计算几何模板1 点部分

//Computational Geometry 1 points
//by kevin_samuel(fenice) Soochow University 2011
//[email protected]
//kevin-samuel.myazure.org
//temple
#include <iostream>
#include <cmath>
#include <algorithm>
#include <cstdio>

using namespace std;

//define
const double EPS = 1e-8;
const double PI = acos(-1.0);

//point
class Point
{
public:
  double x;
  double y;
  Point(){};
  Point(double x,double y):x(x),y(y){};

  //operator
  //operator=
  Point& operator=(const Point& _P)
  {
    x = _P.x;
    y = _P.y;
    return *this;
  }
  //operator*
  double operator*(const Point& _P)const
  {
    return x*_P.y - y *_P.x;
  }
  //operator-
  Point operator-(const Point& _P)const
  {
    return Point(x - _P.x,y - _P.y);
  }
  //operator==
  bool operator==(const Point& _P)const
  {
    if(fabs(_P.x - x) < EPS && fabs(_P.y - y) < EPS)
      return true;
    else
      return false;
  }
  bool operator!=(const Point& _P)const
  {
    return ((*this) == _P) == false;
  }

  //dot product
  static double dotProduct(Point s1,Point e1,Point s2,Point e2)
  {
    double result = 0;
    double x1 = e1.x - s1.x;
    double y1 = e1.y - s1.y;
    double x2 = e2.x - s2.x;
    double y2 = e2.y - s2.y;

    result = x1*x2 + y1*y2;
    return result;
  }

  //cross product 1 (4 point-type params)
  static double crossProduct(Point s1,Point e1,Point s2,Point e2)
  {
    double result = 0;
    double x1 = e1.x - s1.x;
    double y1 = e1.y - s1.y;
    double x2 = e2.x - s2.x;
    double y2 = e2.y - s2.y;

    result = x1*y2 - x2*y1;

    return result;
  }

  //cross product 2 (3 point-type params) 
  static double crossProduct(Point p1,Point p2,Point p0)
  {
    return crossProduct(p0,p1,p0,p2);
  }

  //Is on segment or line
  static bool onSegment(Point Pi,Point Pj,Point Q)
  {
    if(Q.x >= min(Pi.x,Pj.x) && Q.x <= max(Pi.x,Pj.x) &&
       Q.y >= min(Pi.y,Pj.y) && Q.y <= max(Pi.y,Pj.y) &&
       crossProduct(Q,Pj,Pi) == 0
     )
      return true;
    else
      return false;
  }

  //Is on segment
  bool IsOnSegment(Point Pi,Point Pj)
  {
    if(this->x >= min(Pi.x,Pj.x) && this->x <= max(Pi.x,Pj.x) &&
       this->y >= min(Pi.y,Pj.y) && this->y <= max(Pi.y,Pj.y) &&
       Point::crossProduct(*this,Pj,Pi) == 0
     )
      return true;
    else
      return false;
  }

  //Is inside triangle
  bool inTriangle(Point A,Point B,Point C)
  {

    double Sabc = fabs(Point::crossProduct(B,C,A));
    double Spab = fabs(Point::crossProduct(A,B,(*this)));
    double Spac = fabs(Point::crossProduct(A,C,(*this)));
    double Spbc = fabs(Point::crossProduct(B,C,(*this)));

    if(Spbc + Spab + Spac == Sabc)
      return true;
    else
      return false;
  }

  //Is inside polygon
  //polys[] ,0-n
  bool insidePolygon(Point *polys,int n)
  {
    int counter = 0;
    double xinters;
    Point p1,p2;
    p1 = polys[0];
    for(int i = 1; i < n; i++)
      {
	p2 = polys[i % n];
	if(Point::onSegment(p1,p2,(*this)) == true)
	  return true;
	if((*this).y > min(p1.y,p2.y) && (*this).y <= max(p1.y,p2.y))
	  {
	    if((*this).x <= max(p1.x,p2.x) && p1.y != p2.y)
	      {
		xinters = ((*this).y - p1.y)*(p2.x - p1.x)/(p2.y - p1.y) + p1.x;
		if(p1.x == p2.x || (*this).x <= xinters)
		  counter++;
	      }
	  }
	p1 = p2;
      }
    if(counter % 2 == 0)
      return false;
    return true;
  }

  //distance^2
  double dis2(const Point& _P)const
  {
    return (x - _P.x)*(x - _P.x) + (y - _P.y)*(y - _P.y);
  }
  //distance 
  double dis(const Point& _P)const
  {
    return sqrt(dis2(_P));
  }

};

//test zone
  int main()
  {
    //
    return 0;
  }