Intersecting Lines（数学）

最新推荐文章于 2019-03-18 20:48:45 发布

Rki-dor

最新推荐文章于 2019-03-18 20:48:45 发布

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CC 4.0 BY-SA版权

文章标签： c/c++

原文链接：http://www.cnblogs.com/handsomecui/p/4922800.html

本文介绍了一个编程问题，即如何确定二维平面上两直线的交点情况，包括无交点、共线或交于一点，并提供了完整的C++代码实现。

Intersecting Lines

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 12844		Accepted: 5703

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
题解：用%lfwa了半天，好无奈改成%f就过了。。。

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>
#include<cstring>
#define geta(y1,y2)(y1-y2)
#define getb(x1,x2)(x2-x1)
#define getc(x1,x2,y1,y2)(x2*y1-x1*y2)
//int gcd(int x,int y){return y==0?x:gcd(y,x%y);}
int js(double &x,double &y){
    int x1,x2,x3,x4,y1,y2,y3,y4;
    scanf("%d%d%d%d%d%d%d%d",&x1,&y1,&x2,&y2,&x3,&y3,&x4,&y4);
    int a1,a2,b1,b2,c1,c2;
    a1=geta(y1,y2);b1=getb(x1,x2);c1=-getc(x1,y1,x2,y2);
    a2=geta(y3,y4);b2=getb(x3,x4);c2=-getc(x3,y3,x4,y4);
    //int t1=gcd(a1,gcd(b1,c1)),t2=gcd(a2,gcd(b2,c2));
   // a1/=t1;b1/=t1;c1/=t1;a2/=t2;b2/=t2;c2/=t2;
   if(a1*b2==b1*a2){
       if(a1*c2==a2*c1&&b1*c2==b2*c1)return 0;
       else return 1;
   }
    
        y=-1.0*(a2*c1-a1*c2)/(a2*b1-a1*b2);
        x=1.0*(b2*c1-b1*c2)/(a2*b1-a1*b2);
        return 2;
}
void input(int T,int cnt){
    while(T--){
    double x,y;
    int temp=js(x,y);
    if(temp==0)puts("LINE");
    else if(temp==1)puts("NONE");
    else printf("POINT %.2lf %.2lf\n",x,y);}
}
int main(){
    int T;
  // while(~scanf("%d",&T)){
       scanf("%d",&T);
       puts("INTERSECTING LINES OUTPUT");
    input(T,0);
    puts("END OF OUTPUT");
 //  }
    return 0;}