POJ 3525(计算几何+凸多边形最大内切圆)

最新推荐文章于 2024-05-11 11:20:21 发布

wust_cyl

最新推荐文章于 2024-05-11 11:20:21 发布

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分类专栏：计算几何文章标签： POJ 3525

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该问题要求编写程序找出一个由凸多边形表示的岛屿上离海最远的点，并报告其与海的距离。输入包含多个数据集，每个数据集代表一个岛屿的边界，由顺时针排列的顶点坐标定义。解决方案涉及找到凸多边形的最大内切圆，通过平移边直到找不到核（多边形中心）来确定最大半径。

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问题描述:

The main land of Japan called Honshu is an island surrounded by the sea. In such an island, it is natural to ask a question: “Where is the most distant point from the sea?” The answer to this question for Honshu was found in 1996. The most distant point is located in former Usuda Town, Nagano Prefecture, whose distance from the sea is 114.86 km.

In this problem, you are asked to write a program which, given a map of an island, finds the most distant point from the sea in the island, and reports its distance from the sea. In order to simplify the problem, we only consider maps representable by convex polygons.

Input

The input consists of multiple datasets. Each dataset represents a map of an island, which is a convex polygon. The format of a dataset is as follows.