1. 程式人生 > 實用技巧 >判斷平面上是否有一點與所有點相交

判斷平面上是否有一點與所有點相交

poj 3304

#include<iostream>
#include<algorithm>
#include<cmath> 
#include<cstdio>
using namespace std;
#define ll long long
const int N = 200+10;
const int maxp = 1010;
const double eps = 1e-8;//精度
const double inf = 1e20;
const double pi = acos(-1.0);
int sgn(double x)
{
	if(fabs(x) < eps)
		return 0;
	if(x < 0)
		return -1;
	else
		return 1;
}
struct Point{
	double x,y;
	Point(){}
	Point(double _x,double _y)
	{
		x = _x;
		y = _y;
	}
	void input()
	{
		scanf("%lf%lf",&x,&y);
	}
	void output()
	{
		printf("%.2f,%.2f\n",x,y);
	}
	bool operator == (Point b)const{
		return sgn(x-b.x) == 0 && sgn(y-b.y) == 0;
	}
	bool operator < (Point b)const{
		return sgn(x-b.x)== 0?sgn(y-b.y)<0:x<b.x;
	}
	Point operator -(const Point &b)const{
		return Point(x-b.x,y-b.y);
	}
	//叉積
	double operator ^(const Point &b)const{
		return x*b.y - y*b.x;
	}
	//點積
	double operator *(const Point &b)const{
		return x*b.x + y*b.y;
	}
	//返回長度
	double len(){
		return hypot(x,y);//庫函式
	}
	//返回長度的平方
	double len2(){
		return x*x + y*y;
	}
	//返回兩點的距離
	double distance(Point p){
		return hypot(x-p.x,y-p.y);
	}
	Point operator +(const Point &b)const{
		return Point(x+b.x,y+b.y);
	}
	Point operator *(const double &k)const{
		return Point(x*k,y*k);
	}
	Point operator /(const double &k)const{
		return Point(x/k,y/k);
	}
	//`計算pa  和  pb 的夾角`
	//`就是求這個點看a,b 所成的夾角`
	//`測試 LightOJ1203`
	double rad(Point a,Point b){
		Point p = *this;
		return fabs(atan2( fabs((a-p)^(b-p)),(a-p)*(b-p) ));
	}
	//`化為長度為r的向量`
	Point trunc(double r){
		double l = len();
		if(!sgn(l))return *this;
		r /= l;
		return Point(x*r,y*r);
	}
	//`逆時針旋轉90度`
	Point rotleft(){
		return Point(-y,x);
	}
	//`順時針旋轉90度`
	Point rotright(){
		return Point(y,-x);
	}
	//`繞著p點逆時針旋轉angle`
	Point rotate(Point p,double angle){
		Point v = (*this) - p;
		double c = cos(angle), s = sin(angle);
		return Point(p.x + v.x*c - v.y*s,p.y + v.x*s + v.y*c);
	}
};

struct Line{
	Point s,e;
	Line(){}
	Line(Point _s,Point _e){
		s = _s;
		e = _e;
	}
	bool operator ==(Line v){
		return (s == v.s)&&(e == v.e);
	}
	//`根據一個點和傾斜角angle確定直線,0<=angle<pi`
	Line(Point p,double angle){
		s = p;
		if(sgn(angle-pi/2) == 0){
			e = (s + Point(0,1));
		}
		else{
			e = (s + Point(1,tan(angle)));
		}
	}
	//ax+by+c=0
	Line(double a,double b,double c){
		if(sgn(a) == 0){
			s = Point(0,-c/b);
			e = Point(1,-c/b);
		}
		else if(sgn(b) == 0){
			s = Point(-c/a,0);
			e = Point(-c/a,1);
		}
		else{
			s = Point(0,-c/b);
			e = Point(1,(-c-a)/b);
		}
	}
	void input(){
		s.input();
		e.input();
	}
	void adjust(){
		if(e < s)swap(s,e);
	}
	//求線段長度
	double length(){
		return s.distance(e);
	}
	//`返回直線傾斜角 0<=angle<pi`
	double angle(){
		double k = atan2(e.y-s.y,e.x-s.x);
		if(sgn(k) < 0)k += pi;
		if(sgn(k-pi) == 0)k -= pi;
		return k;
	}
	//`點和直線關係`
	//`1  在左側`
	//`2  在右側`
	//`3  在直線上`
	int relation(Point p){
		int c = sgn((p-s)^(e-s));
		if(c < 0)return 1;
		else if(c > 0)return 2;
		else return 3;
	}
	// 點線上段上的判斷
	bool pointonseg(Point p){
		return sgn((p-s)^(e-s)) == 0 && sgn((p-s)*(p-e)) <= 0;
	}
	//`兩向量平行(對應直線平行或重合)`
	bool parallel(Line v){
		return sgn((e-s)^(v.e-v.s)) == 0;
	}
	//`兩線段相交判斷`
	//`2 規範相交`
	//`1 非規範相交`
	//`0 不相交`
	int segcrossseg(Line v){
		int d1 = sgn((e-s)^(v.s-s));
		int d2 = sgn((e-s)^(v.e-s));
		int d3 = sgn((v.e-v.s)^(s-v.s));
		int d4 = sgn((v.e-v.s)^(e-v.s));
		if( (d1^d2)==-2 && (d3^d4)==-2 )return 2;
		return (d1==0 && sgn((v.s-s)*(v.s-e))<=0) ||
			(d2==0 && sgn((v.e-s)*(v.e-e))<=0) ||
			(d3==0 && sgn((s-v.s)*(s-v.e))<=0) ||
			(d4==0 && sgn((e-v.s)*(e-v.e))<=0);
	}
	//`直線和線段相交判斷`
	//`-*this line   -v seg`
	//`2 規範相交`
	//`1 非規範相交`
	//`0 不相交`
	int linecrossseg(Line v){
		int d1 = sgn((e-s)^(v.s-s));
		int d2 = sgn((e-s)^(v.e-s));
		if((d1^d2)==-2) return 2;
		return (d1==0||d2==0);
	}
	//`兩直線關係`
	//`0 平行`
	//`1 重合`
	//`2 相交`
	int linecrossline(Line v){
		if((*this).parallel(v))
			return v.relation(s)==3;
		return 2;
	}
	//`求兩直線的交點`
	//`要保證兩直線不平行或重合`
	Point crosspoint(Line v){
		double a1 = (v.e-v.s)^(s-v.s);
		double a2 = (v.e-v.s)^(e-v.s);
		return Point((s.x*a2-e.x*a1)/(a2-a1),(s.y*a2-e.y*a1)/(a2-a1));
	}
	//點到直線的距離
	double dispointtoline(Point p){
		return fabs((p-s)^(e-s))/length();
	}
	//點到線段的距離
	double dispointtoseg(Point p){
		if(sgn((p-s)*(e-s))<0 || sgn((p-e)*(s-e))<0)
			return min(p.distance(s),p.distance(e));
		return dispointtoline(p);
	}
	//`返回線段到線段的距離`
	//`前提是兩線段不相交,相交距離就是0了`
	double dissegtoseg(Line v){
		return min(min(dispointtoseg(v.s),dispointtoseg(v.e)),min(v.dispointtoseg(s),v.dispointtoseg(e)));
	}
	//`返回點p在直線上的投影`
	Point lineprog(Point p){
		return s + ( ((e-s)*((e-s)*(p-s)))/((e-s).len2()) );
	}
	//`返回點p關於直線的對稱點`
	Point symmetrypoint(Point p){
		Point q = lineprog(p);
		return Point(2*q.x-p.x,2*q.y-p.y);
	}
};
Line line[1005];
int n;
int check(Point s,Point e)
{
	Line l1 = Line(s,e);
	if(sgn(l1.length()) == 0)
		return 0;
	for(int i=1;i<=n;i++)
	{	

		if(l1.linecrossseg(line[i]) == 0)
		{
			return 0; 
		}
	}
	return 1;
}
void solve()
{
	
	cin >> n;
	for(int i=1;i<=n;i++)
	{
		line[i].input();
	}
	int flag = 0;
	for(int i=1;i<=n;i++)
	{		
		if(flag == 1)
			break;
		for(int j=1;j<=n;j++)
		{
			if(check(line[i].s,line[j].s) || check(line[i].s,line[j].e) || 
			check(line[i].e,line[j].s) || check(line[i].e,line[j].e))
			{
				flag = 1;
				break;
			}
		}

	}
	if(flag)
	{
		puts("Yes!");
	}
	else
	{
		puts("No!");
	}
}
int main()
{
	int T;
	scanf("%d",&T);
	while(T--)
	{
		solve();
	}
    return 0;
}