POJ1269_Intersecting Lines (ry/Cross Product)

POJ1269_Intersecting Lines (ry/Cross Product)

Solution report

Question Portal

Question:

Determine the positional relationship of a straight line (parallel, coincidence, intersection)

Ideas:

You can use cross product to determine the positional relationship between two straight lines.

AB and CD straight lines

If it is parallel, the endpoint C and the endpoint D will be on the same side of the Line AB.

The coincidence is on the line AB.

The rest is intersection.

For the intersection of two straight lines, the area ratio and the side length ratio can be used.

You can see the figure below, and the derivation is easier.

#include 
 
  #include 
  
   #include 
   
    #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"<
    
     0&&c*d>0)        {            cout<<"NONE"<
     
      
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
      
50 0 4 4 0 4 4 05 0 7 6 1 0 2 35 0 7 6 3 -6 4 -32 0 2 27 1 5 18 50 3 4 0 1 2 2 5
      
Sample Output
      
INTERSECTING LINES OUTPUTPOINT 2.00 2.00NONELINEPOINT 2.00 5.00POINT 1.07 2.20END OF OUTPUT
      
Source
Mid-Atlantic 1996