题意： 二维平面，给两条线段，判断形成的直线是否重合，或是相交于一点，或是不相交。
解法： 简单几何。
重合： 叉积为0，且一条线段的一个端点到另一条直线的距离为0
不相交： 不满足重合的情况下叉积为0
相交于一点： 直线相交的模板
代码：
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#define pi acos(-1.0)
#define eps 1e-8
using namespace std;
#define N 100017 struct Point{
double x,y;
Point(double x=, double y=):x(x),y(y) {}
void input() { scanf("%lf%lf",&x,&y); }
};
typedef Point Vector;
struct Circle{
Point c;
double r;
Circle(){}
Circle(Point c,double r):c(c),r(r) {}
Point point(double a) { return Point(c.x + cos(a)*r, c.y + sin(a)*r); }
void input() { scanf("%lf%lf%lf",&c.x,&c.y,&r); }
};
struct Line{
Point p;
Vector v;
double ang;
Line(){}
Line(Point p, Vector v):p(p),v(v) { ang = atan2(v.y,v.x); }
Point point(double t) { return Point(p.x + t*v.x, p.y + t*v.y); }
bool operator < (const Line &L)const { return ang < L.ang; }
};
int dcmp(double x) {
if(x < -eps) return -;
if(x > eps) return ;
return ;
}
template <class T> T sqr(T x) { return x * x;}
Vector operator + (Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); }
Vector operator - (Vector A, Vector B) { return Vector(A.x - B.x, A.y - B.y); }
Vector operator * (Vector A, double p) { return Vector(A.x*p, A.y*p); }
Vector operator / (Vector A, double p) { return Vector(A.x/p, A.y/p); }
bool operator < (const Point& a, const Point& b) { return a.x < b.x || (a.x == b.x && a.y < b.y); }
bool operator >= (const Point& a, const Point& b) { return a.x >= b.x && a.y >= b.y; }
bool operator <= (const Point& a, const Point& b) { return a.x <= b.x && a.y <= b.y; }
bool operator == (const Point& a, const Point& b) { return dcmp(a.x-b.x) == && dcmp(a.y-b.y) == ; }
double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }
double Length(Vector A) { return sqrt(Dot(A, A)); }
double Angle(Vector A, Vector B) { return acos(Dot(A, B) / Length(A) / Length(B)); }
double Cross(Vector A, Vector B) { return A.x*B.y - A.y*B.x; }
Vector VectorUnit(Vector x){ return x / Length(x);}
Vector Normal(Vector x) { return Point(-x.y, x.x) / Length(x);}
double angle(Vector v) { return atan2(v.y, v.x); } bool OnSegment(Point P, Point A, Point B) {
return dcmp(Cross(A-P,B-P)) == && dcmp(Dot(A-P,B-P)) < ;
}
double DistanceToSeg(Point P, Point A, Point B)
{
if(A == B) return Length(P-A);
Vector v1 = B-A, v2 = P-A, v3 = P-B;
if(dcmp(Dot(v1, v2)) < ) return Length(v2);
if(dcmp(Dot(v1, v3)) > ) return Length(v3);
return fabs(Cross(v1, v2)) / Length(v1);
}
double DistanceToLine(Point P, Point A, Point B){
Vector v1 = B-A, v2 = P-A;
return fabs(Cross(v1,v2)) / Length(v1);
}
Point GetLineIntersection(Line A, Line B){
Vector u = A.p - B.p;
double t = Cross(B.v, u) / Cross(A.v, B.v);
return A.p + A.v*t;
} //data segment
//data ends int main()
{
Point A,B,C,D;
int n,i,j;
scanf("%d",&n);
{
puts("INTERSECTING LINES OUTPUT");
for(i=;i<=n;i++)
{
scanf("%lf%lf%lf%lf",&A.x,&A.y,&B.x,&B.y);
scanf("%lf%lf%lf%lf",&C.x,&C.y,&D.x,&D.y);
Line L1 = Line(A,B-A);
Line L2 = Line(C,D-C);
if(dcmp(Cross(L1.v,L2.v)) == && dcmp(DistanceToLine(A,C,D)) == )
puts("LINE");
else if(dcmp(Cross(L1.v,L2.v)) == )
puts("NONE");
else
printf("POINT %.2f %.2f\n",GetLineIntersection(L1,L2).x,GetLineIntersection(L1,L2).y);
}
puts("END OF OUTPUT");
}
return ;
}