poj 1269 Intersecting Lines 计算几何

Intersecting Lines

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 14236 Accepted: 6298

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 2.20
END OF OUTPUT
题意:判断两条直线是平行,重合,还是相交,相交的话输出交点
#include<iostream>#include<cstdio>#include<algorithm>#include<cmath>using namespace std;const double eps=1E-12;struct Point{    double x,y;    Point (double a=0,double b=0):x(a),y(b)  { }};struct Line //直线{    double A,B,C;    Line(double A=1,double B=-1,double C=0):A(A),B(B),C(C) {}};int lineintersect(Line l1,Line l2,Point &p){    double d=l1.A*l2.B-l2.A*l1.B;    if(abs(d)<eps)    {   if(fabs(l1.C*(l2.A/l1.A)-l2.C)<eps) return 2;        return 0;    }    p.x = (l2.C*l1.B-l1.C*l2.B)/d;    p.y = (l2.A*l1.C-l1.A*l2.C)/d;    return 1;}Line makeline(Point p1,Point p2){    Line tl;    int sign = 1;    tl.A=p2.y-p1.y;    if(tl.A<0)    {        sign = -1;        tl.A=sign*tl.A;    }    tl.B=sign*(p1.x-p2.x);    tl.C=sign*(p1.y*p2.x-p1.x*p2.y);    return tl;}int main(){    int n;    Line L1,L2;    Point a,b,c,d,p;    while(~scanf("%d",&n))    {        printf("INTERSECTING LINES OUTPUT\n");        while(n--)        {            scanf("%lf %lf %lf %lf %lf %lf %lf %lf",&a.x,&a.y,&b.x,&b.y,&c.x,&c.y,&d.x,&d.y);            L1=makeline(a,b);            L2=makeline(c,d);            if(lineintersect(L1,L2,p)==2) printf("LINE\n");            else if(lineintersect(L1,L2,p)==0) printf("NONE\n");            else            {                printf("POINT %.2lf %.2lf\n",p.x,p.y);            }        }        printf("END OF OUTPUT\n");    }    return 0;}