#include<iostream>#include<cstdlib>#include<cstring>#include<algorithm>#include<cmath>#include<stdio.h>using namespace std;double fenzi[2],fenmu,S,x,y,eps=1e-7,arg,delta,X,Y,pi=acos(-1.00),ansx,ansy,oox=1412.000,ooy=3756.000;struct pp{ char flag[11]; double x,y,r,arg,x0,y0;};pp aa[111];int n,cnt;double area(double x1,double y1,double x2,double y2,double x3,double y3){ return ((x2-x1)*(y3-y1)-(y2-y1)*(x3-x1))/2.00;}void G(double x1,double y1,double x2,double y2,double x3,double y3){ x=(x1+x2+x3)/3.00; y=(y1+y2+y3)/3.00;}bool inter(double x1,double y1,double x2,double y2,double x3,double y3,double x4,double y4){ double a1,b1,c1,a2,b2,c2; a1=y2-y1; b1=x1-x2; c1=y1*x2-y2*x1; a2=y4-y3; b2=x3-x4; c2=y3*x4-y4*x3; if(a1*b2==a2*b1) return false; x=(c2*b1-c1*b2)/(a1*b2-a2*b1); y=(c2*a1-c1*a2)/(b1*a2-b2*a1); if(!((x<x1+eps&&x>x2-eps)||(x<x2+eps&&x>x1-eps))) return false; if(!((y<y1+eps&&y>y2-eps)||(y<y2+eps&&y>y1-eps))) return false; if(!((x<x3+eps&&x>x4-eps)||(x<x4+eps&&x>x3-eps))) return false; if(!((y<y3+eps&&y>y4-eps)||(y<y4+eps&&y>y3-eps))) return false; return true;}int main(){ int i,j,s,p,q; double a,b,c,A,B,C,k,arg1,arg2; while(scanf("%s",aa[0].flag)&&strcmp(aa[0].flag,"end")!=0) { scanf("%lf%lf",&aa[0].x,&aa[0].y); n=1; while(true) { scanf("%s",aa[n].flag); if(strcmp(aa[n].flag,"close")==0) { if(aa[n-1].x!=aa[0].x||aa[n-1].y!=aa[0].y) { strcpy(aa[n].flag,"line"); aa[n].x=aa[0].x; aa[n++].y=aa[0].y; } break; } scanf("%lf%lf",&aa[n].x,&aa[n].y); if(strcmp(aa[n].flag,"arc")==0) scanf("%lf",&aa[n].r); n++; } fenzi[0]=fenzi[1]=fenmu=0; for(i=1;i<n;i++) { if(i+1<n) { S=area(aa[0].x,aa[0].y,aa[i].x,aa[i].y,aa[i+1].x,aa[i+1].y); if(S!=0) { G(aa[0].x,aa[0].y,aa[i].x,aa[i].y,aa[i+1].x,aa[i+1].y); fenzi[0]+=S*x; fenzi[1]+=S*y; fenmu+=S; } } if(strcmp(aa[i].flag,"arc")==0) { a=2*(aa[i].x-aa[i-1].x); b=2*(aa[i].y-aa[i-1].y); c=aa[i].x*aa[i].x-aa[i-1].x*aa[i-1].x+aa[i].y*aa[i].y-aa[i-1].y*aa[i-1].y; if(b==0) { x=c/a; y=aa[i].y+sqrt(aa[i].r*aa[i].r-(x-aa[i].x)*(x-aa[i].x)); if((aa[i].r<0&&(aa[i].y-y)*(aa[i-1].x-x)<(aa[i-1].y-y)*(aa[i].x-x))||(aa[i].r>0&&(aa[i].y-y)*(aa[i-1].x-x)>(aa[i-1].y-y)*(aa[i].x-x))) { y=aa[i].y-sqrt(aa[i].r*aa[i].r-(x-aa[i].x)*(x-aa[i].x)); while((aa[i].y-y)*(aa[i-1].x-x)<(aa[i-1].y-y)*(aa[i].x-x)); } } else { A=a*a+b*b; B=2*(b*aa[i].y-c)*a-2*b*b*aa[i].x; C=b*b*aa[i].x*aa[i].x+(c-aa[i].y*b)*(c-aa[i].y*b)-aa[i].r*aa[i].r*b*b; delta=B*B-4*A*C; x=(-B+sqrt(delta))/(2*A); y=(c-a*x)/b; if((aa[i].r<0&&(aa[i].y-y)*(aa[i-1].x-x)<(aa[i-1].y-y)*(aa[i].x-x))||(aa[i].r>0&&(aa[i].y-y)*(aa[i-1].x-x)>(aa[i-1].y-y)*(aa[i].x-x))) { x=(-B-sqrt(delta))/(2*A); y=(c-a*x)/b; } } aa[i].x0=x; aa[i].y0=y; X=(aa[i].x+aa[i-1].x)/2.0; Y=(aa[i].y+aa[i-1].y)/2.0; arg=sqrt((aa[i].x-X)*(aa[i].x-X)+(aa[i].y-Y)*(aa[i].y-Y))/abs(aa[i].r); arg=2*asin(arg); aa[i].arg=arg; S=aa[i].r*aa[i].r*(arg-sin(arg))/2.00; if(aa[i].r>0) S=-S; double val=sin(arg/2.00); double len1=2.0*abs(aa[i].r*aa[i].r*aa[i].r)*val*val*val/(3.0*abs(S)),len2=sqrt((aa[i].x0-X)*(aa[i].x0-X)+(aa[i].y0-Y)*(aa[i].y0-Y)); x=aa[i].x0+len1*(X-aa[i].x0)/len2; y=aa[i].y0+len1*(Y-aa[i].y0)/len2; fenzi[0]+=S*x; fenzi[1]+=S*y; fenmu+=S; } } ansx=fenzi[0]/fenmu; ansy=fenzi[1]/fenmu; printf("%.4lf %.4lf",ansx+eps,ansy+eps); cnt=0; for(i=1;i<n;i++) { if(strcmp(aa[i].flag,"line")==0) cnt+=inter(ansx,ansy,oox,ooy,aa[i-1].x,aa[i-1].y,aa[i].x,aa[i].y); else if(strcmp(aa[i].flag,"arc")==0) { k=(ansy-ooy)/(ansx-oox); b=(ansy*oox-ooy*ansx)/(oox-ansx); A=1+k*k; B=2*(b-aa[i].y0)*k-2*aa[i].x0; C=aa[i].x0*aa[i].x0+(b-aa[i].y0)*(b-aa[i].y0)-aa[i].r*aa[i].r; delta=B*B-4*A*C; if(delta>=0) {x=(-B+sqrt(delta))/(2*A);y=k*x+b;if((x<oox+eps&&x>ansx-eps)){ arg=aa[i].arg; arg1=(x-aa[i].x0)*(aa[i-1].x-aa[i].x0)+(y-aa[i].y0)*(aa[i-1].y-aa[i].y0); arg1/=(aa[i].r*aa[i].r); arg1=acos(arg1); arg2=(x-aa[i].x0)*(aa[i].x-aa[i].x0)+(y-aa[i].y0)*(aa[i].y-aa[i].y0); arg2/=(aa[i].r*aa[i].r); arg2=acos(arg2); if(abs(arg1+arg2-arg)<eps) cnt++;}x=(-B-sqrt(delta))/(2*A);y=k*x+b;if((x<oox+eps&&x>ansx-eps)){ arg=aa[i].arg; arg1=(x-aa[i].x0)*(aa[i-1].x-aa[i].x0)+(y-aa[i].y0)*(aa[i-1].y-aa[i].y0); arg1/=(aa[i].r*aa[i].r); arg1=acos(arg1); arg2=(x-aa[i].x0)*(aa[i].x-aa[i].x0)+(y-aa[i].y0)*(aa[i].y-aa[i].y0); arg2/=(aa[i].r*aa[i].r); arg2=acos(arg2); if(abs(arg1+arg2-arg)<eps) cnt++;} } } } if(cnt%2==0)printf(" -n"); elseprintf(" +n"); } return 0;}
