Inheritance - SGU 129（线段与多边形相交的长度）

题目大意：给一个凸多边形（点不是按顺序给的），然后计算给出的线段在这个凸多边形里面的长度，如果在边界不计算。

分析：WA2..WA3...WA4..WA11...WA的无话可说，总之细节一定考虑清楚，重合的时候一定是0

代码如下：

=========================================================================================================

#include<stdio.h>
#include<math.h>
#include<algorithm>
#include<iostream>
using namespace std;

const int MAXN = 1007;
const double EPS = 1e-14;
const double FarX = 4e4+7;

int Sign(double x)
{
    if(x > EPS)return 1;
    if(fabs(x) < EPS)return 0;
    return -1;
}
struct point
{
    double x, y;
    point(double x=0, double y=0):x(x),y(y){}
    point operator - (const point &t)const{
        return point(x-t.x, y-t.y);
    }
    bool operator == (const point &t)const{
        return Sign(x-t.x) ==0 && Sign(y-t.y) == 0;
    }
    double operator ^(const point &t)const{
        return x*t.y - y*t.x;
    }
    double operator *(const point &t)const{
        return x*t.x + y*t.y;
    }
};
double Dist(point t1, point t2)
{
    return sqrt((t1-t2)*(t1-t2));
}
struct segment
{
    point S, E;
    double a, b, c;///ax + by = c;

    segment(point S=0, point E=0):S(S), E(E){
        a = S.y - E.y;
        b = E.x - S.x;
        c = E.x*S.y - S.x*E.y;
    }
    int  Inter(const segment &tmp)const{
        int t1 = Sign((S-E)^(tmp.S-E));
        int t2 = Sign((S-E)^(tmp.E-E));

        if(t1 == 0 && t2 == 0)
            return -1;

        if(t1*t2 == -1)
            return 1;
        if(abs(t1+t2) == 1)///如果完全相交或者有一点相交，不考虑重合
            return 2;
        return false;
    }
    point crossNode(const segment &tmp)const
    {///两条线段的交点
        point result;
        result.x = (c*tmp.b-tmp.c*b) / (a*tmp.b-tmp.a*b);
        result.y = (c*tmp.a-tmp.c*a) / (b*tmp.a-tmp.b*a);

        return result;
    }
    bool OnSeg(const point &p)
    {///判断点是否在线段上
        if(Sign((S-E)^(p-E)) == 0)
        if(Sign((p.x-S.x)*(p.x-E.x)) <= 0)
        if(Sign((p.y-S.y)*(p.y-E.y)) <= 0)
            return true;
        return false;
    }
};
struct Polygon
{
    int N;///有N个点
    point vertex[MAXN];

    int Point_In_Poly(const point &p)
    {///点在多边形里面1，还是外面-1，还是边上 0
        segment ray(p, point(FarX, p.y));
        int cnt = 0;

        for(int i=0; i<N; i++)
        {
            segment L(vertex[i], vertex[i+1]);

            if(L.OnSeg(p))
                return 0;

            if(ray.OnSeg(L.S))
            {
                if(L.E.y-L.S.y > EPS)
                    cnt ++;
            }
            else if(ray.OnSeg(L.E))
            {
                if(L.S.y-L.E.y > EPS)
                    cnt ++;
            }
            else if(L.Inter(ray)==1 && ray.Inter(L)==1)
                cnt++;
        }

        if(cnt % 2)
            return 1;
        return -1;
    }
    double Seg_In_Poly(const segment &L1)
    {///线段与多边形相交的长度,先求出线段与多边形有几个交点
        point p[10];
        int k=0;

        for(int i=0; i<N; i++)
        {
            segment L2(vertex[i], vertex[i+1]);

            if(L1.Inter(L2) == -1 && L2.Inter(L1) == -1)
                return 0;

            if(k<2 && L1.Inter(L2) && L2.Inter(L1))
            {
                point t = L1.crossNode(L2);
                if(!k || !(p[0] == t) )
                    p[k++] = t;
            }
        }

        double len=0;

        if(k == 2)
        {///有两个不同的交点
            len = Dist(p[0], p[1]);
        }
        else if(k == 1)
        {///有一个交点，判断哪个端点在多边形内
            if(Point_In_Poly(L1.S) == 1)
                len = Dist(p[0], L1.S);
            else if(Point_In_Poly(L1.E) == 1)
                len = Dist(p[0], L1.E);
        }
        else if(Point_In_Poly(L1.S) == 1)
        {///没有交点的时候，判断线段是否在多边形内
            len = Dist(L1.S, L1.E);
        }

        return len;
    }
};
Polygon poly;

bool cmp(point t1, point t2)
{
    return Sign((t2-poly.vertex[0])^(t1-poly.vertex[0])) < 0;
}

int main()
{
    int i, M, ki=0;

    scanf("%d", &poly.N);

    for(i=0; i<poly.N; i++)
    {
        scanf("%lf%lf", &poly.vertex[i].x, &poly.vertex[i].y);
        if(poly.vertex[ki].y > poly.vertex[i].y ||
           (poly.vertex[ki].y == poly.vertex[i].y && poly.vertex[ki].x > poly.vertex[i].x) )
           ki = i;
    }

    swap(poly.vertex[0], poly.vertex[ki]);
    sort(poly.vertex+1, poly.vertex+poly.N, cmp);
    poly.vertex[poly.N] = poly.vertex[0];

    scanf("%d", &M);

    while(M--)
    {
        point A, B;

        scanf("%lf%lf%lf%lf", &A.x, &A.y, &B.x, &B.y);
        segment L(A, B);
        printf("%.6f\n",poly.Seg_In_Poly(L));
    }

    return 0;
}
/**
6
1 2
2 1
2 3
3 1
3 3
4 2
200
1 1 4 10
**/