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Re:最多多少点呐?

Posted by xieweibbz at 2012-03-31 20:00:21 on Problem 1584
In Reply To:最多多少点呐? Posted by:zhao0057 at 2006-05-10 19:34:25
题意:已知一个多边形的n个顶点坐标,然后再给一个钉子,给定钉子的半径和圆心坐标,首先判断多边形是否为凸多边形,若为凸多边形,再判断钉子是否可以放到凸多边形内部。
 
思路:很好的计算几何。
1.由于顶点给出的顺序可能为逆时针或顺时针,所以在判断是否为凸边变形,利用叉积的性质,每个点依次扫描看是否都顺着同一的方向转动。
2.判断圆(钉子)是否在多边形内部,第一步判断圆心是否在凸多边形内部(以圆心为定点扫描一周),第二步再判断圆心到某一边的最短距离,若存在某最短距离大于圆心,则圆不能放在凸多边内。

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