Geometric Shapes (poj3449多边形相交)

题意：给你一些多边形的点，判断每个多边形和那些多边形相交，编号按照字典序输出

思路：枚举每个多边形的每条边看是否相交，这里的相交是包括端点的，关键是给你正方形不相邻两个点求另外两个点怎么求，长方形给你3个点求第四个点怎么求？

因为对角线的交点为两条对角线的中点，所以

x0 + x2 =  x1 + x3

y0 + y2 =  y1 + y3

可以证明分割的这几个小三角形是全等的所以有

x1 - x3 = y2 - y1

y1 - y3 = x2 - x0

根据这几个式子可以推出 另外两个点的坐标

剩下的就是枚举每两个多边形的每条边是否相交

就是输入输出格式要细心点

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
struct Point
{
    double x,y;
    Point(double x = 0,double y = 0):x(x),y(y){}
};
typedef Point Vector;
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) ;}
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 Cross(Vector a, Vector b) { return a.x*b.y - a.y*b.x ;}
const double eps = 1e-8;
int dcmp(double x)
{
    if(fabs(x) < eps) return 0;
    else return x < 0 ? -1 : 1;
}
bool operator == (Point a,Point b)
{
    return dcmp(a.x-b.x) == 0&& dcmp(a.y-b.y) == 0;
}
bool operator < (Point a,Point b)
{
    return a.x < b.x || (a.x == b.x && a.y < b.y);
}

bool Onsegment(Point p,Point a,Point b)
{
    return dcmp(Cross(b-a,p-a)) == 0 && dcmp(Dot(b-p,a-p)) < 0 || (p == a) || (p == b);
}

bool OnLine(Point p,Point a,Point b)
{
    return fabs(Cross(p-a,a-b)) / Length(b-a);
}

bool Segmentsection(Point a,Point b,Point c,Point d)
{
    double d1 = Cross(b-a,c-a),d2 = Cross(b-a,d-a),d3 = Cross(d-c,a-c),d4 = Cross(d-c,b-c);
    if(dcmp(d1)*dcmp(d2) < 0 && dcmp(d3)*dcmp(d4) < 0) return true;
    else if(dcmp(d1) == 0 && Onsegment(c,a,b) ) return true;
    else if(dcmp(d2) == 0 && Onsegment(d,a,b) ) return true;
    else if(dcmp(d3) == 0 && Onsegment(a,c,d) ) return true;
    else if(dcmp(d4) == 0 && Onsegment(b,c,d) ) return true;
    else return false;
}

Point Segment(Point p,Vector v,Point q,Vector w)
{
    Vector u = p-q;
    double t = Cross(w,u) / Cross(v,w);
    return p + v*t;
}

double Max(double a,double b)
{
    return a > b ? a : b;
}
struct Line
{
    Point s,e;
    Line(Point s = 0,Point e = 0) :s(s),e(e){}
};

struct polygon
{
    Point p[30];
    int num;
}poly[50];

bool Ispoly(polygon a,polygon b)
{
    if(a.num != 0 && b.num != 0)
    {
         for(int i = 0; i < a.num; i++)
        {
            for(int j = 0; j < b.num; j++)
            {
                if( Segmentsection(a.p[i],a.p[(i+1)%a.num],b.p[j],b.p[(j+1)%b.num]) )
                    return true;
            }
        }
    }
    return false;
}
int main()
{
    char str[10],strr[20];
    memset(poly,0,sizeof(poly));
    while(scanf("%s",str) != EOF)
    {
        if(strcmp(str,".") == 0)
        {
            break;
        }
        if(strcmp(str,"-") == 0)
        {
            char c[30];
            int k,j;
            for(int i = 0; i < 26; i++)
            {
                k = 0;
                for(j = 0; j < 26; j++)
                {
                    if( i != j && Ispoly(poly[i],poly[j]))
                    {
                        c[k++] = j + 'A';
                    }
                }
                if(k == 0 && poly[i].num != 0)
                {
                    printf("%c has no intersections\n",i+'A');
                }
                else if(poly[i].num != 0)
                {
                    printf("%c intersects with %c",i+'A',c[0]);
                    if(k == 2)
                    {
                        printf(" and %c",c[1]);
                    }
                    else if(k > 2)
                    {
                        for(int m = 1; m < k-1; m++)
                        {
                            printf(", %c",c[m]);
                        }
                        printf(", and %c",c[k-1]);
                    }
                    printf("\n");
                }
            }
            printf("\n");
            memset(poly,0,sizeof(poly));
            continue;
        }
        scanf("%s",strr);
        int temp = str[0]-'A';
        double x,y;
        if(strcmp(strr,"square") == 0)
        {
            poly[temp].num = 4;
            scanf(" (%lf,%lf)",&x,&y);
            poly[temp].p[0].x = x, poly[temp].p[0].y = y;
            scanf(" (%lf,%lf)",&x,&y);
            poly[temp].p[2].x = x, poly[temp].p[2].y = y;

            poly[temp].p[1].x = (poly[temp].p[0].x+poly[temp].p[2].x +poly[temp].p[2].y-poly[temp].p[0].y)/2;
            poly[temp].p[1].y = (poly[temp].p[0].y+poly[temp].p[2].y+poly[temp].p[0].x-poly[temp].p[2].x)/2;
            poly[temp].p[3].x = (poly[temp].p[0].x+poly[temp].p[2].x +poly[temp].p[0].y-poly[temp].p[2].y)/2;
            poly[temp].p[3].y = (poly[temp].p[0].y+poly[temp].p[2].y+poly[temp].p[2].x-poly[temp].p[0].x)/2;

        }
        else if(strcmp(strr,"rectangle") == 0)
        {
            poly[temp].num = 4;
            scanf(" (%lf,%lf)",&x,&y);
            poly[temp].p[0].x = x, poly[temp].p[0].y = y;
            scanf(" (%lf,%lf)",&x,&y);
            poly[temp].p[1].x = x, poly[temp].p[1].y = y;
            scanf(" (%lf,%lf)",&x,&y);
            poly[temp].p[2].x = x, poly[temp].p[2].y = y;
            poly[temp].p[3].x = (poly[temp].p[0].x + poly[temp].p[2].x - poly[temp].p[1].x);
            poly[temp].p[3].y = ( poly[temp].p[2].y -  poly[temp].p[1].y +  poly[temp].p[0].y);
        }
        else if(strcmp(strr,"line") == 0)
        {
            poly[temp].num = 2;
            scanf(" (%lf,%lf)",&x,&y);
            poly[temp].p[0].x = x, poly[temp].p[0].y = y;
            scanf(" (%lf,%lf)",&x,&y);
            poly[temp].p[1].x = x, poly[temp].p[1].y = y;
        }
        else if(strcmp(strr,"polygon") == 0)
        {
            int n;
            scanf("%d",&n);
            poly[temp].num = n;
            for(int i = 0; i < n; i++)
            {
                scanf(" (%lf,%lf)",&x,&y);
                poly[temp].p[i].x = x, poly[temp].p[i].y = y;
            }
        }
        else
         {

            poly[temp].num = 3;
            scanf(" (%lf,%lf)",&x,&y);
            poly[temp].p[0].x = x, poly[temp].p[0].y = y;
            scanf(" (%lf,%lf)",&x,&y);
            poly[temp].p[1].x = x, poly[temp].p[1].y = y;
            scanf(" (%lf,%lf)",&x,&y);
            poly[temp].p[2].x = x, poly[temp].p[2].y = y;
        }
    }
    return 0;
}