & Pos2,
                            const Vector2D & Size2)
{
    if ((Pos1.x < Pos2.x + Size2.x) &&
        (Pos1.y < Pos2.y + Size2.y) &&
        (Pos2.x < Pos1.x + Size1.x) &&
        (Pos2.y < Pos1.y + Size1.y))
    {
        return true;
    }
    return false;
}

根据上图给出的函数调用示例:

DoRectanglesOverlap(Vector2D(3, 7),
                    Vector2D(8, 5),
                    Vector2D(6, 4),
                    Vector2D(9, 4));

if块内的比较如下所示:

if ((Pos1.x < Pos2.x + Size2.x) &&
    (Pos1.y < Pos2.y + Size2.y) &&
    (Pos2.x < Pos1.x + Size1.x) &&
    (Pos2.y < Pos1.y + Size1.y))
                 ↓  
if ((   3   <    6   +   9    ) &&
    (   7   <    4   +   4    ) &&
    (   6   <    3   +   8    ) &&
    (   4   <    7   +   5    ))

struct Rect
{
    Rect(int x1, int x2, int y1, int y2)
    : x1(x1), x2(x2), y1(y1), y2(y2)
    {
        assert(x1 < x2);
        assert(y1 < y2);
    }

    int x1, x2, y1, y2;
};

bool
overlap(const Rect &r1, const Rect &r2)
{
    // The rectangles don't overlap if
    // one rectangle's minimum in some dimension 
    // is greater than the other's maximum in
    // that dimension.

    bool noOverlap = r1.x1 > r2.x2 ||
                     r2.x1 > r1.x2 ||
                     r1.y1 > r2.y2 ||
                     r2.y1 > r1.y2;

    return !noOverlap;
}

这是一个用c++快速检查两个矩形是否重叠的方法:

return std::max(rectA.left, rectB.left) < std::min(rectA.right, rectB.right)
    && std::max(rectA.top, rectB.top) < std::min(rectA.bottom, rectB.bottom);

它的工作原理是计算相交矩形的左右边界，然后比较它们:如果右边界等于或小于左边界，这意味着交点是空的，因此矩形不重叠;否则，它将再次尝试顶部和底部边框。

What is the advantage of this method over the conventional alternative of 4 comparisons? It's about how modern processors are designed. They have something called branch prediction, which works well when the result of a comparison is always the same, but have a huge performance penalty otherwise. However, in the absence of branch instructions, the CPU performs quite well. By calculating the borders of the intersection instead of having two separate checks for each axis, we're saving two branches, one per pair.

如果第一个比较有很高的错误几率，那么四个比较方法可能比这个方法更好。但这是非常罕见的，因为这意味着第二个矩形通常在第一个矩形的左边，而不是在右边或重叠;大多数情况下，您需要检查第一个矩形的两侧，这通常会使分支预测的优势失效。

根据矩形的预期分布，这种方法还可以进一步改进:

If you expect the checked rectangles to be predominantly to the left or right of each other, then the method above works best. This is probably the case, for example, when you're using the rectangle intersection to check collisions for a game, where the game objects are predominantly distributed horizontally (e.g. a SuperMarioBros-like game). If you expect the checked rectangles to be predominantly to the top or bottom of each other, e.g. in an Icy Tower type of game, then checking top/bottom first and left/right last will probably be faster:

return std::max(rectA.top, rectB.top) < std::min(rectA.bottom, rectB.bottom)
    && std::max(rectA.left, rectB.left) < std::min(rectA.right, rectB.right);

然而，如果相交的概率接近于不相交的概率，那么最好有一个完全无分支的替代方案:

return std::max(rectA.left, rectB.left) < std::min(rectA.right, rectB.right)
     & std::max(rectA.top, rectB.top) < std::min(rectA.bottom, rectB.bottom);

(注意&&变成了一个&)

最简单的方法是

/**
 * Check if two rectangles collide
 * x_1, y_1, width_1, and height_1 define the boundaries of the first rectangle
 * x_2, y_2, width_2, and height_2 define the boundaries of the second rectangle
 */
boolean rectangle_collision(float x_1, float y_1, float width_1, float height_1, float x_2, float y_2, float width_2, float height_2)
{
  return !(x_1 > x_2+width_2 || x_1+width_1 < x_2 || y_1 > y_2+height_2 || y_1+height_1 < y_2);
}

首先要记住在计算机中坐标系统是颠倒的。x轴与数学中的相同，但y轴向下增大，向上减小。 如果矩形是从中心画的。 如果x1坐标大于x2加上它的一半宽。然后这意味着他们会互相接触。用同样的方法向下+一半高。它会碰撞的。