#include#include#include#include#include#include#include#include#include#include#includeusing namespace std;#define inf 0x3f3f3f3f
#define eps 1e-7
#define ll long long
#define ull unsigned long long
#define mp make_pair
#define pb push_back
#define ls ( i << 1 )
#define rs ( ls | 1 )
#define md ( ( ll[i] + rr[i] ) >> 1 )
#define mxn 5020
#define pi acos( -1.0 )
// 角度轉換為弧度
double torad( double deg )
int dcmp( double x )
struct point
point operator + ( const point &b ) const
point operator - ( const point &b ) const
point operator * ( const double &k ) const
point operator / ( const double &k ) const
bool operator < ( const point &b ) const
bool operator == ( const point &b ) const
double len()
};struct line
line( point v, point p ): v( v ), p( p )
point get_point( double t )
bool operator < ( const line &l ) const
};// 圓
struct circle
circle( point c, double r ): c( c ), r( r ){}
//圓心角為a的點
point get_point( double a )
};double cross( point a, point b )
double dot( point a, point b )
// 極角
double angle( point v )
double angle( point a, point b )
double area( point a, point b, point c )
point rotate( point a, double rad )
point normal( point a )
// 直線的交點,p 和 q是直線上的點， v和w是方向向量
point getlineintersection( point p, point v, point q, point w )
// 點到直線的距離
double distoline( point p, point a, point b )
// 點到線段的距離
double distoseg( point p, point a, point b )
// 點在直線的投影
point getlinepro( point p, point a, point b )
// 線段規範相交
bool segprointers( point a1, point a2, point b1, point b2 )
bool ons( point p, point a1, point a2 )
//多邊形有向面積
double polygonarea( point *p, int n )
int getlinecirins( line l, circle c, double &t1, double &t2, vector&sol )
t1 = ( - f - sqrt( delta ) ) / ( 2 * e );
sol.push_back( l.get_point( t1 ) );
t2 = ( - f + sqrt( delta ) ) / ( 2 * e );
sol.push_back( l.get_point( t2 ) );
return 2;
}// 兩圓相交
int getccins( circle c1, circle c2, vector&sol )
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 * c2.r * d ) );
point p1 = c1.get_point( a - da ), p2 = c1.get_point( a + da );
sol.push_back( p1 );
if( p1 == p2 )
return 1;
sol.push_back( p2 );
return 2;
}// 過點p到圓c的切線，v[i]是第i條切線。返回切線條數
int gettangents( point p, circle c, point *v )
double ang = asin( c.r / dist );
v[0] = rotate( u, - ang );
v[1] = rotate( u, + ang );
return 2;
}// 求兩圓的切線，返回切線條數，-1表示無窮條，
// a[i] 和 b[i]分別是第i條切線在圓a和圓b上的切點
int gettangents( circle a, circle b, point *a, point *b )
double ang = acos( ( a.r - b.r ) / sqrt( d2 ) );
a[cnt] = a.get_point( base + ang );
b[cnt++] = b.get_point( base + ang );
a[cnt] = a.get_point( base - ang );
b[cnt++] = b.get_point( base - ang );
if( dcmp( d2 - rsum * rsum ) == 0 )
else
} return cnt;
}// 點在多邊形內判定, -1 在邊界，0,不在，1在
// 點在凸多邊形內的判定, 判斷點是不是在所有邊的左邊
int inpoly( point p, point * poly, int n )
if( wn )
return 1;
return 0;
}// 凸包
int tb( point *p, int n, point *ch )
int k = m;
for( int i = n - 2; i >= 0; --i )
if( n > 1 )
m--;
return m;
}// 點在有向線段左邊
bool onleft( line l, point p )
// 二直線交點，假設交點唯一存在
point getintersection( line a, line b )
// 半平面交
int halfins( line *l, int n, point *poly )
if( first < last )
p[last-1] = getintersection( q[last-1], q[last] );
} while( first < last && !onleft( q[first], p[last-1] ) )
last--;
if( last - first <= 1 )
return 0;
p[last] = getintersection( q[last], q[first] );
int m = 0;
for( int i = first; i <= last; ++i )
poly[m++] = p[i];
return m;
} // */
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