圆和多边形面积交模板
hdu5130
//#pragma comment(linker, "/stack:200000000")
//#pragma GCC optimize("Ofast,no-stack-protector")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
//#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
#define fi first
#define se second
#define mp make_pair
#define pb push_back
//#define pi acos(-1.0)
#define ll long long
#define vi vector<int>
#define mod 1000000007
#define ld long double
//#define C 0.5772156649
#define ls l,m,rt<<1
#define rs m+1,r,rt<<1|1
#define pil pair<int,ll>
#define pli pair<ll,int>
#define pii pair<int,int>
#define cd complex<double>
#define ull unsigned long long
#define base 1000000000000000000
#define fio ios::sync_with_stdio(false);cin.tie(0)
using namespace std;
const double eps=1e-6,PI = acos( -1.0 ) ;
const int N=500000+10,maxn=20000+10,inf=0x3f3f3f3f,INF=0x3f3f3f3f3f3f3f3f;
inline double sqr( double x ){ return x * x ; }
inline int sgn( double x ){
if ( fabs(x) < eps ) return 0 ;
return x > 0? 1 : -1 ;
}
struct Point{
double x , y ;
Point(){}
Point( double _x , double _y ): x(_x) , y(_y) {}
void input() { scanf( "%lf%lf" ,&x ,&y ); }
double norm() { return sqrt( sqr(x) + sqr(y) ); }
friend Point operator + ( const Point &a , const Point &b ) { return Point( a.x + b.x , a.y + b.y ) ; }
friend Point operator - ( const Point &a , const Point &b ) { return Point( a.x - b.x , a.y - b.y ) ; }
friend Point operator * ( const Point &a , const double &b ) { return Point( a.x * b , a.y * b ) ; }
friend Point operator * ( const double &a , const Point &b ) { return Point( b.x * a , b.y * a ) ; }
friend Point operator / ( const Point &a , const double &b ) { return Point( a.x / b , a.y / b ) ; }
friend bool operator == ( const Point &a , const Point &b ) { return sgn( a.x - b.x ) == 0 && sgn( a.y - b.y ) == 0 ; }
bool operator < ( const Point &a )const{
return ( sgn( x - a.x ) < 0 ) || ( sgn( x - a.x ) == 0 && sgn( y - a.y ) < 0 ) ;
}
};
double dot( Point a , Point b ) { return a.x * b.x + a.y * b.y ; }
double det( Point a , Point b ) { return a.x * b.y - a.y * b.x ; }
double dist( Point a , Point b ) { return ( a - b ).norm() ; }
int n ;
double k ;
Point A,B ;
Point p[505] ;
Point o ;
double r ;
int CircleInterLine( Point a, Point b, Point o, double r, Point *p )
{
Point p1 = a - o ;
Point d = b - a ;
double A = dot( d, d ) ;
double B = 2 * dot( d, p1 ) ;
double C = dot( p1, p1 ) - sqr(r) ;
double delta = sqr(B) - 4*A*C ;
if ( sgn(delta) < 0 ) return 0 ;//相离
if ( sgn(delta) == 0 ) { //相切
double t = -B / (2*A) ; // 0 <= t <= 1说明交点在线段上
if ( sgn( t - 1 ) <= 0 && sgn( t ) >= 0 ) {
p[0] = a + t * d ;
return 1 ;
}
}
if ( sgn(delta) > 0 ) { //相交
double t1 = ( -B - sqrt(delta) ) / (2*A) ;
double t2 = ( -B + sqrt(delta) ) / (2*A) ; //0 <= t1, t2 <= 1说明交点在线段上
int k = 0 ;
if ( sgn( t1 - 1 ) <= 0 && sgn( t1 ) >= 0 )
p[k++] = a + t1 * d ;
if ( sgn( t2 - 1 ) <= 0 && sgn( t2 ) >= 0 )
p[k++] = a + t2 * d ;
return k ;
}
}
double Triangle_area( Point a, Point b )
{
return fabs( det( a , b ) ) / 2.0 ;
}
double Sector_area( Point a, Point b )
{
double ang = atan2( a.y , a.x ) - atan2( b.y, b.x ) ;
while ( ang <= 0 ) ang += 2 * PI ;
while ( ang > 2 * PI ) ang -= 2 * PI ;
ang = min( ang, 2*PI - ang ) ;
return sqr(r) * ang/2 ;
}
double calc( Point a , Point b , double r )
{
Point pi[2] ;
if ( sgn( a.norm() - r ) < 0 ) {
if ( sgn( b.norm() - r ) < 0 ) {
return Triangle_area( a, b ) ;
}
else {
CircleInterLine( a, b, Point(0,0), r, pi) ;
return Sector_area( b, pi[0] ) + Triangle_area( a, pi[0] ) ;
}
}
else {
int cnt = CircleInterLine( a, b, Point(0,0), r, pi ) ;
if ( sgn( b.norm() - r ) < 0 ) {
return Sector_area( a, pi[0] ) + Triangle_area( b, pi[0] ) ;
}
else {
if ( cnt == 2 )
return Sector_area( a, pi[0] ) + Sector_area( b, pi[1] ) + Triangle_area( pi[0], pi[1] ) ;
else
return Sector_area( a, b ) ;
}
}
}
double area_CircleAndPolygon( Point *p , int n , Point o , double r )
{
double res = 0 ;
p[n] = p[0] ;
for ( int i = 0 ; i < n ; i++ ) {
int tmp = sgn( det( p[i] - o , p[i+1] - o ) ) ;
if ( tmp )
res += tmp * calc( p[i] - o , p[i+1] - o , r ) ;
}
return fabs( res ) ;
}
void gao()
{
double a1=1.0-k*k,b1=2.0*(sqr(k)*A.x-B.x),c=sqr(B.x)+sqr(B.y)-sqr(k)*(sqr(A.x)+sqr(A.y));
double a2=1.0-k*k,b2=2.0*(sqr(k)*A.y-B.y);
o.x=-b1/2.0/a1,o.y=-b2/2.0/a2;
r=sqrt(sqr(o.x)+sqr(o.y)+(sqr(k*A.x)-sqr(B.x)+sqr(k*A.y)-sqr(B.y))/a1);
// printf("%.12f %.12f %.12f\n",o.x,o.y,r);
}
int main()
{
int cnt=1;
while(~scanf("%d%lf",&n,&k))
{
for(int i=0;i<n;i++)
p[i].input();
A.input(),B.input();
gao();
printf("Case %d: %.12f\n",cnt++,area_CircleAndPolygon(p,n,o,r));
}
return 0;
}
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