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3329：Twirl Around

Special Judge 特殊评判
题目描述
Let's think about a bar rotating clockwise as if it were a twirling baton moving on a planar surface surrounded by a polygonal wall (see Figure 1).

Figure 1. A bar rotating in a polygon

Initially, an end of the bar (called "end A") is at (0,0), and the other end (called "end B") is at (0,L) where L is the length of the bar. Initially, the bar is touching the wall only at the end A.

The bar turns fixing a touching point as the center. The center changes as a new point touches the wall.

Your task is to calculate the coordinates of the end A when the bar has fully turned by the given count R.


Figure 2. Examples of turning bars

In Figure 2, some examples are shown. In cases (D) and (E), the bar is stuck prematurely (cannot rotate clockwise anymore with any point touching the wall as the center) before R rotations. In such cases, you should answer the coordinates of the end A in that (stuck) position.

You can assume the following:

When the bar's length L changes by ε (|ε| < 0.00001), the final (x,y) coordinates will not change more than 0.0005.
输入解释

The input consists of multiple datasets. The number of datasets is no more than 100. The end of the input is represented by "0 0 0".

The format of each dataset is as follows:

L R N
X1 Y1
X2 Y2
...
XN YN

L is the length of the bar. The bar rotates 2π× R radians (if it is not stuck prematurely). N is the number of vertices which make the polygon.

The vertices of the polygon are arranged in a counter-clockwise order. You may assume that the polygon is simple, that is, its border never crosses or touches itself.

N, Xi and Yi are integer numbers; R and L are decimal fractions. Ranges of those values are as follows:

1.0 ≤ L ≤ 500.0,
1.0 ≤ R ≤ 10.0,
3 ≤ N ≤ 100,
-1000 ≤ Xi ≤ 1000,
-1000 ≤ Yi ≤ 1000,
X1 ≤ -1, Y1 = 0,
X2 ≥ 1, Y2 = 0.
输出解释

For each dataset, print one line containing x- and y-coordinates of the final position of the end A, separated by a space. The value may contain an error less than or equal to 0.001. You may print any number of digits after the decimal point.

输入样例 
4.0 2.0 8
-1 0
5 0
5 -2
7 -2
7 0
18 0
18 6
-1 6
4.0 2.0 4
-1 0
10 0
10 12
-1 12
4.0 1.0 7
-1 0
2 0
-1 -3
-1 -8
6 -8
6 6
-1 6
4.0 2.0 6
-1 0
10 0
10 3
7 3
7 5
-1 5
5.0 2.0 6
-1 0
2 0
2 -4
6 -4
6 6
-1 6
6.0 1.0 8
-1 0
8 0
7 2
9 2
8 4
11 4
11 12
-1 12
0 0 0
输出样例 
16.0 0.0
9.999999999999998 7.4641016151377535
0.585786437626906 -5.414213562373095
8.0 0.0
6.0 0.0
9.52786404500042 4.0
提示

Note that the above sample input corresponds to the cases in Figure 2. For convenience, in Figure 3, we will show an animation and corresponding photographic playback for the case (C).

该题目是Virtual Judge题目，来自 北京大学POJ
题目来源 Japan 2007 Domestic
源链接： POJ-3329
最后修改于 2020-10-29T06:58:50+00:00 由爬虫自动更新
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通过率 --%
时间上限 内存上限
10000 65536