基本函数

1、基本函数 
1.1 Point 定义 
const double eps = 1e-8; 
const double PI = acos(-1.0); 
int sgn(double x) 
{ 
  if(fabs(x) < eps)return 0; 
  if(x < 0)return -1; 
  else return 1; 
} 
struct Point 
{ 
  double x,y; 
  Point(){} 
  Point(double _x,double _y) 
  { 
    x = _x;y = _y; 
  } 
  Point operator -(const Point &b)const 
  { 
    return Point(x - b.x,y - b.y); 
  } 
  //叉积 
  double operator ^(const Point &b)const 
  { 
    return x*b.y - y*b.x; 
  } 
  //点积 
  double operator *(const Point &b)const 
  { 
    return x*b.x + y*b.y; 
  } 
  //绕原点旋转角度B（弧度值），后x,y的变化 
  void transXY(double B) 
  { 
    double tx = x,ty = y; 
    x = tx*cos(B) - ty*sin(B); 
    y = tx*sin(B) + ty*cos(B); 
  } 
}; 
 
 
1.2 Line 定义 
struct Line 
{ 
  Point s,e; 
  Line(){} 
  Line(Point _s,Point _e) 
  { 
    s = _s;e = _e; 
  } 
  //两直线相交求交点 
  //第一个值为0表示直线重合，为1表示平行，为0表示相交,为2是相交 
  //只有第一个值为2时，交点才有意义 
    pair<int,Point> operator &(const Line &b)const 
    { 
        Point res = s; 
        if(sgn((s-e)^(b.s-b.e)) == 0) 
        { 
            if(sgn((s-b.e)^(b.s-b.e)) == 0) 
                return make_pair(0,res);//重合 
            else return make_pair(1,res);//平行 
        } 
        double t = ((s-b.s)^(b.s-b.e))/((s-e)^(b.s-b.e)); 
        res.x += (e.x-s.x)*t; 
        res.y += (e.y-s.y)*t; 
        return make_pair(2,res); 
    } 
}; 
 
 
1.3  两点间距离 
//*两点间距离 
double dist(Point a,Point b) 
{ 
    return sqrt((a-b)*(a-b)); 
} 


1.4  判断：线段相交 
//*判断线段相交 
bool inter(Line l1,Line l2) 
{ 
  return 
    max(l1.s.x,l1.e.x) >= min(l2.s.x,l2.e.x) && 
    max(l2.s.x,l2.e.x) >= min(l1.s.x,l1.e.x) && 
    max(l1.s.y,l1.e.y) >= min(l2.s.y,l2.e.y) && 
    max(l2.s.y,l2.e.y) >= min(l1.s.y,l1.e.y) && 
    sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0 && 
    sgn((l1.s-l2.e)^(l2.s-l2.e))*sgn((l1.e-l2.e)^(l2.s-l2.e)) <= 0; 
} 
 
 
1.5  判断：直线和线段相交 
//判断直线和线段相交 
bool Seg_inter_line(Line  l1,Line  l2) //判断直线l1和线段l2是否相交 
{ 
  return sgn((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0; 
} 


1.6  点到直线距离 
//点到直线距离 
//返回为result,是点到直线最近的点 
Point PointToLine(Point P,Line L) 
{ 
    Point result; 
    double t = ((P-L.s)*(L.e-L.s))/((L.e-L.s)*(L.e-L.s)); 
    result.x = L.s.x + (L.e.x-L.s.x)*t; 
    result.y = L.s.y + (L.e.y-L.s.y)*t; 
    return result; 
} 


1.7  点到线段距离 
//点到线段的距离 
//返回点到线段最近的点 
Point NearestPointToLineSeg(Point P,Line L) 
{ 
    Point result; 
    double t = ((P-L.s)*(L.e-L.s))/((L.e-L.s)*(L.e-L.s)); 
    if(t >= 0 && t <= 1) 
    { 
        result.x = L.s.x + (L.e.x - L.s.x)*t; 
        result.y = L.s.y + (L.e.y - L.s.y)*t; 
    } 
    else 
    { 
        if(dist(P,L.s) < dist(P,L.e)) 
            result = L.s; 
        else result = L.e; 
    } 
    return result; 
} 


1.8  计算多边形面积 
//计算多边形面积 
//点的编号从0~n-1 
double CalcArea(Point p[],int n) 
{ 
    double res = 0; 
    for(int i = 0;i < n;i++) 
        res += (p[i]^p[(i+1)%n])/2; 
    return fabs(res); 
} 


1.9  判断点在线段上 
//*判断点在线段上 
bool OnSeg(Point P,Line L) 
{ 
    return 
    sgn((L.s-P)^(L.e-P)) == 0 && 
    sgn((P.x - L.s.x) * (P.x - L.e.x)) <= 0 && 
    sgn((P.y - L.s.y) * (P.y - L.e.y)) <= 0; 
} 


1.10  判断点在凸多边形内 
//*判断点在凸多边形内 
//点形成一个凸包，而且按逆时针排序（如果是顺时针把里面的<0改为>0） 
//点的编号:0~n-1 
//返回值： 
//-1:点在凸多边形外 
//0:点在凸多边形边界上 
//1:点在凸多边形内 
int inConvexPoly(Point a,Point p[],int n) 
{ 
  for(int i = 0;i < n;i++) 
  { 
    if(sgn((p[i]-a)^(p[(i+1)%n]-a)) < 0)return -1; 
    else if(OnSeg(a,Line(p[i],p[(i+1)%n])))return 0; 
  } 
  return 1; 
} 


1.11  判断点在任意多边形内 
//*判断点在任意多边形内 
//射线法，poly[]的顶点数要大于等于3,点的编号0~n-1 
//返回值 
//-1:点在凸多边形外 
//0:点在凸多边形边界上 
//1:点在凸多边形内 
int inPoly(Point p,Point poly[],int n) 
{ 
  int cnt; 
  Line ray,side; 
  cnt = 0; 
  ray.s = p; 
  ray.e.y = p.y; 
  ray.e.x  = -100000000000.0;//-INF,注意取值防止越界 
 
  for(int i = 0;i < n;i++) 
  { 
    side.s = poly[i]; 
    side.e = poly[(i+1)%n];
    if(OnSeg(p,side))return 0; 
 
    //如果平行轴则不考虑 
    if(sgn(side.s.y - side.e.y) == 0) 
      continue; 
 
    if(OnSeg(side.s,ray)) 
    { 
      if(sgn(side.s.y - side.e.y) > 0)cnt++; 
    } 
    else if(OnSeg(side.e,ray)) 
    { 
      if(sgn(side.e.y - side.s.y) > 0)cnt++; 
    } 
    else if(inter(ray,side)) 
      cnt++; 
  } 
  if(cnt % 2 == 1)return 1; 
  else return -1; 
} 


1.12  判断凸多边形 
//判断凸多边形 
//允许共线边 
//点可以是顺时针给出也可以是逆时针给出 
//点的编号1~n-1 
bool isconvex(Point poly[],int n) 
{ 
  bool s[3]; 
  memset(s,false,sizeof(s)); 
  for(int i = 0;i < n;i++) 
  { 
    s[sgn( (poly[(i+1)%n]-poly[i])^(poly[(i+2)%n]-poly[i]) )+1] = true; 
    if(s[0] && s[2])return false; 
  } 
  return true; 
}