We all know that a pair of distinct points on a plane defines a line and that a pair of lines on a plane will intersect in one of three ways: 1) no intersection because they are parallel, 2) intersect in a line because they are on top of one another…

rt,计算几何入门: TOYS Calculate the number of toys that land in each bin of a partitioned toy box. Mom and dad have a problem - their child John never puts his toys away when he is finished playing with them. They gave John a rectangular box to put his toy…

题目:POJ1269 题意:给你两条直线的坐标,判断两条直线是否共线.平行.相交,若相交,求出交点. 思路:直线相交判断.如果相交求交点. 首先先判断是否共线,之后判断是否平行,如果都不是就直接求交点了. #include <iostream> #include <string.h> #include <stdio.h> #include <algorithm> #include <math.h> #include <queue> #…

题意: 二维平面,给两条线段,判断形成的直线是否重合,或是相交于一点,或是不相交. 解法: 简单几何. 重合: 叉积为0,且一条线段的一个端点到另一条直线的距离为0 不相交: 不满足重合的情况下叉积为0 相交于一点: 直线相交的模板 代码: #include <iostream> #include <cstdio> #include <cstring> #include <cstdlib> #include <cmath> #include &l…

Intersecting Lines Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 15145   Accepted: 6640 Description We all know that a pair of distinct points on a plane defines a line and that a pair of lines on a plane will intersect in one of three…

题目大意:求两条直线的交点坐标. 解题关键:叉积的运用. 证明: 直线的一般方程为$F(x) = ax + by + c = 0$.既然我们已经知道直线的两个点,假设为$(x_0,y_0), (x_1, y_1)$,那么可以得到$a = {y_0} - {y_1}$,$b = x_1 – x_0$,$c = x_0y_1 – x_1y_0$. 因此我们可以将两条直线分别表示为 ${F_0}(x) = {\rm{ }}{a_0}x{\rm{ }} + {\rm{ }}{b_0}y{\rm{ }}…

Intersecting Lines Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 15478   Accepted: 6751 Description We all know that a pair of distinct points on a plane defines a line and that a pair of lines on a plane will intersect in one of three…

题意:给定4个点的坐标,前2个点是一条线,后2个点是另一条线,求这两条线的关系,如果相交,就输出交点. 题解:先判断是否共线,我用的是叉积的性质,用了2遍就可以判断4个点是否共线了,在用斜率判断是否平行,最后就是相交了,求交点就好了. 求交点的过程和高中知识差不多,用y=kx+c来求,只不过要注意斜率不存在的时候特殊处理,还有就是求斜率的时候一定要强制转换,(坑爹的我,调试了一小时才找到这个bug) AC代码: #include <map> #include <set> #incl…

http://poj.org/problem?id=1269 题目大意:给四个点,求前两个点所构成的直线和后两个点所构成的直线的位置关系(平行,重合,相交),如果是相交,输出交点坐标. —————————————————————— http://blog.csdn.net/zxy_snow/article/details/6341282 这个人的博客有详细的证明过程,这里直接拿来用即可. 应当优先判断向量平行,这样再判断是否重合能更方便些. #include<cstdio> #include&…

题链: http://poj.org/problem?id=1269 题解: 计算几何,直线交点 模板题,试了一下直线的向量参数方程求交点的方法. (方法详见<算法竞赛入门经典——训练指南>P257) 代码: #include<cstdio> #include<cstring> #include<iostream> using namespace std; struct Point{ double x,y; Point(double _x=0,double…