UVA12304 2D Geometry 110 in 1!
原题链接--UVA12304 2D Geometry 110 in 1!
这是一道圆的入门基础题,要求有点多,写了一个下午写完,然后WA了六发,
最后隔了一周再做,找了一下午bug终于AC了,难受啊。。。。。 上代码:
#include<cstdio> #include<vector> #include<iostream> #include<algorithm> #include<cmath> using namespace std; const double Pi=acos(-1); const double eps=1e-6; 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 B){return Vector(A.x*B,A.y*B);} Vector operator /(Vector A,double B){return Vector(A.x/B,A.y/B);} int dcmp(double x){ if(fabs(x)<eps)return 0; return x<0?-1:1; } bool operator<(const Point&a,const Point&b){return a.x<b.x||(a.x==b.x&&a.y<b.y);} bool operator == (const Point &a,const Point &b){return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;} void Correct(double &A){ while(dcmp(A)<0)A+=Pi; while(dcmp(A-Pi)>=0)A-=Pi; } 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;} double Angle(Vector A,Vector B){return acos(Dot(A,B)/Length(A)/Length(B));} double Angle(Vector A) {return atan2(A.y, A.x);} Vector Normal(Vector A){return Vector(-A.y,A.x);} Vector Rotate(Vector A,double rad){return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));} Vector unit_Vector(Vector A){ Vector B; double s=sqrt((A.x*A.x+A.y*A.y)); B.x=A.x/s,B.y/s; return B; } vector<Point>sol; struct Circle{ //圆 Point c; double r; Circle(Point c = Point(0, 0), double r = 0):c(c),r(r){} Point point(double a){ return Point(c.x+cos(a)*r,c.y+sin(a)*r); } }; struct Line{ //直线 Point p; Vector v; double ang; Line(){} Line(Point p,Vector v):p(p),v(v){ang=atan2(v.y,v.x);} bool operator < (const Line &L)const { return ang<L.ang; } Point point(double a){ return p+v*a; } }; Point line_point(Point p,Vector v,Point q,Vector w){//直线交点 Vector u=p-q; double t=Cross(w,u)/Cross(v,w); return p+v*t; } double dist_point_line(Point A,Point B,Point C){//点到直线的距离 Vector BC=C-B; Vector _BC=Rotate(BC,Pi/2); Point D=line_point(B,BC,A,_BC); Vector DA=A-D; return Length(DA); } Point mid_point(Point A,Point B){//中点 Point C; C.x=(A.x+B.x)/2,C.y=(A.y+B.y)/2; return C; } void parallel(Point A,Point B,double d,vector<Line>&sol){//平行线 Vector AB=B-A; Vector _AB=Normal(AB); _AB=_AB/(Length(_AB))*d; Point ta,tb; ta=A+_AB; tb=B+_AB; Line l1=Line(ta,tb-ta); sol.push_back(l1); ta=A-_AB; tb=B-_AB; Line l2=Line(ta,tb-ta); sol.push_back(l2); } int line_circle(Line L,Circle C,double &t1,double &t2,vector<Point>&sol){//直线与圆的交点 double a=L.v.x,b=L.p.x-C.c.x,c=L.v.y,d=L.p.y-C.c.y; double e=a*a+c*c,f=2*(a*b+c*d),g=b*b+d*d-C.r*C.r; double delta=f*f-4.*e*g; if(dcmp(delta)<0) return 0;//相离 if(dcmp(delta)==0)//相切 { t1=t2=-f/(2.*e); sol.push_back(L.point(t1)); return 1; } //相切 t1=(-f-sqrt(delta))/(2.*e); sol.push_back(L.point(t1)); t2=(-f+sqrt(delta))/(2.*e); sol.push_back(L.point(t2)); return 2; } int circle_circle(Circle C1,Circle C2,vector<Point>&sol){//圆与圆的交点 double d=Length(C1.c-C2.c); if(dcmp(d)==0){ if(dcmp(C1.r-C2.r)==0)return -1; return 0; } if(dcmp(C1.r+C2.r-d)<0)return 0; if(dcmp(fabs(C1.r-C2.r)-d)>0)return 0; double a=Angle(C2.c-C1.c); double da=acos((C1.r*C1.r+d*d-C2.r*C2.r)/(2*d*C1.r)); Point p1=C1.point(a-da),p2=C1.point(a+da); sol.push_back(p1); if(p1==p2)return 1; sol.push_back(p2); return 2; } int gettangents(Point p,Circle C,Vector *v){//直线与圆的切线 Vector u=C.c-p; double dist=Length(u); if(dist<C.r)return 0; else if(dcmp(dist-C.r)==0){ v[0]=Rotate(u,Pi/2); return 1; } else{ double ang=asin(C.r/dist); v[0]=Rotate(u,-ang); v[1]=Rotate(u,+ang); return 2; } } Circle tangle_out_cir(Point A,Point B,Point C){//外接圆 Point D=mid_point(A,B); Point E=mid_point(A,C); Vector AB=B-A; Vector AC=C-A; Vector DO=Rotate(AB,Pi/2); Vector OE=Rotate(AC,Pi/2); Point O=line_point(D,DO,E,OE); Vector AO=O-A; Circle C1=Circle(O,Length(AO)); return C1; } Circle tangle_in_cir(Point A,Point B,Point C){//内接圆 Vector AB=B-A; Vector AC=C-A; if(Cross(AB,AC)<0){ Point t=A; A=C; C=t; } AB=B-A; AC=C-A; Vector BA=A-B; Vector BC=C-B; double a=Angle(AB,AC); double b=Angle(BA,BC); Vector AO=Rotate(AB,a/2); Vector BO=Rotate(BC,b/2); Point O=line_point(A,AO,B,BO); double r=dist_point_line(O,A,B); Circle C1=Circle(O,r); return C1; } void tangent_point_cir(Point O,double r,Point A){//过A与圆O的切线 Circle C1=Circle(O,r); Vector v[10]; int n=gettangents(A,C1,v); double a[10]; for(int i=0;i<n;i++){ a[i]=atan2(v[i].y,v[i].x); Correct(a[i]); } sort(a,a+n); printf("["); for(int i=0;i<n;i++){ printf("%.6lf",a[i]*180/Pi); if(i<n-1)printf(","); } printf("]\n"); } void point_line_r_cir(Point A,Point B,Point C,double r){//过A与BC相切的圆 Circle C1=Circle(A,r); vector<Line>L; vector<Point>p; parallel(B,C,r,L); double t1,t2; for(int i=0;i<L.size();i++){ line_circle(L[i],C1,t1,t2,p); } sort(p.begin(),p.end()); printf("["); int h=p.size(); for(int i=0;i<p.size();i++){ printf("(%.6lf,%.6lf)",p[i].x,p[i].y); if(i<h-1)printf(","); } printf("]\n"); } void line_line_cir(Point A,Point B,Point C,Point D,double r){//与AB和CD相切的圆 vector<Line>L1; vector<Line>L2; parallel(A,B,r,L1); parallel(C,D,r,L2); Point t; vector<Point>sol; for(int i=0;i<2;i++){ for(int j=0;j<2;j++){ t=line_point(L1[i].p,L1[i].v,L2[j].p,L2[j].v); sol.push_back(t); } } sort(sol.begin(),sol.end()); printf("["); for(int i=0;i<4;i++){ printf("(%.6lf,%.6lf)",sol[i].x,sol[i].y); if(i<3)printf(","); } printf("]\n"); } void cir_cir_out_cir(Point A,double r1,Point B,double r2,double r){//与圆A和圆B外切的圆 Circle C1=Circle(A,r1+r); Circle C2=Circle(B,r2+r); vector<Point>sol; circle_circle(C1,C2,sol); sort(sol.begin(),sol.end()); int n=sol.size(); printf("["); for(int i=0;i<n;i++){ printf("(%.6lf,%.6lf)",sol[i].x,sol[i].y); if(i<n-1)printf(","); } printf("]\n"); } Point A,B,C,D,O; double r,r1,r2; string s; int main(){ while(cin>>s){ if(s=="CircumscribedCircle"){ scanf("%lf%lf%lf%lf%lf%lf",&A.x,&A.y,&B.x,&B.y,&C.x,&C.y); Circle C1=tangle_out_cir(A,B,C); printf("(%.6lf,%.6lf,%.6lf)\n",C1.c.x,C1.c.y,C1.r); } else if(s=="InscribedCircle"){ scanf("%lf%lf%lf%lf%lf%lf",&A.x,&A.y,&B.x,&B.y,&C.x,&C.y); Circle C1=tangle_in_cir(A,B,C); printf("(%.6lf,%.6lf,%.6lf)\n",C1.c.x,C1.c.y,C1.r); } else if(s=="TangentLineThroughPoint"){ scanf("%lf%lf%lf%lf%lf",&A.x,&A.y,&r,&B.x,&B.y); tangent_point_cir(A,r,B); } else if(s=="CircleThroughAPointAndTangentToALineWithRadius"){ scanf("%lf%lf%lf%lf%lf%lf%lf",&A.x,&A.y,&B.x,&B.y,&C.x,&C.y,&r); point_line_r_cir(A,B,C,r); } else if(s=="CircleTangentToTwoLinesWithRadius"){ scanf("%lf%lf%lf%lf%lf%lf%lf%lf%lf",&A.x,&A.y,&B.x,&B.y,&C.x,&C.y,&D.x,&D.y,&r); line_line_cir(A,B,C,D,r); } else{ scanf("%lf%lf%lf%lf%lf%lf%lf",&A.x,&A.y,&r1,&B.x,&B.y,&r2,&r); cir_cir_out_cir(A,r1,B,r2,r); } } }