POJ 3675/2986(Telescope/A Triangle and a Circle-三角形与圆的面积并)
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这两题数据很强把我以前的板子卡掉了。。
贴个三角形与圆的面积并的板子
POJ 3675 Telescope
#include<cstdio>#include<cstring>#include<cstdlib>#include<algorithm>#include<functional>#include<iostream>#include<cmath>#include<cctype>#include<ctime>#include<iomanip> #include<vector>#include<string>#include<queue>#include<stack>#include<map>#include<sstream>#include<complex>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=Pre[x];p;p=Next[p])#define Forpiter(x) for(int &p=iter[x];p;p=Next[p]) #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,127,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define INF (2139062143)#define F (100000007)#define pb push_back#define mp make_pair #define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())#define ALL(x) (x).begin(),(x).end()typedef long long ll;typedef double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}void upd(ll &a,ll b){a=(a%F+b%F)%F;}int read(){ int x=0,f=1; char ch=getchar(); while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();} while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();} return x*f;} ll sqr(ll a){return a*a;}ld sqr(ld a){return a*a;}const double eps=1e-10;int dcmp(double x) { if (fabs(x)<eps) return 0; else return x<0 ? -1 : 1; }ld PI = acos(-1.0);class P{public: double x,y; P(double x=0,double y=0):x(x),y(y){} friend ld dis2(P A,P B){return sqr(A.x-B.x)+sqr(A.y-B.y); } friend ld Dot(P A,P B) {return A.x*B.x+A.y*B.y; } friend ld Length(P A) {return sqrt(Dot(A,A)); } friend ld Angle(P A,P B) { if (dcmp(Dot(A,A))==0||dcmp(Dot(B,B))==0||dcmp(Dot(A-B,A-B))==0) return 0; return acos(max((ld)-1.0, min((ld)1.0, Dot(A,B) / Length(A) / Length(B) )) ); } friend P operator- (P A,P B) { return P(A.x-B.x,A.y-B.y); } friend P operator+ (P A,P B) { return P(A.x+B.x,A.y+B.y); } friend P operator* (P A,double p) { return P(A.x*p,A.y*p); } friend P operator/ (P A,double p) { return P(A.x/p,A.y/p); } friend bool operator< (const P& a,const P& b) {return dcmp(a.x-b.x)<0 ||(dcmp(a.x-b.x)==0&& dcmp(a.y-b.y)<0 );}}; P read_point() { P a; scanf("%lf%lf",&a.x,&a.y); return a; } bool operator==(const P& a,const P& b) { return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y) == 0;} typedef P V;double Cross(V A,V B) {return A.x*B.y - A.y*B.x;}double Area2(P A,P B,P C) {return Cross(B-A,C-A);}namespace complex_G{ typedef complex<double> Point; //real(p):实部 imag(p):虚部 conj(p):共轭 typedef Point Vector; double Dot(Vector A,Vector B) {return real(conj(A)*B); } double Cross(Vector A,Vector B) {return imag(conj(A)*B); } Vector Rotate(Vector A,double rad) {return A*exp(Point(0,rad)); }}//Cross(v,w)==0(平行)时,不能调这个函数 P GetLineIntersection(P p,V v,P Q,V w){ V u = p-Q; double t = Cross(w,u)/Cross(v,w); return p+v*t;}P GetLineIntersectionB(P p,V v,P Q,V w){ return GetLineIntersection(p,v-p,Q,w-Q);}double DistanceToLine(P p,P A,P B) { V v1 = B-A, v2 = p-A; return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(P p,P A,P B) { if (A==B) return Length(p-A); V v1 = B-A, v2 = p-A, v3 = p - B; if (dcmp(Dot(v1,v2))<0) return Length(v2); else if (dcmp(Dot(v1,v3))>0 ) return Length(v3); else return fabs(Cross(v1,v2) ) / Length(v1);}P GetLineProjection(P p,P A,P B) { V v=B-A; return A+v*(Dot(v,p-A)/Dot(v,v));}//规范相交-线段相交且交点不在端点 bool SegmentProperIntersection(P a1,P a2,P b1,P b2) { double c1 = Cross(a2-a1,b1-a1) , c2 = Cross(a2-a1,b2-a1), c3 = Cross(b2-b1,a1-b1) , c4 = Cross(b2-b1,a2-b1); return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}//点在线段上（不包含端点） bool OnSegment(P p,P a1,P a2) { return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;}double PolygonArea(P *p,int n) { double area=0; For(i,n-2) area+=Cross(p[i]-p[0],p[i+1]-p[0]); return area/2;} /*欧拉公式： V+F-E=2 V-点数 F面数 E边数 */struct C{ P c; double r,x,y; C(P c,double r):c(c),r(r),x(c.x),y(c.y){} P point(double a) { return P(c.x+cos(a)*r,c.y+sin(a)*r); }};struct Line{ P p; V v; double ang; Line(){} Line(P p,V v):p(p),v(v) {ang=atan2(v.y,v.x); } bool operator<(const Line & L) const { return ang<L.ang; } P point(double a) { return p+v*a; }};int getLineCircleIntersection(Line L,C cir,double &t1,double &t2,vector<P> & sol) { if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) { P A=GetLineProjection(cir.c,L.p,L.p+L.v); sol.pb(A); t1 = (A-L.p).x / L.v.x; return 1; } double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y; double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r; double delta = f*f - 4*e*g; if (dcmp(delta)<0) return 0; else if (dcmp(delta)==0) { t1 = t2 = -f / (2*e); sol.pb(L.point(t1)); return 1; } t1 = (-f - sqrt(delta)) / (2*e); sol.pb(L.point(t1)); t2 = (-f + sqrt(delta)) / (2*e); sol.pb(L.point(t2)); return 2;}double angle(V v) {return atan2(v.y,v.x);}int getSegCircleIntersection(Line L,C cir,vector<P> & sol) { if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) { P A= GetLineProjection(cir.c,L.p,L.p+L.v); if (OnSegment(A,L.p,L.p+L.v) || L.p==A || L.p+L.v==A ) sol.pb(A); return sol.size(); } double t1,t2; double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y; double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r; double delta = f*f - 4*e*g; if (dcmp(delta)<0) return 0; else if (dcmp(delta)==0) { t1 = -f / (2*e); if (dcmp(t1)>=0&&dcmp(t1-1)<=0) { sol.pb(L.point(t1)); } return sol.size(); } t1 = (-f - sqrt(delta)) / (2*e); if (dcmp(t1)>=0&&dcmp(t1-1)<=0) sol.pb(L.point(t1)); t2 = (-f + sqrt(delta)) / (2*e); if (dcmp(t2)>=0&&dcmp(t2-1)<=0) sol.pb(L.point(t2)); if(SI(sol)==2 && t1>t2) swap(sol[1],sol[0]); return sol.size();}int isPointInOrOnCircle(P p,C c) { return dcmp(Length(p-c.c)-c.r)<=0;}// Triangle(O,A,B) and Circle(O,m)double CircleTriangleArea(P A,P B,double m) { double ans=0; C c=C(P(),m); P O=c.c; if (A==O||B==O) return 0; bool b = isPointInOrOnCircle(A,c); bool b2 = isPointInOrOnCircle(B,c); double opr; if (dcmp(Area2(O,A,B))>=0) opr=1; else opr=-1; if (b&&b2) { ans+=opr*fabs(Area2(A,B,O))/2; } else if (!b&&!b2){ Line l=Line(A,B-A); vector<P> sol; getSegCircleIntersection(l,c,sol); if (SI(sol)==2) { ans+=opr*fabs(Area2(sol[0],sol[1],O))/2; ans+=opr*m*m/2*(Angle(A,sol[0])+Angle(sol[1],B)); } else { ans+=opr*m*m/2*(Angle(A,B)); } } else { Line l=Line(A,B-A); vector<P> sol; getSegCircleIntersection(l,c,sol); if (SI(sol)==2) { ans+=opr*fabs(Area2(sol[0],sol[1],O))/2; ans+=opr*m*m/2*(Angle(A,sol[0])+Angle(sol[1],B)); } else if(b) { ans+=opr*fabs(Area2(sol[0],A,O))/2; ans+=opr*m*m/2*(Angle(sol[0],B)); } else { ans+=opr*fabs(Area2(sol[0],B,O))/2; ans+=opr*m*m/2*(Angle(sol[0],A)); } } return ans;}P a[10000];int main(){// freopen("poj3675.in","r",stdin);// freopen(".out","w",stdout); double R; while(cin>>R) { int n=read(); Rep(i,n) a[i]=read_point(); double ans=0; Rep(i,n) { ans+=CircleTriangleArea(a[i],a[(i+1)%n],R); } printf("%.2f\n",fabs(ans)); } return 0;}POJ 2986 A Triangle and a Circle
#include<cstdio>#include<cstring>#include<cstdlib>#include<algorithm>#include<functional>#include<iostream>#include<cmath>#include<cctype>#include<ctime>#include<iomanip> #include<vector>#include<string>#include<queue>#include<stack>#include<map>#include<sstream>#include<complex>using namespace std;#define For(i,n) for(int i=1;i<=n;i++)#define Fork(i,k,n) for(int i=k;i<=n;i++)#define Rep(i,n) for(int i=0;i<n;i++)#define ForD(i,n) for(int i=n;i;i--)#define ForkD(i,k,n) for(int i=n;i>=k;i--)#define RepD(i,n) for(int i=n;i>=0;i--)#define Forp(x) for(int p=Pre[x];p;p=Next[p])#define Forpiter(x) for(int &p=iter[x];p;p=Next[p]) #define Lson (o<<1)#define Rson ((o<<1)+1)#define MEM(a) memset(a,0,sizeof(a));#define MEMI(a) memset(a,127,sizeof(a));#define MEMi(a) memset(a,128,sizeof(a));#define INF (2139062143)#define F (100000007)#define pb push_back#define mp make_pair #define fi first#define se second#define vi vector<int> #define pi pair<int,int>#define SI(a) ((a).size())#define ALL(x) (x).begin(),(x).end()typedef long long ll;typedef double ld;typedef unsigned long long ull;ll mul(ll a,ll b){return (a*b)%F;}ll add(ll a,ll b){return (a+b)%F;}void upd(ll &a,ll b){a=(a%F+b%F)%F;}int read(){ int x=0,f=1; char ch=getchar(); while(!isdigit(ch)) {if (ch=='-') f=-1; ch=getchar();} while(isdigit(ch)) { x=x*10+ch-'0'; ch=getchar();} return x*f;} ll sqr(ll a){return a*a;}ld sqr(ld a){return a*a;}const double eps=1e-10;int dcmp(double x) { if (fabs(x)<eps) return 0; else return x<0 ? -1 : 1; }ld PI = acos(-1.0);class P{public: double x,y; P(double x=0,double y=0):x(x),y(y){} friend ld dis2(P A,P B){return sqr(A.x-B.x)+sqr(A.y-B.y); } friend ld Dot(P A,P B) {return A.x*B.x+A.y*B.y; } friend ld Length(P A) {return sqrt(Dot(A,A)); } friend ld Angle(P A,P B) { if (dcmp(Dot(A,A))==0||dcmp(Dot(B,B))==0||dcmp(Dot(A-B,A-B))==0) return 0; return acos(max((ld)-1.0, min((ld)1.0, Dot(A,B) / Length(A) / Length(B) )) ); } friend P operator- (P A,P B) { return P(A.x-B.x,A.y-B.y); } friend P operator+ (P A,P B) { return P(A.x+B.x,A.y+B.y); } friend P operator* (P A,double p) { return P(A.x*p,A.y*p); } friend P operator/ (P A,double p) { return P(A.x/p,A.y/p); } friend bool operator< (const P& a,const P& b) {return dcmp(a.x-b.x)<0 ||(dcmp(a.x-b.x)==0&& dcmp(a.y-b.y)<0 );}}; P read_point() { P a; scanf("%lf%lf",&a.x,&a.y); return a; } bool operator==(const P& a,const P& b) { return dcmp(a.x-b.x)==0 && dcmp(a.y-b.y) == 0;} typedef P V;double Cross(V A,V B) {return A.x*B.y - A.y*B.x;}double Area2(P A,P B,P C) {return Cross(B-A,C-A);}namespace complex_G{ typedef complex<double> Point; //real(p):实部 imag(p):虚部 conj(p):共轭 typedef Point Vector; double Dot(Vector A,Vector B) {return real(conj(A)*B); } double Cross(Vector A,Vector B) {return imag(conj(A)*B); } Vector Rotate(Vector A,double rad) {return A*exp(Point(0,rad)); }}//Cross(v,w)==0(平行)时,不能调这个函数 P GetLineIntersection(P p,V v,P Q,V w){ V u = p-Q; double t = Cross(w,u)/Cross(v,w); return p+v*t;}P GetLineIntersectionB(P p,V v,P Q,V w){ return GetLineIntersection(p,v-p,Q,w-Q);}double DistanceToLine(P p,P A,P B) { V v1 = B-A, v2 = p-A; return fabs(Cross(v1,v2))/Length(v1);}double DistanceToSegment(P p,P A,P B) { if (A==B) return Length(p-A); V v1 = B-A, v2 = p-A, v3 = p - B; if (dcmp(Dot(v1,v2))<0) return Length(v2); else if (dcmp(Dot(v1,v3))>0 ) return Length(v3); else return fabs(Cross(v1,v2) ) / Length(v1);}P GetLineProjection(P p,P A,P B) { V v=B-A; return A+v*(Dot(v,p-A)/Dot(v,v));}//规范相交-线段相交且交点不在端点 bool SegmentProperIntersection(P a1,P a2,P b1,P b2) { double c1 = Cross(a2-a1,b1-a1) , c2 = Cross(a2-a1,b2-a1), c3 = Cross(b2-b1,a1-b1) , c4 = Cross(b2-b1,a2-b1); return dcmp(c1)*dcmp(c2)<0 && dcmp(c3)*dcmp(c4)<0;}//点在线段上（不包含端点） bool OnSegment(P p,P a1,P a2) { return dcmp(Cross(a1-p,a2-p)) == 0 && dcmp(Dot(a1-p,a2-p))<0;}double PolygonArea(P *p,int n) { double area=0; For(i,n-2) area+=Cross(p[i]-p[0],p[i+1]-p[0]); return area/2;} /*欧拉公式： V+F-E=2 V-点数 F面数 E边数 */struct C{ P c; double r,x,y; C(P c,double r):c(c),r(r),x(c.x),y(c.y){} P point(double a) { return P(c.x+cos(a)*r,c.y+sin(a)*r); }};struct Line{ P p; V v; double ang; Line(){} Line(P p,V v):p(p),v(v) {ang=atan2(v.y,v.x); } bool operator<(const Line & L) const { return ang<L.ang; } P point(double a) { return p+v*a; }};int getLineCircleIntersection(Line L,C cir,double &t1,double &t2,vector<P> & sol) { if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) { P A=GetLineProjection(cir.c,L.p,L.p+L.v); sol.pb(A); t1 = (A-L.p).x / L.v.x; return 1; } double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y; double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r; double delta = f*f - 4*e*g; if (dcmp(delta)<0) return 0; else if (dcmp(delta)==0) { t1 = t2 = -f / (2*e); sol.pb(L.point(t1)); return 1; } t1 = (-f - sqrt(delta)) / (2*e); sol.pb(L.point(t1)); t2 = (-f + sqrt(delta)) / (2*e); sol.pb(L.point(t2)); return 2;}double angle(V v) {return atan2(v.y,v.x);}int getSegCircleIntersection(Line L,C cir,vector<P> & sol) { if (dcmp(DistanceToLine(cir.c,L.p,L.p+L.v)-cir.r)==0) { P A= GetLineProjection(cir.c,L.p,L.p+L.v); if (OnSegment(A,L.p,L.p+L.v) || L.p==A || L.p+L.v==A ) sol.pb(A); return sol.size(); } double t1,t2; double a = L.v.x, b = L.p.x - cir.c.x, c = L.v.y, d= L.p.y - cir.c.y; double e = a*a+c*c, f = 2*(a*b + c*d), g = b*b+d*d-cir.r*cir.r; double delta = f*f - 4*e*g; if (dcmp(delta)<0) return 0; else if (dcmp(delta)==0) { t1 = -f / (2*e); if (dcmp(t1)>=0&&dcmp(t1-1)<=0) { sol.pb(L.point(t1)); } return sol.size(); } t1 = (-f - sqrt(delta)) / (2*e); if (dcmp(t1)>=0&&dcmp(t1-1)<=0) sol.pb(L.point(t1)); t2 = (-f + sqrt(delta)) / (2*e); if (dcmp(t2)>=0&&dcmp(t2-1)<=0) sol.pb(L.point(t2)); if(SI(sol)==2 && t1>t2) swap(sol[1],sol[0]); return sol.size();}int isPointInOrOnCircle(P p,C c) { return dcmp(Length(p-c.c)-c.r)<=0;}// Triangle(O,A,B) and Circle(O,m)double CircleTriangleArea(P A,P B,double m) { double ans=0; C c=C(P(),m); P O=c.c; if (A==O||B==O) return 0; bool b = isPointInOrOnCircle(A,c); bool b2 = isPointInOrOnCircle(B,c); double opr; if (dcmp(Area2(O,A,B))>=0) opr=1; else opr=-1; if (b&&b2) { ans+=opr*fabs(Area2(A,B,O))/2; } else if (!b&&!b2){ Line l=Line(A,B-A); vector<P> sol; getSegCircleIntersection(l,c,sol); if (SI(sol)==2) { ans+=opr*fabs(Area2(sol[0],sol[1],O))/2; ans+=opr*m*m/2*(Angle(A,sol[0])+Angle(sol[1],B)); } else { ans+=opr*m*m/2*(Angle(A,B)); } } else { Line l=Line(A,B-A); vector<P> sol; getSegCircleIntersection(l,c,sol); if (SI(sol)==2) { ans+=opr*fabs(Area2(sol[0],sol[1],O))/2; ans+=opr*m*m/2*(Angle(A,sol[0])+Angle(sol[1],B)); } else if(b) { ans+=opr*fabs(Area2(sol[0],A,O))/2; ans+=opr*m*m/2*(Angle(sol[0],B)); } else { ans+=opr*fabs(Area2(sol[0],B,O))/2; ans+=opr*m*m/2*(Angle(sol[0],A)); } } return ans;}P a[10000];int main(){// freopen("poj2986.in","r",stdin);// freopen(".out","w",stdout); double R; while(~scanf("%lf%lf%lf%lf%lf%lf%lf%lf%lf",&a[0].x,&a[0].y,&a[1].x,&a[1].y,&a[2].x,&a[2].y,&a[3].x,&a[3].y,&R)) { double ans=0; Rep(i,3) { ans+=CircleTriangleArea(a[i]-a[3],a[(i+1)%3]-a[3],R); } printf("%.2f\n",fabs(ans)); } return 0;} 0 0
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