Scrambled Polygon(poj2007极角排序输出凸包)

最新推荐文章于 2022-06-28 21:34:51 发布

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本文介绍了一种基于极角排序的凸包算法实现方法，通过向量叉乘判断点的位置，并详细展示了如何使用C++实现该算法，包括点的定义、向量运算、排序等关键步骤。

题意：给你一些点，让你按照极角的顺序输出凸包的顶点

思路：直接按照向量排序

按照向量叉乘的正负判断点所在的位置，类似于卷包裹的凸包，每次按照一条边排序，选择最外面的一条边，再按照选择的边在排序，再选直到点重合位置

这道题直接按照(0,0)点极角排序，如果极角相同选择最近的那个因为在一条直线上先选近的再选远的，如果选择远的那点的顺序都不对了

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<vector>
#include<algorithm>
using namespace std;

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) ;}
const double eps = 1e-9;
const double PI = acos(-1.0);
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 Cross(Vector a,Vector b) { return a.x*b.y - a.y*b.x ;}
int dcmp(double x)
{
	if(fabs(x) < eps) return 0;
	else return x < 0 ? -1 : 1;
}
bool operator < (Point a,Point b) { return a.x < b.x || (a.x == b.x && a.y < b.y) ;}
bool operator == ( Point a, Point b) { return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0 ;}
double Angle(Vector a,Vector b) { return acos( Dot(a,b) / Length(a) / Length(b) ) ;}
double Area(Point a,Point b,Point c) { return fabs(Cross(b-a,c-a))/2 ;}
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);
}

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;
}

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(c3) < 0;
}

bool OnSengment(Point p,Point a,Point b)
{
	return dcmp(Cross(p-a,b-a)) == 0 && dcmp(Dot(a-p,b-p) < 0);
}


double PolyArea(Point *p,int n)
{
	double area = 0;
	int i;
	for(i = 0; i < n; i++)
	{
		area += Cross(p[i]-p[0],p[i+1]-p[0]);
	}
	return area/2;
}
struct Line
{
	Point s,e;
};

int ConvexHull(Point* p,int n,Point* ch)
{
    sort(p,p+n);
    int m = 0;
    for(int i = 0; i < n; i++)
    {
        while( m > 1 && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]) <= 0) m--;
        ch[m++] = p[i];
    }

    int k = m;
    for(int i = n-2 ; i >= 0; i--)
    {
        while(m > k && Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2]) <= 0) m--;
        ch[m++] = p[i];
    }
    if(n > 1) m--;
    return m;
}

Point p[1005];
bool cmp(Point a,Point b)
{
    double temp = Cross(a-p[0],b-p[0]);
    if(dcmp(temp) > 0) return true;
    else if(dcmp(temp) == 0 && dcmp( Length(a-p[0]) - Length(b-p[0]) ) <= 0) return true;
    else return false;
}

int main()
{
    int n = 0;
    while(scanf("%lf%lf",&p[n].x,&p[n].y) != EOF) n++;
    sort(p,p+n,cmp);
    for(int i = 0; i < n; i++)
    {
        printf("(%.0lf,%.0lf)\n",p[i].x,p[i].y);
    }
    return 0;
}