301484: CF280A. Rectangle Puzzle
Memory Limit:256 MB
Time Limit:2 S
Judge Style:Text Compare
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Description
Rectangle Puzzle
题意翻译
## 题目背景 一个平面上有两个矩形。 ## 题目描述 两个矩形的中心都位于坐标轴原点(即矩形对称的中心)。 第一个矩形的边与坐标轴平行,与$x$轴平行的边的长度等于$w$,与$y$轴平行的边的长度等于$h$。 第二个矩形可以通过用角度$α$相对于坐标原点旋转第一个矩形来获得。 请你求出两个矩形的重叠面积(图中阴影面积) ![](https://cdn.luogu.org/upload/vjudge_pic/CF280A/052b43ecd665cd6e4ffd3e118c46f92dcd4eb612.png)题目描述
You are given two rectangles on a plane. The centers of both rectangles are located in the origin of coordinates (meaning the center of the rectangle's symmetry). The first rectangle's sides are parallel to the coordinate axes: the length of the side that is parallel to the $ Ox $ axis, equals $ w $ , the length of the side that is parallel to the $ Oy $ axis, equals $ h $ . The second rectangle can be obtained by rotating the first rectangle relative to the origin of coordinates by angle $ α $ . ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF280A/052b43ecd665cd6e4ffd3e118c46f92dcd4eb612.png)Your task is to find the area of the region which belongs to both given rectangles. This region is shaded in the picture.输入输出格式
输入格式
The first line contains three integers $ w,h,α $ $ (1<=w,h<=10^{6}; 0<=α<=180) $ . Angle $ α $ is given in degrees.
输出格式
In a single line print a real number — the area of the region which belongs to both given rectangles. The answer will be considered correct if its relative or absolute error doesn't exceed $ 10^{-6} $ .
输入输出样例
输入样例 #1
1 1 45
输出样例 #1
0.828427125
输入样例 #2
6 4 30
输出样例 #2
19.668384925