题意：给出多边形的顶点坐标、圆的圆心坐标和半径，求面积交
sol：又是模板题啦= =
注意poj的C++好像认不出hypot函数，要稍微改写一下。
hypot(double x,double y)：即返回sqrt(x*x+y*y)的值
1 #include<vector> 2 #include<list> 3 #include<map> 4 #include<set> 5 #include<deque> 6 #include<queue> 7 #include<stack> 8 #include<bitset> 9 #include<algorithm> 10 #include<functional> 11 #include<numeric> 12 #include<utility> 13 #include<iostream> 14 #include<sstream> 15 #include<iomanip> 16 #include<cstdio> 17 #include<cmath> 18 #include<cstdlib> 19 #include<cctype> 20 #include<string> 21 #include<cstring> 22 #include<cstdio> 23 #include<cmath> 24 #include<cstdlib> 25 #include<ctime> 26 #include<climits> 27 #include<complex> 28 #define mp make_pair 29 #define pb push_back 30 using namespace std; 31 const double eps=1e-8; 32 const double pi=acos(-1.0); 33 const double inf=1e20; 34 const int maxp=1111; 35 int dblcmp(double d) 36 { 37 if (fabs(d)<eps)return 0; 38 return d>eps?1:-1; 39 } 40 inline double sqr(double x){return x*x;} 41 struct point 42 { 43 double x,y; 44 point(){} 45 point(double _x,double _y): 46 x(_x),y(_y){}; 47 void input() 48 { 49 scanf("%lf%lf",&x,&y); 50 } 51 void output() 52 { 53 printf("%.2f %.2f ",x,y); 54 } 55 bool operator==(point a)const 56 { 57 return dblcmp(a.x-x)==0&&dblcmp(a.y-y)==0; 58 } 59 bool operator<(point a)const 60 { 61 return dblcmp(a.x-x)==0?dblcmp(y-a.y)<0:x<a.x; 62 } 63 double len() 64 { 65 //return hypot(x,y); 66 return (sqrt(x*x+y*y)); 67 } 68 double len2() 69 { 70 return x*x+y*y; 71 } 72 double distance(point p) 73 { 74 //return hypot(x-p.x,y-p.y); 75 double tx=x-p.x,ty=y-p.y; 76 return (sqrt(tx*tx+ty*ty)); 77 } 78 point add(point p) 79 { 80 return point(x+p.x,y+p.y); 81 } 82 point sub(point p) 83 { 84 return point(x-p.x,y-p.y); 85 } 86 point mul(double b) 87 { 88 return point(x*b,y*b); 89 } 90 point div(double b) 91 { 92 return point(x/b,y/b); 93 } 94 double dot(point p) 95 { 96 return x*p.x+y*p.y; 97 } 98 double det(point p) 99 { 100 return x*p.y-y*p.x; 101 } 102 double rad(point a,point b) 103 { 104 point p=*this; 105 return fabs(atan2(fabs(a.sub(p).det(b.sub(p))),a.sub(p).dot(b.sub(p)))); 106 } 107 point trunc(double r) 108 { 109 double l=len(); 110 if (!dblcmp(l))return *this; 111 r/=l; 112 return point(x*r,y*r); 113 } 114 point rotleft() 115 { 116 return point(-y,x); 117 } 118 point rotright() 119 { 120 return point(y,-x); 121 } 122 point rotate(point p,double angle)//绕点p逆时针旋转angle角度 123 { 124 point v=this->sub(p); 125 double c=cos(angle),s=sin(angle); 126 return point(p.x+v.x*c-v.y*s,p.y+v.x*s+v.y*c); 127 } 128 }; 129 struct line 130 { 131 point a,b; 132 line(){} 133 line(point _a,point _b) 134 { 135 a=_a; 136 b=_b; 137 } 138 bool operator==(line v) 139 { 140 return (a==v.a)&&(b==v.b); 141 } 142 //倾斜角angle 143 line(point p,double angle) 144 { 145 a=p; 146 if (dblcmp(angle-pi/2)==0) 147 { 148 b=a.add(point(0,1)); 149 } 150 else 151 { 152 b=a.add(point(1,tan(angle))); 153 } 154 } 155 //ax+by+c=0 156 line(double _a,double _b,double _c) 157 { 158 if (dblcmp(_a)==0) 159 { 160 a=point(0,-_c/_b); 161 b=point(1,-_c/_b); 162 } 163 else if (dblcmp(_b)==0) 164 { 165 a=point(-_c/_a,0); 166 b=point(-_c/_a,1); 167 } 168 else 169 { 170 a=point(0,-_c/_b); 171 b=point(1,(-_c-_a)/_b); 172 } 173 } 174 void input() 175 { 176 a.input(); 177 b.input(); 178 } 179 void adjust() 180 { 181 if (b<a)swap(a,b); 182 } 183 double length() 184 { 185 return a.distance(b); 186 } 187 double angle()//直线倾斜角 0<=angle<180 188 { 189 double k=atan2(b.y-a.y,b.x-a.x); 190 if (dblcmp(k)<0)k+=pi; 191 if (dblcmp(k-pi)==0)k-=pi; 192 return k; 193 } 194 //点和线段关系 195 //1 在逆时针 196 //2 在顺时针 197 //3 平行 198 int relation(point p) 199 { 200 int c=dblcmp(p.sub(a).det(b.sub(a))); 201 if (c<0)return 1; 202 if (c>0)return 2; 203 return 3; 204 } 205 bool pointonseg(point p) 206 { 207 return dblcmp(p.sub(a).det(b.sub(a)))==0&&dblcmp(p.sub(a).dot(p.sub(b)))<=0; 208 } 209 bool parallel(line v) 210 { 211 return dblcmp(b.sub(a).det(v.b.sub(v.a)))==0; 212 } 213 //2 规范相交 214 //1 非规范相交 215 //0 不相交 216 int segcrossseg(line v) 217 { 218 int d1=dblcmp(b.sub(a).det(v.a.sub(a))); 219 int d2=dblcmp(b.sub(a).det(v.b.sub(a))); 220 int d3=dblcmp(v.b.sub(v.a).det(a.sub(v.a))); 221 int d4=dblcmp(v.b.sub(v.a).det(b.sub(v.a))); 222 if ((d1^d2)==-2&&(d3^d4)==-2)return 2; 223 return (d1==0&&dblcmp(v.a.sub(a).dot(v.a.sub(b)))<=0|| 224 d2==0&&dblcmp(v.b.sub(a).dot(v.b.sub(b)))<=0|| 225 d3==0&&dblcmp(a.sub(v.a).dot(a.sub(v.b)))<=0|| 226 d4==0&&dblcmp(b.sub(v.a).dot(b.sub(v.b)))<=0); 227 } 228 int linecrossseg(line v)//*this seg v line 229 { 230 int d1=dblcmp(b.sub(a).det(v.a.sub(a))); 231 int d2=dblcmp(b.sub(a).det(v.b.sub(a))); 232 if ((d1^d2)==-2)return 2; 233 return (d1==0||d2==0); 234 } 235 //0 平行 236 //1 重合 237 //2 相交 238 int linecrossline(line v) 239 { 240 if ((*this).parallel(v)) 241 { 242 return v.relation(a)==3; 243 } 244 return 2; 245 } 246 point crosspoint(line v) 247 { 248 double a1=v.b.sub(v.a).det(a.sub(v.a)); 249 double a2=v.b.sub(v.a).det(b.sub(v.a)); 250 return point((a.x*a2-b.x*a1)/(a2-a1),(a.y*a2-b.y*a1)/(a2-a1)); 251 } 252 double dispointtoline(point p) 253 { 254 return fabs(p.sub(a).det(b.sub(a)))/length(); 255 } 256 double dispointtoseg(point p) 257 { 258 if (dblcmp(p.sub(b).dot(a.sub(b)))<0||dblcmp(p.sub(a).dot(b.sub(a)))<0) 259 { 260 return min(p.distance(a),p.distance(b)); 261 } 262 return dispointtoline(p); 263 } 264 point lineprog(point p) 265 { 266 return a.add(b.sub(a).mul(b.sub(a).dot(p.sub(a))/b.sub(a).len2())); 267 } 268 point symmetrypoint(point p) 269 { 270 point q=lineprog(p); 271 return point(2*q.x-p.x,2*q.y-p.y); 272 } 273 }; 274 struct circle 275 { 276 point p; 277 double r; 278 circle(){} 279 circle(point _p,double _r): 280 p(_p),r(_r){}; 281 circle(double x,double y,double _r): 282 p(point(x,y)),r(_r){}; 283 circle(point a,point b,point c)//三角形的外接圆 284 { 285 p=line(a.add(b).div(2),a.add(b).div(2).add(b.sub(a).rotleft())).crosspoint(line(c.add(b).div(2),c.add(b).div(2).add(b.sub(c).rotleft()))); 286 r=p.distance(a); 287 } 288 circle(point a,point b,point c,bool t)//三角形的内切圆 289 { 290 line u,v; 291 double m=atan2(b.y-a.y,b.x-a.x),n=atan2(c.y-a.y,c.x-a.x); 292 u.a=a; 293 u.b=u.a.add(point(cos((n+m)/2),sin((n+m)/2))); 294 v.a=b; 295 m=atan2(a.y-b.y,a.x-b.x),n=atan2(c.y-b.y,c.x-b.x); 296 v.b=v.a.add(point(cos((n+m)/2),sin((n+m)/2))); 297 p=u.crosspoint(v); 298 r=line(a,b).dispointtoseg(p); 299 } 300 void input() 301 { 302 p.input(); 303 scanf("%lf",&r); 304 } 305 void output() 306 { 307 printf("%.2lf %.2lf %.2lf ",p.x,p.y,r); 308 } 309 bool operator==(circle v) 310 { 311 return ((p==v.p)&&dblcmp(r-v.r)==0); 312 } 313 bool operator<(circle v)const 314 { 315 return ((p<v.p)||(p==v.p)&&dblcmp(r-v.r)<0); 316 } 317 double area() 318 { 319 return pi*sqr(r); 320 } 321 double circumference() 322 { 323 return 2*pi*r; 324 } 325 //0 圆外 326 //1 圆上 327 //2 圆内 328 int relation(point b) 329 { 330 double dst=b.distance(p); 331 if (dblcmp(dst-r)<0)return 2; 332 if (dblcmp(dst-r)==0)return 1; 333 return 0; 334 } 335 int relationseg(line v) 336 { 337 double dst=v.dispointtoseg(p); 338 if (dblcmp(dst-r)<0)return 2; 339 if (dblcmp(dst-r)==0)return 1; 340 return 0; 341 } 342 int relationline(line v) 343 { 344 double dst=v.dispointtoline(p); 345 if (dblcmp(dst-r)<0)return 2; 346 if (dblcmp(dst-r)==0)return 1; 347 return 0; 348 } 349 //过a b两点 半径r的两个圆 350 int getcircle(point a,point b,double r,circle&c1,circle&c2) 351 { 352 circle x(a,r),y(b,r); 353 int t=x.pointcrosscircle(y,c1.p,c2.p); 354 if (!t)return 0; 355 c1.r=c2.r=r; 356 return t; 357 } 358 //与直线u相切 过点q 半径r1的圆 359 int getcircle(line u,point q,double r1,circle &c1,circle &c2) 360 { 361 double dis=u.dispointtoline(q); 362 if (dblcmp(dis-r1*2)>0)return 0; 363 if (dblcmp(dis)==0) 364 { 365 c1.p=q.add(u.b.sub(u.a).rotleft().trunc(r1)); 366 c2.p=q.add(u.b.sub(u.a).rotright().trunc(r1)); 367 c1.r=c2.r=r1; 368 return 2; 369 } 370 line u1=line(u.a.add(u.b.sub(u.a).rotleft().trunc(r1)),u.b.add(u.b.sub(u.a).rotleft().trunc(r1))); 371 line u2=line(u.a.add(u.b.sub(u.a).rotright().trunc(r1)),u.b.add(u.b.sub(u.a).rotright().trunc(r1))); 372 circle cc=circle(q,r1); 373 point p1,p2; 374 if (!cc.pointcrossline(u1,p1,p2))cc.pointcrossline(u2,p1,p2); 375 c1=circle(p1,r1); 376 if (p1==p2) 377 { 378 c2=c1;return 1; 379 } 380 c2=circle(p2,r1); 381 return 2; 382 } 383 //同时与直线u,v相切 半径r1的圆 384 int getcircle(line u,line v,double r1,circle &c1,circle &c2,circle &c3,circle &c4) 385 { 386 if (u.parallel(v))return 0; 387 line u1=line(u.a.add(u.b.sub(u.a).rotleft().trunc(r1)),u.b.add(u.b.sub(u.a).rotleft().trunc(r1))); 388 line u2=line(u.a.add(u.b.sub(u.a).rotright().trunc(r1)),u.b.add(u.b.sub(u.a).rotright().trunc(r1))); 389 line v1=line(v.a.add(v.b.sub(v.a).rotleft().trunc(r1)),v.b.add(v.b.sub(v.a).rotleft().trunc(r1))); 390 line v2=line(v.a.add(v.b.sub(v.a).rotright().trunc(r1)),v.b.add(v.b.sub(v.a).rotright().trunc(r1))); 391 c1.r=c2.r=c3.r=c4.r=r1; 392 c1.p=u1.crosspoint(v1); 393 c2.p=u1.crosspoint(v2); 394 c3.p=u2.crosspoint(v1); 395 c4.p=u2.crosspoint(v2); 396 return 4; 397 } 398 //同时与不相交圆cx,cy相切 半径为r1的圆 399 int getcircle(circle cx,circle cy,double r1,circle&c1,circle&c2) 400 { 401 circle x(cx.p,r1+cx.r),y(cy.p,r1+cy.r); 402 int t=x.pointcrosscircle(y,c1.p,c2.p); 403 if (!t)return 0; 404 c1.r=c2.r=r1; 405 return t; 406 } 407 int pointcrossline(line v,point &p1,point &p2)//求与线段交要先判断relationseg 408 { 409 if (!(*this).relationline(v))return 0; 410 point a=v.lineprog(p); 411 double d=v.dispointtoline(p); 412 d=sqrt(r*r-d*d); 413 if (dblcmp(d)==0) 414 { 415 p1=a; 416 p2=a; 417 return 1; 418 } 419 p1=a.sub(v.b.sub(v.a).trunc(d)); 420 p2=a.add(v.b.sub(v.a).trunc(d)); 421 return 2; 422 } 423 //5 相离 424 //4 外切 425 //3 相交 426 //2 内切 427 //1 内含 428 int relationcircle(circle v) 429 { 430 double d=p.distance(v.p); 431 if (dblcmp(d-r-v.r)>0)return 5; 432 if (dblcmp(d-r-v.r)==0)return 4; 433 double l=fabs(r-v.r); 434 if (dblcmp(d-r-v.r)<0&&dblcmp(d-l)>0)return 3; 435 if (dblcmp(d-l)==0)return 2; 436 if (dblcmp(d-l)<0)return 1; 437 } 438 int pointcrosscircle(circle v,point &p1,point &p2) 439 { 440 int rel=relationcircle(v); 441 if (rel==1||rel==5)return 0; 442 double d=p.distance(v.p); 443 double l=(d+(sqr(r)-sqr(v.r))/d)/2; 444 double h=sqrt(sqr(r)-sqr(l)); 445 p1=p.add(v.p.sub(p).trunc(l).add(v.p.sub(p).rotleft().trunc(h))); 446 p2=p.add(v.p.sub(p).trunc(l).add(v.p.sub(p).rotright().trunc(h))); 447 if (rel==2||rel==4) 448 { 449 return 1; 450 } 451 return 2; 452 } 453 //过一点做圆的切线 (先判断点和圆关系) 454 int tangentline(point q,line &u,line &v) 455 { 456 int x=relation(q); 457 if (x==2)return 0; 458 if (x==1) 459 { 460 u=line(q,q.add(q.sub(p).rotleft())); 461 v=u; 462 return 1; 463 } 464 double d=p.distance(q); 465 double l=sqr(r)/d; 466 double h=sqrt(sqr(r)-sqr(l)); 467 u=line(q,p.add(q.sub(p).trunc(l).add(q.sub(p).rotleft().trunc(h)))); 468 v=line(q,p.add(q.sub(p).trunc(l).add(q.sub(p).rotright().trunc(h)))); 469 return 2; 470 } 471 double areacircle(circle v) 472 { 473 int rel=relationcircle(v); 474 if (rel>=4)return 0.0; 475 if (rel<=2)return min(area(),v.area()); 476 double d=p.distance(v.p); 477 double hf=(r+v.r+d)/2.0; 478 double ss=2*sqrt(hf*(hf-r)*(hf-v.r)*(hf-d)); 479 double a1=acos((r*r+d*d-v.r*v.r)/(2.0*r*d)); 480 a1=a1*r*r; 481 double a2=acos((v.r*v.r+d*d-r*r)/(2.0*v.r*d)); 482 a2=a2*v.r*v.r; 483 return a1+a2-ss; 484 } 485 double areatriangle(point a,point b) 486 { 487 if (dblcmp(p.sub(a).det(p.sub(b))==0))return 0.0; 488 point q[5]; 489 int len=0; 490 q[len++]=a; 491 line l(a,b); 492 point p1,p2; 493 if (pointcrossline(l,q[1],q[2])==2) 494 { 495 if (dblcmp(a.sub(q[1]).dot(b.sub(q[1])))<0)q[len++]=q[1]; 496 if (dblcmp(a.sub(q[2]).dot(b.sub(q[2])))<0)q[len++]=q[2]; 497 } 498 q[len++]=b; 499 if (len==4&&(dblcmp(q[0].sub(q[1]).dot(q[2].sub(q[1])))>0))swap(q[1],q[2]); 500 double res=0; 501 int i; 502 for (i=0;i<len-1;i++) 503 { 504 if (relation(q[i])==0||relation(q[i+1])==0) 505 { 506 double arg=p.rad(q[i],q[i+1]); 507 res+=r*r*arg/2.0; 508 } 509 else 510 { 511 res+=fabs(q[i].sub(p).det(q[i+1].sub(p))/2.0); 512 } 513 } 514 return res; 515 } 516 }; 517 struct polygon 518 { 519 int n; 520 point p[maxp]; 521 line l[maxp]; 522 void input(int X) 523 { 524 n=X; 525 for (int i=0;i<n;i++) 526 { 527 p[i].input(); 528 } 529 } 530 void add(point q) 531 { 532 p[n++]=q; 533 } 534 void getline() 535 { 536 for (int i=0;i<n;i++) 537 { 538 l[i]=line(p[i],p[(i+1)%n]); 539 } 540 } 541 struct cmp 542 { 543 point p; 544 cmp(const point &p0){p=p0;} 545 bool operator()(const point &aa,const point &bb) 546 { 547 point a=aa,b=bb; 548 int d=dblcmp(a.sub(p).det(b.sub(p))); 549 if (d==0) 550 { 551 return dblcmp(a.distance(p)-b.distance(p))<0; 552 } 553 return d>0; 554 } 555 }; 556 void norm() 557 { 558 point mi=p[0]; 559 for (int i=1;i<n;i++)mi=min(mi,p[i]); 560 sort(p,p+n,cmp(mi)); 561 } 562 void getconvex(polygon &convex) 563 { 564 int i,j,k; 565 sort(p,p+n); 566 convex.n=n; 567 for (i=0;i<min(n,2);i++) 568 { 569 convex.p[i]=p[i]; 570 } 571 if (n<=2)return; 572 int &top=convex.n; 573 top=1; 574 for (i=2;i<n;i++) 575 { 576 while (top&&convex.p[top].sub(p[i]).det(convex.p[top-1].sub(p[i]))<=0) 577 top--; 578 convex.p[++top]=p[i]; 579 } 580 int temp=top; 581 convex.p[++top]=p[n-2]; 582 for (i=n-3;i>=0;i--) 583 { 584 while (top!=temp&&convex.p[top].sub(p[i]).det(convex.p[top-1].sub(p[i]))<=0) 585 top--; 586 convex.p[++top]=p[i]; 587 } 588 } 589 bool isconvex() 590 { 591 bool s[3]; 592 memset(s,0,sizeof(s)); 593 int i,j,k; 594 for (i=0;i<n;i++) 595 { 596 j=(i+1)%n; 597 k=(j+1)%n; 598 s[dblcmp(p[j].sub(p[i]).det(p[k].sub(p[i])))+1]=1; 599 if (s[0]&&s[2])return 0; 600 } 601 return 1; 602 } 603 //3 点上 604 //2 边上 605 //1 内部 606 //0 外部 607 int relationpoint(point q) 608 { 609 int i,j; 610 for (i=0;i<n;i++) 611 { 612 if (p[i]==q)return 3; 613 } 614 getline(); 615 for (i=0;i<n;i++) 616 { 617 if (l[i].pointonseg(q))return 2; 618 } 619 int cnt=0; 620 for (i=0;i<n;i++) 621 { 622 j=(i+1)%n; 623 int k=dblcmp(q.sub(p[j]).det(p[i].sub(p[j]))); 624 int u=dblcmp(p[i].y-q.y); 625 int v=dblcmp(p[j].y-q.y); 626 if (k>0&&u<0&&v>=0)cnt++; 627 if (k<0&&v<0&&u>=0)cnt--; 628 } 629 return cnt!=0; 630 } 631 //1 在多边形内长度为正 632 //2 相交或与边平行 633 //0 无任何交点 634 int relationline(line u) 635 { 636 int i,j,k=0; 637 getline(); 638 for (i=0;i<n;i++) 639 { 640 if (l[i].segcrossseg(u)==2)return 1; 641 if (l[i].segcrossseg(u)==1)k=1; 642 } 643 if (!k)return 0; 644 vector<point>vp; 645 for (i=0;i<n;i++) 646 { 647 if (l[i].segcrossseg(u)) 648 { 649 if (l[i].parallel(u)) 650 { 651 vp.pb(u.a); 652 vp.pb(u.b); 653 vp.pb(l[i].a); 654 vp.pb(l[i].b); 655 continue; 656 } 657 vp.pb(l[i].crosspoint(u)); 658 } 659 } 660 sort(vp.begin(),vp.end()); 661 int sz=vp.size(); 662 for (i=0;i<sz-1;i++) 663 { 664 point mid=vp[i].add(vp[i+1]).div(2); 665 if (relationpoint(mid)==1)return 1; 666 } 667 return 2; 668 } 669 //直线u切割凸多边形左侧 670 //注意直线方向 671 void convexcut(line u,polygon &po) 672 { 673 int i,j,k; 674 int &top=po.n; 675 top=0; 676 for (i=0;i<n;i++) 677 { 678 int d1=dblcmp(p[i].sub(u.a).det(u.b.sub(u.a))); 679 int d2=dblcmp(p[(i+1)%n].sub(u.a).det(u.b.sub(u.a))); 680 if (d1>=0)po.p[top++]=p[i]; 681 if (d1*d2<0)po.p[top++]=u.crosspoint(line(p[i],p[(i+1)%n])); 682 } 683 } 684 double getcircumference() 685 { 686 double sum=0; 687 int i; 688 for (i=0;i<n;i++) 689 { 690 sum+=p[i].distance(p[(i+1)%n]); 691 } 692 return sum; 693 } 694 double getarea() 695 { 696 double sum=0; 697 int i; 698 for (i=0;i<n;i++) 699 { 700 sum+=p[i].det(p[(i+1)%n]); 701 } 702 return fabs(sum)/2; 703 } 704 bool getdir()//1代表逆时针 0代表顺时针 705 { 706 double sum=0; 707 int i; 708 for (i=0;i<n;i++) 709 { 710 sum+=p[i].det(p[(i+1)%n]); 711 } 712 if (dblcmp(sum)>0)return 1; 713 return 0; 714 } 715 point getbarycentre() 716 { 717 point ret(0,0); 718 double area=0; 719 int i; 720 for (i=1;i<n-1;i++) 721 { 722 double tmp=p[i].sub(p[0]).det(p[i+1].sub(p[0])); 723 if (dblcmp(tmp)==0)continue; 724 area+=tmp; 725 ret.x+=(p[0].x+p[i].x+p[i+1].x)/3*tmp; 726 ret.y+=(p[0].y+p[i].y+p[i+1].y)/3*tmp; 727 } 728 if (dblcmp(area))ret=ret.div(area); 729 return ret; 730 } 731 double areaintersection(polygon po) 732 { 733 } 734 double areaunion(polygon po) 735 { 736 return getarea()+po.getarea()-areaintersection(po); 737 } 738 double areacircle(circle c) 739 { 740 int i,j,k,l,m; 741 double ans=0; 742 for (i=0;i<n;i++) 743 { 744 int j=(i+1)%n; 745 if (dblcmp(p[j].sub(c.p).det(p[i].sub(c.p)))>=0) 746 { 747 ans+=c.areatriangle(p[i],p[j]); 748 } 749 else 750 { 751 ans-=c.areatriangle(p[i],p[j]); 752 } 753 } 754 return fabs(ans); 755 } 756 //多边形和圆关系 757 //0 一部分在圆外 758 //1 与圆某条边相切 759 //2 完全在圆内 760 int relationcircle(circle c) 761 { 762 getline(); 763 int i,x=2; 764 if (relationpoint(c.p)!=1)return 0; 765 for (i=0;i<n;i++) 766 { 767 if (c.relationseg(l[i])==2)return 0; 768 if (c.relationseg(l[i])==1)x=1; 769 } 770 return x; 771 } 772 void find(int st,point tri[],circle &c) 773 { 774 if (!st) 775 { 776 c=circle(point(0,0),-2); 777 } 778 if (st==1) 779 { 780 c=circle(tri[0],0); 781 } 782 if (st==2) 783 { 784 c=circle(tri[0].add(tri[1]).div(2),tri[0].distance(tri[1])/2.0); 785 } 786 if (st==3) 787 { 788 c=circle(tri[0],tri[1],tri[2]); 789 } 790 } 791 void solve(int cur,int st,point tri[],circle &c) 792 { 793 find(st,tri,c); 794 if (st==3)return; 795 int i; 796 for (i=0;i<cur;i++) 797 { 798 if (dblcmp(p[i].distance(c.p)-c.r)>0) 799 { 800 tri[st]=p[i]; 801 solve(i,st+1,tri,c); 802 } 803 } 804 } 805 circle mincircle()//点集最小圆覆盖 806 { 807 random_shuffle(p,p+n); 808 point tri[4]; 809 circle c; 810 solve(n,0,tri,c); 811 return c; 812 } 813 int circlecover(double r)//单位圆覆盖 814 { 815 int ans=0,i,j; 816 vector<pair<double,int> >v; 817 for (i=0;i<n;i++) 818 { 819 v.clear(); 820 for (j=0;j<n;j++)if (i!=j) 821 { 822 point q=p[i].sub(p[j]); 823 double d=q.len(); 824 if (dblcmp(d-2*r)<=0) 825 { 826 double arg=atan2(q.y,q.x); 827 if (dblcmp(arg)<0)arg+=2*pi; 828 double t=acos(d/(2*r)); 829 v.push_back(make_pair(arg-t+2*pi,-1)); 830 v.push_back(make_pair(arg+t+2*pi,1)); 831 } 832 } 833 sort(v.begin(),v.end()); 834 int cur=0; 835 for (j=0;j<v.size();j++) 836 { 837 if (v[j].second==-1)++cur; 838 else --cur; 839 ans=max(ans,cur); 840 } 841 } 842 return ans+1; 843 } 844 int pointinpolygon(point q)//点在凸多边形内部的判定 845 { 846 if (getdir())reverse(p,p+n); 847 if (dblcmp(q.sub(p[0]).det(p[n-1].sub(p[0])))==0) 848 { 849 if (line(p[n-1],p[0]).pointonseg(q))return n-1; 850 return -1; 851 } 852 int low=1,high=n-2,mid; 853 while (low<=high) 854 { 855 mid=(low+high)>>1; 856 if (dblcmp(q.sub(p[0]).det(p[mid].sub(p[0])))>=0&&dblcmp(q.sub(p[0]).det(p[mid+1].sub(p[0])))<0) 857 { 858 polygon c; 859 c.p[0]=p[mid]; 860 c.p[1]=p[mid+1]; 861 c.p[2]=p[0]; 862 c.n=3; 863 if (c.relationpoint(q))return mid; 864 return -1; 865 } 866 if (dblcmp(q.sub(p[0]).det(p[mid].sub(p[0])))>0) 867 { 868 low=mid+1; 869 } 870 else 871 { 872 high=mid-1; 873 } 874 } 875 return -1; 876 } 877 }; 878 879 880 circle CR; double R; 881 polygon PL; 882 int n; 883 884 int main() 885 { 886 while(cin>>R) 887 { 888 CR=circle(point(0,0),R); 889 cin>>n; 890 PL.input(n); 891 892 double ans=PL.areacircle(CR); 893 printf("%.2lf ",ans); 894 } 895 896 return 0; 897 }