2d_template.cpp

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <vector> 
using namespace std;
const double PI=acos(0)*2;
struct Point
{
	double x,y;
	Point(double x=0,double y=0):x(x),y(y){}  //构造函数
};
typedef Point Vector;  //从程序的实现上，Vector只是Point的别名
Vector operator +(Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}
Vector operator -(Point A,Point B){ return Vector(A.x-B.x,A.y-B.y); }
Vector operator *(Vector A,double p){return Vector(A.x*p,A.y*p);}
Vector operator /(Vector A,double p){return Vector(A.x/p,A.y/p);}
bool operator< (const Point& a ,const Point& b){
	return a.x<b.x||(a.x==b.x&&a.y<b.y);
}
const double eps=1e-10;
int dcmp(double x){
	if(fabs(x)<eps)return 0;else return x<0?-1:1;
}
bool operator == (const Point& a,const Point &b)
{
	return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;
}
double Dot(Vector A,Vector B){  return A.x*B.x+A.y*B.y;}
double Dist2(const Point& A, const Point& B) {    return (A.x-B.x)*(A.x-B.x) + (A.y-B.y)*(A.y-B.y);  } 
double Length(Vector A){return sqrt(Dot(A,A));}
double Angle(Vector A,Vector B) { return acos(Dot(A,B)/Length(A)/Length(B)); }
double Cross(Vector A,Vector B){ return A.x*B.y-A.y*B.x;}
double Area2(Point A,Point B,Point C){return Cross(B-A,C-A);}
Vector Rotate(Vector A,double rad){
   return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
Vector Normal(Vector A){
   double L=Length(A);
   return Vector(-A.y/L,A.x/L);
}
double torad(double deg){
   return deg/180*acos(-1);
}
Point GetlineIntersection(Point P,Vector v,Point Q,Vector  w){
	Vector u=P-Q;
	double t=Cross(w,u)/Cross(v,w);
	return P+v*t;
}
double DistanceToLine(Point P,Point A,Point B){
   Vector v1=B-A,v2=P-A;
   return fabs(Cross(v1,v2))/Length(v1);
}
double DistanceToSegment(Point P,Point A,Point B){
   if(A==B)return Length(P-A);
   Vector v1=B-A,v2=P-A,v3=P-B;
   if(dcmp(Dot(v1,v2))<0) return Length(v2);
   else if(dcmp(Dot(v1,v3))>0) return Length(v3);
   else return fabs(Cross(v1,v2))/Length(v1);
}
Point GetLineProjection(Point P,Point A,Point B){
   Vector v=B-A;
   return A+v*(Dot(v,P-A)/Dot(v,v));
}
bool SegmentProperIntersection(Point a1,Point a2,Point b1,Point b2){
   double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),
		  c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
   return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;
}
bool OnSegment(Point P,Point a1,Point a2){
   return dcmp(Cross(a1-P,a2-P))==0&&dcmp(Dot(a1-P,a2-P))<0;
}
double PolygonArea(Point *p,int n)
{
	double area=0;
	for(int i=1;i<n-1;i++)
		area+=Cross(p[i]-p[0],p[i+1]-p[0]);
	return area/2;
}
int isPointInPolygon(Point p,Point poly[],int n){  //点是否在多边形内
	int wn=0;
	for(int i=0;i<n;i++){
		if(OnSegment(p,poly[i],poly[(i+1)%n])) return -1;  //在边界上
		int k=dcmp(Cross(poly[(i+1)%n]-poly[i],p-poly[i]));
		int d1=dcmp(poly[i].y-p.y);
		int d2=dcmp(poly[(i+1)%n].y-p.y);
		if(k>0&&d1<=0&&d2>0)wn++;
		if(k<0&&d2<=0&&d1>0)wn--;
	}
	if(wn!=0) return 1;  //点在内部
	return 0;  //点在外部
}
Point Gravity(Point *p, int n) {  //返回多边形的重心
	double area = 0;
	Point center;
	center.x = 0;
	center.y = 0;
	for (int i = 0; i < n-1; i++) {
		area += (p[i].x*p[i+1].y - p[i+1].x*p[i].y)/2;
		center.x += (p[i].x*p[i+1].y - p[i+1].x*p[i].y) * (p[i].x + p[i+1].x);
		center.y += (p[i].x*p[i+1].y - p[i+1].x*p[i].y) * (p[i].y + p[i+1].y);
	}
	area += (p[n-1].x*p[0].y - p[0].x*p[n-1].y)/2;
	center.x += (p[n-1].x*p[0].y - p[0].x*p[n-1].y) * (p[n-1].x + p[0].x);
	center.y += (p[n-1].x*p[0].y - p[0].x*p[n-1].y) * (p[n-1].y + p[0].y);
	center.x /= 6*area;
	center.y /= 6*area;
	return center;
}