poj 3304(直线与线段相交)

 

传送门:Segments

题意:线段在一个直线上的摄影相交 求求是否存在一条直线,使所有线段到这条直线的投影至少有一个交点 

分析:可以在共同投影处作原直线的垂线,则该垂线与所有线段都相交<==> 是否存在一条直线与所有线段都相交。 去盗了一份bin神的模板,用起来太方便了。。。

#include <iostream>

#include <stdio.h>

#include <string.h>

#include <algorithm>

#include <queue>

#include <map>

#include <vector>

#include <set>

#include <string>

#include <math.h>



using namespace std;



const double eps = 1e-8;

const double PI = acos(-1.0);

const int N = 110;

int sgn(double x)

{

    if(fabs(x) < eps)return 0;

    if(x < 0)return -1;

    else return 1;

}

struct Point

{

    double x,y;

    Point(){}

    Point(double _x,double _y)

    {

        x = _x;y = _y;

    }

    Point operator -(const Point &b)const

    {

        return Point(x - b.x,y - b.y);

    }

    //叉积

    double operator ^(const Point &b)const

    {

        return x*b.y - y*b.x;

    }

    //点积

    double operator *(const Point &b)const

    {

        return x*b.x + y*b.y;

    }

    //绕原点旋转角度B(弧度值),后x,y的变化

    void transXY(double B)

    {

        double tx = x,ty = y;

        x = tx*cos(B) - ty*sin(B);

        y = tx*sin(B) + ty*cos(B);

    }

    //绕点p逆时针旋转角度B(弧度值)

    void rotate(Point p,double B)

    {

        Point v=(*this)-p;

        double tx = v.x,ty = v.y;

        x = tx*cos(B) - ty*sin(B);

        y = tx*sin(B) + ty*cos(B);

    }

};

struct Line

{

    Point s,e;

    Line(){}

    Line(Point _s,Point _e)

    {

        s = _s;e = _e;

    }

    //两直线相交求交点

    //第一个值为0表示直线重合,为1表示平行,为0表示相交,为2是相交

    //只有第一个值为2时,交点才有意义

    pair<int,Point> operator &(const Line &b)const

    {

        Point res = s;

        if(sgn((s-e)^(b.s-b.e)) == 0)

        {

            if(sgn((s-b.e)^(b.s-b.e)) == 0)

                return make_pair(0,res);//重合

            else return make_pair(1,res);//平行

        }

        double t = ((s-b.s)^(b.s-b.e))/((s-e)^(b.s-b.e));

        res.x += (e.x-s.x)*t;

        res.y += (e.y-s.y)*t;

        return make_pair(2,res);

    }

};

//*两点间距离

double dist(Point a,Point b)

{

    return sqrt((a-b)*(a-b));

}

//*判断线段相交

bool inter(Line l1,Line l2)

{

    return

    max(l1.s.x,l1.e.x) >= min(l2.s.x,l2.e.x) &&

    max(l2.s.x,l2.e.x) >= min(l1.s.x,l1.e.x) &&

    max(l1.s.y,l1.e.y) >= min(l2.s.y,l2.e.y) &&

    max(l2.s.y,l2.e.y) >= min(l1.s.y,l1.e.y) &&

    sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0 &&

    sgn((l1.s-l2.e)^(l2.s-l2.e))*sgn((l1.e-l2.e)^(l2.s-l2.e)) <= 0;

}

//判断直线和线段相交

bool Seg_inter_line(Line l1,Line l2) //判断直线l1和线段l2是否相交

{

    return sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0;

}

//点到直线距离

//返回为result,是点到直线最近的点

Point PointToLine(Point P,Line L)

{

    Point result;

    double t = ((P-L.s)*(L.e-L.s))/((L.e-L.s)*(L.e-L.s));

    result.x = L.s.x + (L.e.x-L.s.x)*t;

    result.y = L.s.y + (L.e.y-L.s.y)*t;

    return result;

}

//点到线段的距离

//返回点到线段最近的点

Point NearestPointToLineSeg(Point P,Line L)

{

    Point result;

    double t = ((P-L.s)*(L.e-L.s))/((L.e-L.s)*(L.e-L.s));

    if(t >= 0 && t <= 1)

    {

        result.x = L.s.x + (L.e.x - L.s.x)*t;

        result.y = L.s.y + (L.e.y - L.s.y)*t;

    }

    else

    {

        if(dist(P,L.s) < dist(P,L.e))

            result = L.s;

        else result = L.e;

    }

    return result;

}

//计算多边形面积

//点的编号从0~n-1

double CalcArea(Point p[],int n)

{

    double res = 0;

    for(int i = 0;i < n;i++)

        res += (p[i]^p[(i+1)%n])/2;

    return fabs(res);

}

//*判断点在线段上

bool OnSeg(Point P,Line L)

{

    return

    sgn((L.s-P)^(L.e-P)) == 0 &&

    sgn((P.x - L.s.x) * (P.x - L.e.x)) <= 0 &&

    sgn((P.y - L.s.y) * (P.y - L.e.y)) <= 0;

}

//*判断点在凸多边形内

//点形成一个凸包,而且按逆时针排序(如果是顺时针把里面的<0改为>0)

//点的编号:0~n-1

//返回值:

//-1:点在凸多边形外

//0:点在凸多边形边界上

//1:点在凸多边形内

int inConvexPoly(Point a,Point p[],int n)

{

    for(int i = 0;i < n;i++)

    {

        if(sgn((p[i]-a)^(p[(i+1)%n]-a)) < 0)return -1;

        else if(OnSeg(a,Line(p[i],p[(i+1)%n])))return 0;

    }

    return 1;

}

//*判断点在任意多边形内

//射线法,poly[]的顶点数要大于等于3,点的编号0~n-1

//返回值

//-1:点在凸多边形外

//0:点在凸多边形边界上

//1:点在凸多边形内

int inPoly(Point p,Point poly[],int n)

{

    int cnt;

    Line ray,side;

    cnt = 0;

    ray.s = p;

    ray.e.y = p.y;

    ray.e.x = -100000000000.0;//-INF,注意取值防止越界



    for(int i = 0;i < n;i++)

    {

        side.s = poly[i];

        side.e = poly[(i+1)%n];



        if(OnSeg(p,side))return 0;



        //如果平行轴则不考虑

        if(sgn(side.s.y - side.e.y) == 0)

            continue;



        if(OnSeg(side.s,ray))

        {

            if(sgn(side.s.y - side.e.y) > 0)cnt++;

        }

        else if(OnSeg(side.e,ray))

        {

            if(sgn(side.e.y - side.s.y) > 0)cnt++;

        }

        else if(inter(ray,side))

            cnt++;

    }

    if(cnt % 2 == 1)return 1;

    else return -1;

}

//判断凸多边形

//允许共线边

//点可以是顺时针给出也可以是逆时针给出

//点的编号1~n-1

bool isconvex(Point poly[],int n)

{

    bool s[3];

    memset(s,false,sizeof(s));

    for(int i = 0;i < n;i++)

    {

        s[sgn( (poly[(i+1)%n]-poly[i])^(poly[(i+2)%n]-poly[i]) )+1] = true;

        if(s[0] && s[2])return false;

    }

    return true;

}

Line seg[N];

int n;

bool judge(Point a,Point b)

{

    if(sgn(dist(a,b))==0)return false;

    Line l=Line(a,b);

    for(int i=1;i<=n;i++)

        if(!Seg_inter_line(l,seg[i]))return false;

    return true;

}

int main()

{

    int T;

    scanf("%d",&T);

    while(T--)

    {

        scanf("%d",&n);

        for(int i=1;i<=n;i++)

        {

            double a,b,c,d;

            scanf("%lf%lf%lf%lf",&a,&b,&c,&d);

            seg[i]=Line(Point(a,b),Point(c,d));

        }

        bool flag=false;

        for(int i=1;i<=n&&!flag;i++)

        {

            for(int j=1;j<=n;j++)

                if(judge(seg[i].s,seg[j].s)||judge(seg[i].s,seg[j].e)||

                   judge(seg[i].e,seg[j].s)||judge(seg[i].e,seg[j].e))

                {

                    flag=true;break;

                }

        }

        if(flag)puts("Yes!");

        else puts("No!");

    }

    return 0;

}
View Code

 

你可能感兴趣的:(poj)