计算几何——判断点是否在线段上

 汇总篇：计算几何汇总

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先判断是否在直线L上，然后在判断其坐标是否在线段范围内

class point{
 	public:
	double x;
	double y;
	point(double x_=0,double y_=0):x(x_),y(y_){} 
	friend const point operator+(const point& p1,const point& p2){
		return point(p1.x+p2.x,p1.y+p2.y);
	};
	friend const point operator-(const point& p1,const point& p2){
		return point(p1.x-p2.x,p1.y-p2.y);
	};
	friend const point operator*(const point& p,const double& m){
		return point(p.x*m,p.y*m);
	};
	friend const point operator*(const double& m,const point& p){
		return point(p.x*m,p.y*m);
	};
	friend const point operator/(const point& p,const double& m){
		return point(p.x/m,p.y/m);
	};
	friend ostream& operator <<(ostream& out,point& a){
		printf("(%lf,%lf)",a.x,a.y);
		return out;
	};
};
typedef point vect2;//重命名，向量也是用坐标表示 

class line{
	public:
	point start;
	point end; 
	line(point s=point(0,0),point e=point(0,0)):start(s),end(e){}
};

double cross(point O,point A,point B){//叉乘 
	double oa_x=A.x-O.x;
	double oa_y=A.y-O.y;
	double ob_x=B.x-O.x;
	double ob_y=B.y-O.y;
	return oa_x*ob_y-oa_y*ob_x;
}
bool pointIsOnLine(point O,line L){
	point S=L.start;
	point E=L.end;
	if(cross(O,S,E)==0//在直线L上 
	and min(S.x,E.x)<=O.x&&O.x<=max(S.x,E.x)
	and min(S.y,E.y)<=O.y&&O.y<=max(S.y,E.y))
		return true;
	else return false; 
}