Points.cpp

typedef double type;
typedef pair<type,type> Pt;
typedef pair<Pt,Pt> Line;
typedef pair<Pt,type> Circle;
#define X first
#define Y second
#define O first
#define R second
Pt operator+( const Pt& p1 , const Pt& p2 ){
  return { p1.X + p2.X , p1.Y + p2.Y };
}
Pt operator-( const Pt& p1 , const Pt& p2 ){
  return { p1.X - p2.X , p1.Y - p2.Y };
}
Pt operator*( const Pt& tp , const type& tk ){
  return { tp.X * tk , tp.Y * tk };
}
Pt operator/( const Pt& tp , const type& tk ){
  return { tp.X / tk , tp.Y / tk };
}
type operator*( const Pt& p1 , const Pt& p2 ){
  return p1.X * p2.X + p1.Y * p2.Y;
}
type operator^( const Pt& p1 , const Pt& p2 ){
  return p1.X * p2.Y - p1.Y * p2.X;
}
type norm2( const Pt& tp ){
  return tp * tp;
}
double norm( const Pt& tp ){
  return sqrt( norm2( tp ) );
}
Pt perp( const Pt& tp ){
  return { tp.Y , -tp.X };
}