Geometric Shapes (poj3449多邊形相交)

題意：給你一些多邊形的點，判斷每個多邊形和那些多邊形相交，編號按照字典序輸出

思路：枚舉每個多邊形的每條邊看是否相交，這裡的相交是包括端點的，關鍵是給你正方形不相鄰兩個點求另外兩個點怎麼求，長方形給你3個點求第四個點怎麼求？

因為對角線的交點為兩條對角線的中點，所以 

x0 + x2 =  x1 + x3

y0 + y2 =  y1 + y3

可以證明分割的這幾個小三角形是全等的所以有

x1 - x3 = y2 - y1

y1 - y3 = x2 - x0

根據這幾個式子可以推出 另外兩個點的座標

剩下的就是枚舉每兩個多邊形的每條邊是否相交

就是輸入輸出格式要細心點

#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;}