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Problem J

Posted by ACRush at 2009-11-01 10:31:04
In Reply To:武汉赛区比赛9:00-14:00,清华校内PK最终决战 Posted by:ACRush at 2009-11-01 08:59:48
给定两条线段L1和L2,计算所有点P{存在A,B,使得A\in L1,B\in L2并且\angle{A,P,B}=90\degree}形成区域的面积

换一个方向思考,对于两个点A和B,能看到他们的点就是以他们为直径的圆周。

所以这个问题就是计算:
令L1(A1-B1)和L2(A2-B2),分别以A1A2,A1B2,B1A2,B1B2为直径作4个圆,计算不超过4个圆和4个三角形的面积并或者交,其实只要计算面积交就可以了,面积并可以用容斥原理来计算。

有个难点:判断一个圆(三角形)内部都可以看到

有两个不确定因素:
(1)THU的两个队伍好像都没有圆面积并的模板,如果一些队伍有模板,效果会比较好
(2)龙贝格积分精度够不够。

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