Polar angle sorting

Polar angle

The so-called polar angle refers to the angle that takes the positive half axis of the x axis as the starting edge, establishes polar coordinates and turns counter-clockwise. The range of this angle is [0,2pi].

purpose

1. Computing convex hull

Links:

2, some strange path questions.

You can only turn left and right to find the nearest inflection point by sorting the polar corners.
For example: POJ 1696

Code

Calculating Polar Angle with Cross Product (High Accuracy, Slow Time)

struct point{
    double x,y;
    point(double x=0, double y=0):x(x), y(y){}
    point operator - (const point &t)const{
        return point(x-t.x, y-t.y);
    }//a - b
    double operator *(const point &t)const{
        return x*t.x + y*t.y;
    }//a * b
    double operator ^(const point &t)const{
        return x*t.y - y*t.x;
    }//a X b
};
double compare(point a,point b,point c)//Calculation of polar angle ab * ac 
{
    return (b-a)^(c-a);
}
bool cmp(point a,point b)
{
	double f=compare(p[pos],a,b);
	if(f==0) return a.x-p[pos].x<b.x-p[pos].x;
	else if(f>0) return true;
	else return false;
}

If the selected point is not the point of the corner, it needs to be sorted according to the quadrant first.

int Quadrant(point a)//Quadrant sorting, note that there are four coordinate axes
{
    if(a.x>0&&a.y>=0)  return 1;
    if(a.x<=0&&a.y>0)  return 2;
    if(a.x<0&&a.y<=0)  return 3;
    if(a.x>=0&&a.y<0)  return 4;
}


bool cmp2(point a,point b)//First quadrant and then polar angle
{
    if(Quadrant(a)==Quadrant(b))//The return value is the quadrant
        return cmp(a,b);
    else Quadrant(a)<Quadrant(b);
}

atan2 function (fast time, poor accuracy)

atan2(y,x) denotes that the point (x,y) is connected to the point. The angle between the line and the positive half-axis of the x-axis is [pi, pi]. The range of the polar angle here is [pi, pi]. The one-two quadrants are positive and the three-four quadrants are negative. So when we have finished ordering from small to large, it is actually the third quadrant < the fourth quadrant < the first quadrant < the second quadrant.

struct point{
	double x,y;
	double angle;
	bool operator <(const point &t)
	{
		return angle<t.angle;
	}
}p[N];
bool cmp(point a,point b)
{
	if(a.angle==b.angle) return a.x<b.x;
	else
	{
		return a.angle<b.angle;
	}
}
for(int i=1;i<=n;i++)
{
	cin>>p[i].x>>p[i].y;
	p[i].angle=atan2(p[i].y,p[i].x);
}
sort(a+1,a+1+n,cmp);