poj 1269 Intersecting Lines（判断两条直线三种状态）

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本文介绍了一种通过输入四个点坐标来确定两直线相交情况的算法，包括无交点、共线或交于一点，并提供了具体的实现代码。

Intersecting Lines

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 16792		Accepted: 7233

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 ways: 1) no intersection because they are parallel, 2) intersect in a line because they are on top of one another (i.e. they are the same line), 3) intersect in a point. In this problem you will use your algebraic knowledge to create a program that determines how and where two lines intersect.
Your program will repeatedly read in four points that define two lines in the x-y plane and determine how and where the lines intersect. All numbers required by this problem will be reasonable, say between -1000 and 1000.

Input

The first line contains an integer N between 1 and 10 describing how many pairs of lines are represented. The next N lines will each contain eight integers. These integers represent the coordinates of four points on the plane in the order x1y1x2y2x3y3x4y4. Thus each of these input lines represents two lines on the plane: the line through (x1,y1) and (x2,y2) and the line through (x3,y3) and (x4,y4). The point (x1,y1) is always distinct from (x2,y2). Likewise with (x3,y3) and (x4,y4).

Output

There should be N+2 lines of output. The first line of output should read INTERSECTING LINES OUTPUT. There will then be one line of output for each pair of planar lines represented by a line of input, describing how the lines intersect: none, line, or point. If the intersection is a point then your program should output the x and y coordinates of the point, correct to two decimal places. The final line of output should read "END OF OUTPUT".

Sample Input

5
0 0 4 4 0 4 4 0
5 0 7 6 1 0 2 3
5 0 7 6 3 -6 4 -3
2 0 2 27 1 5 18 5
0 3 4 0 1 2 2 5

Sample Output

INTERSECTING LINES OUTPUT
POINT 2.00 2.00
NONE
LINE
POINT 2.00 5.00
POINT 1.07 2.20
END OF OUTPUT

分析：这个提示真的坑，代码注释自己看吧。

代码如下：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<cstdlib>
#include<algorithm>
using namespace std;

int main()
{
	int n;
	double x1,x2,x3,x4,y1,y2,y3,y4;
	scanf("%d",&n);
	printf("INTERSECTING LINES OUTPUT\n");
	while(n--)
	{
		scanf("%lf%lf%lf%lf%lf%lf%lf%lf",&x1,&y1,&x2,&y2,&x3,&y3,&x4,&y4);
		
		if((x4-x3)*(y2-y1)==(y4-y3)*(x2-x1)) //斜率判断 
		{
			if((x2-x1)*(y3-y1)==(y2-y1)*(x3-x1))// 叉乘判断是否重合 （取一条线上俩点加另外一条直线上一个点） 
				printf("LINE\n");
			else
				printf("NONE\n");
		}
		else
		{
			double A1=y2-y1;	double B1=x1-x2;	double C1=x2*y1-x1*y2;
			double A2=y4-y3;	double B2=x3-x4;	double C2=x4*y3-x3*y4;
			double x0=((C1*B2)-(C2*B1))/((A2*B1)-(A1*B2));
			double y0=(A2*x0+C2)/(-B2);
			//y0=((A1*C2)-(A2*C1))/((A2*B1)-(A1*B2));
			printf("POINT %.2lf %.2lf\n",x0,y0);	//注意double类型，在g++中会出错，提交用c++; 
		}
	}
	printf("END OF OUTPUT\n");
	return 0;
}