We study the problem of finding maximum-area and maximum-perimeter rectangles that are inscribed in polygons in the plane. There has been a fair amount of work on this problem when the rectangles have to be axis-aligned or when the polygons are convex. We consider this problem in polygons with n vertices that are not necessarily convex, possibly with holes, and with no restriction on the orientation of the rectangles. We present an algorithm that computes a maximum-area rectangle and a maximum-perimeter rectangle in $O(n^3\log n)$ time using $O(k{n}^2+n)$ space, where k is the number of reflex vertices of the polygon. Our algorithm can report all maximum-area rectangles in the same time using $O(n^3)$ space. We also present a simple algorithm that finds a maximum-area rectangle inscribed in a convex polygon with n vertices in $O(n^3)$ time using $O(n)$ space.

我们研究寻找平面中内接多边形的最大面积和最大周长矩形的问题。当矩形必须轴向对齐或多边形为凸形时，在此问题上已经进行了大量工作。我们在具有n个顶点（不一定是凸的，可能有孔）且对矩形的方向没有限制的多边形中考虑此问题。我们提出了一种算法，该算法可计算出以下区域中的最大面积矩形和最大周边矩形$Ø（{ñ}^3\mathrm{日志}ñ）$ 时间使用 $Ø（ķ{ñ}^2+ñ）$空间，其中k是多边形的反射顶点数。我们的算法可以使用以下命令同时报告所有最大面积的矩形$Ø（{ñ}^3）$空间。我们还提出了一种简单的算法，该算法可以找到一个内接n个顶点的凸多边形中所刻的最大面积矩形$Ø（{ñ}^3）$ 时间使用 $Ø（ñ）$ 空间。