Geometric Shapes (poj3449 polygon intersection)

Question: give you some polygon points to determine the intersection between each polygon and those polygon. The numbers are output in Lexicographic Order.

Idea: enumerate each side of each polygon to see if there is any intersection. The intersection here includes the endpoint. The key is to find the other two points for a square that is not adjacent to each other, the rectangle gives you three points. How do you find the fourth point?

Because the intersection of diagonal lines is the midpoint of two diagonal lines

X0 + x2 = x1 + x3

Y0 + y2 = y1 + y3

It can be proved that these small triangles are completely equal, so there are

X1-x3 = y2-y1

Y1-y3 = x2-x0

The coordinates of the other two points can be introduced based on these formulas.

The rest is to enumerate the intersection of each edge of each two polygon.

That is, the input and output formats must be careful.

#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;}