來自《演算法競賽入門經典-訓練指南》 劉汝佳/陳峰 清華大學出版社

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <cmath>

using namespace std;

const double eps = 1e-8;

int dcmp(double x) //三態函式 處理與double零有關的精度問題 
{
	if(fabs(x) < eps)	return 0;
	return x<0 ? -1 : 1;
}

#define Vector Point
//向量使用點作為表示方法 結構相同 為了程式碼清晰定義巨集加以區別
struct Point//點 向量 
{ 
	double x,y;
	Point(double x=0,double y=0):x(x),y(y) {}
}; 

//向量運算 
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 Vector& A, const Vector& B) {return dcmp(A.x-B.x)==0 && dcmp(A.y-B.y)==0;}

double Dis(Point A, Point B)//兩點距離 
{
	return sqrt((A.x - B.x)*(A.x - B.x) + (A.y - B.y)*(A.y - B.y));
}

double Dot(Vector A, Vector B){//向量點積 
	return A.x * B.x + A.y * B.y;
}

double Length(Vector A){//向量長度 
	return sqrt(Dot(A,A)); 
} 

double Angle(Vector A, Vector B){ //向量夾角 
	return acos(Dot(A,B) / Length(A) / Length(B));
}

double Cross(Vector A, Vector B){ //向量叉積
	return A.x * B.y - A.y * B.x;
}

double Area2(Point A, Point B, Point C){ // 三角形有向面積兩倍
	return Cross(B-A,C-A);
}

Vector Rotate(Vector A, double rad){//向量旋轉 rad為弧度
	return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad)); 
}

Vector Normal(Vector A){ //單位法線 (左轉90度後的單位向量)
	//呼叫需確定A為非零向量
	double L = Length(A);
	return Vector(-A.y/L , A.x/L);
}

//直線向量引數方程 P+tv P為點,v為單位向量 (v長度無用)
Point GetLineIntersection(Point P, Vector v, Point Q, Vector w)//獲取直線交點 
{
	//呼叫應保證P,Q有交點 : 即 Cross(v,w)!=0 
	Vector u = P-Q;
	double t = Cross(w,u) / Cross(v,w);
	return P+v*t;
} 

//點到直線距離 使用叉積 即平行四邊形的面積除以底 
double DisToLine(Point P, Point A, Point B){
	Vector v1 = B - A, v2 = P - A;
	return fabs(Cross(v1,v2)) / Length(v1); //不取絕對值是有向距離 
} 

// 直線 
struct Line_v //vector form
{
	//P+t*v;  v長度無關 
	Point P;
	Vector v;
	Line_v(Point A,Point B)
	{
		v = B-A;
		P = A;
	}
};
struct Line_n //normal form
{
	//ax+by+c=0
	double a,b,c;
	Line_n(Point x,Point y)
	{
		a = y.y - x.y;
		b = x.x - y.x;
		c = x.x * y.x - x.x * y.y;
	}
};

double PolygonArea(Point *p, int n)//多邊形有向面積 支援非凸多邊形 
{
	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 main()
{
	return 0;
}