POJ 1269(计算几何初步——简单处理解析几何，求直线交点)

此题给出N组直线，每组2条直线，求出直线是否相交。

如果共线则输出LINE，相交则输入点坐标，否则输出NONE.

解析几何初中都学过一些，不过写成程序还真是麻烦。

情况分成3种：

1.看直线的横坐标是否相等。

2.看直线的纵坐标是否相等。

3.直接用直线公式求解。

View Code

  1 #include<iostream>
  2 #define EPS 1e-8
  3 using namespace std;
  4 
  5 bool equal(double x, double y)
  6 {
  7     return x - y <= EPS && -EPS <= x - y;     
  8 }
  9 
 10 void X_Get_point(double x1, double x2, double y1, double y2, double x0)
 11 {
 12     double k = (y2 - y1)/(x2 - x1);
 13     double b = y2 - k*x2;
 14     double y0 = k*x0 + b;
 15     printf("POINT %.2lf %.2lf\n",x0,y0);
 16 }//已知X,求Y
 17 
 18 void Y_Get_point(double x1, double x2, double y1, double y2, double y0)
 19 {
 20     double k = (y2 - y1)/(x2 - x1);
 21     double b = y2 - k*x2;
 22     double x0 = (y0 - b)/k;
 23     printf("POINT %.2lf %.2lf\n",x0,y0);        
 24 }//已知y，求X
 25 
 26 double cross(double x0, double y0, double x1, double y1)
 27 {
 28     return y1*x0 - x1*y0;    
 29 }
 30 
 31 bool on_line(double x1, double x2, double y1, double y2, double x0, double y0)
 32 {
 33         if (equal(cross(x2-x1,y2-y1,x0-x1,y0-y1),0))return true;
 34         return false;
 35 }//判断点是否在直线上
 36 
 37 int main()
 38 {
 39     int T;
 40     while (scanf("%d",&T) != EOF) {
 41         for (int i(0); i<T; ++i) {
 42             if (i == 0)cout<<"INTERSECTING LINES OUTPUT\n";
 43             double x[4];
 44             double y[4];
 45             scanf("%lf%lf%lf%lf%lf%lf%lf%lf",&x[0],&y[0],&x[1],&y[1],&x[2],&y[2],&x[3],&y[3]);
 46             if (equal(x[0],x[1])) {
 47                 if (equal(x[2],x[3])) {
 48                     if (equal(x[2],x[0])) {
 49                         cout<<"LINE\n";
 50                         continue;        
 51                     }    else {
 52                         cout<<"NONE\n";
 53                         continue;    
 54                     }
 55                 }    else {
 56                     X_Get_point(x[2],x[3],y[2],y[3],x[0]);
 57                     continue;      
 58                 }
 59             }    else {
 60                 if (equal(x[3],x[2])) {
 61                     X_Get_point(x[0],x[1],y[0],y[1],x[2]);
 62                     continue;      
 63                 }    
 64             }
 65             
 66             if (equal(y[0],y[1])) {
 67                 if (equal(y[2],y[3])) {
 68                     if (equal(y[2],y[0])) {
 69                         cout<<"LINE\n";
 70                         continue;    
 71                     }    else {
 72                         cout<<"NONE\n";
 73                         continue;    
 74                     }
 75                 }    else {
 76                     Y_Get_point(x[2],x[3],y[2],y[3],y[0]);
 77                     continue;      
 78                 }
 79             } else {
 80                 if (equal(y[2],y[3])) {
 81                     Y_Get_point(x[0],x[1],y[0],y[1],y[2]);
 82                     continue;                              
 83                 }    
 84             }
 85             
 86             double k1 = (y[1] - y[0])/(x[1] - x[0]);
 87             double k2 = (y[3] - y[2])/(x[3] - x[2]);
 88             if (equal(k1,k2)) {
 89                 if (on_line(x[0],x[1],y[0],y[1],x[2],y[2])) {
 90                     cout<<"LINE\n";    
 91                     continue;
 92                 } else {
 93                     cout<<"NONE\n";    
 94                 }    
 95             }    else {
 96                 double b1 = y[1] - k1*x[1];
 97                 double b2 = y[2] - k2*x[2];
 98                 double y0 = (b2*k1 - b1*k2)/(k1 - k2);
 99                 double x0 = (y0 - b2)/k2;
100                 printf("POINT %.2lf %.2lf\n",x0,y0);
101                 continue;        
102             } 
103         }
104         cout<<"END OF OUTPUT\n";    
105     }
106     return 0;    
107 }