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POJ1269_Intersecting Lines(几何/叉积判断直线位置关系)

2024-07-17 12:02:46   227人阅读

解题报告

题目传送门

题意：

判断直线的位置关系（平行，重合，相交）

思路：

两直线可以用叉积来判断位置关系。

AB直线和CD直线

平行的话端点C和端点D会在直线AB的同一侧。

重合的话在直线AB上。

剩下就是相交。

求两直线交点可以用面积比和边长比来求。

看下面的图就知道了，推导就比较容易了



#include <iostream>
#include <cstring>
#include <cstdio>
#define eps 1e-6
#define zero(x) (((x)>0?(x):-(x))>eps)
using namespace std;
struct Point
{
    double x,y;
};
struct L
{
    Point l,r;
};
double xmulti(Point a,Point b,Point p)
{
    return (b.x-a.x)*(p.y-a.y)-(p.x-a.x)*(b.y-a.y);
}
int main()
{
    int n,i,j;
    scanf("%d",&n);
    cout<<"INTERSECTING LINES OUTPUT"<<endl;
    L l1,l2;
    Point p;
    for(i=0; i<n; i++)
    {
        scanf("%lf%lf%lf%lf%lf%lf%lf%lf",&l1.l.x,&l1.l.y,&l1.r.x,&l1.r.y,&l2.l.x,&l2.l.y,&l2.r.x,&l2.r.y);
        double a,b,c,d;
        a=xmulti(l1.l,l1.r,l2.l);//c
        b=xmulti(l1.l,l1.r,l2.r);//d
        c=xmulti(l2.l,l2.r,l1.l);
        d=xmulti(l2.l,l2.r,l1.r);
        if(a==0&&b==0)
            cout<<"LINE"<<endl;
        else if(a*b>0&&c*d>0)
        {
            cout<<"NONE"<<endl;
        }
        else
        {
            p.x=(b*l2.l.x-a*l2.r.x)/(b-a);
            p.y=(b*l2.l.y-a*l2.r.y)/(b-a);
            printf("POINT %.2lf %.2lf\n",p.x,p.y);
        }
    }
    cout<<"END OF OUTPUT"<<endl;
}

Intersecting Lines
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 10764 Accepted: 4803

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

Source

Mid-Atlantic 1996


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