【计算几何】点、向量、点与直线、多边形模板大集合

#include<iostream>
#include<complex>
#include<cmath>
#include<cstdio>
#include<cstring>
#include<vector>
using namespace std;
#define eps 1e-9
#define inf 99999999
typedef long long ll;
struct Point{
	double x,y;
	Point(double x=0,double y=0):x(x),y(y){}
}; 
typedef Point Vector;

Vector operator + (Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}
Vector operator - (Vector A,Vector 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);
}

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;
}

struct Line{
	Point v,p;
	Line(Point v,Point p):v(v),p(p){}
	Point point(double t){
		return v+(p-v)*t;
	}
};

//点积
double Dot(Vector A,Vector B){ return A.x*B.x+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)); }
 
//叉积
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);}

//向量 旋转，rad是弧度
Vector Rotate(Vector A,double rad)
{
	return Vector(A.x*cos(rad)-A.y*sin(rad),A.x*sin(rad)+A.y*cos(rad));
}
//计算单位法线
Vector Normal(Vector A)
{
	double L=Length(A);
	return Vector(-A.y/L,A.x/L);
} 

//判断折线bc是不是向ab的逆时针方向转
bool ToLeftTest(Point a,Point b,Point c)
{
	return Cross(b-a,c-b)>0;
 } 
 
//直线交点
Point GetLineIntersection(Point P,Vector v,Point Q,Vector w)
{
	Vector u=P-Q;
	//确保Cross(v,w)!=0
	double t=Cross(w,u)/Cross(v,w);
	return P+v*t; 
}

//点到直线距离
double DistanceToLine(Point P,Point A,Point B)
{
	Vector v1=B-A,v2=P-A;
	return fabs(Cross(v1,v2))/Length(v1);
	//如果不取绝对值，得到的是有向距离	
} 

//点到线段的距离
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);	
}  

//点在直线上的投影
Point GetLineProjection(Point P,Point A,Point B)
{
	Vector v=B-A;
	return A+v*(Dot(v,P-A)/Dot(v,v));
} 

//点是否在线段上
bool OnSegment(Point p,Point a1,Point a2)
{
	return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;
 } 

//线段相交判定
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;	
} 

//允许在线段端点相交
bool SegmentProperIntersection_duan(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);
	//if判断控制是否允许线段在端点处相交，根据需要添加
	if(!dcmp(c1)||!dcmp(c2)||!dcmp(c3)||!dcmp(c4))
	{
		bool f1=OnSegment(b1,a1,a2);
		bool f2=OnSegment(b2,a1,a2);
		bool f3=OnSegment(a1,b1,b2);
		bool f4=OnSegment(a2,b1,b2);
		bool f=(f1|f2|f3|f4);
		return f;	
	}	   
	return (dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0);
} 

//多边形有向面积
//p为端点集合，n为端点个数 
double PolygonArea(Point* p,int n)
{
	double s=0;
	for(int i=0;i<n-1;i++)
		s+=Cross(p[i]-p[0],p[i+1]-p[0]);
	return s/2;
} 

//判断点在多边形内
int isPointPolygon(Point p,vector<Point> poly)
{
	int wn=0;
	int n=poly.size();
	for(int i=0;i<n;i++)
	{
		if(OnSegment(p,poly[i],poly[(i+1)%n]))
			return -1;
		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;
	return 0;
} 
//-------------------------------------------------------------------------------------------------------

 
int main()
{
	
	
	return 0;
}