●POJ 1269 Intersecting Lines

Posted 2020-10-20 *ZJ

题链：

http://poj.org/problem?id=1269

题解：

计算几何，直线交点

模板题，试了一下直线的向量参数方程求交点的方法。

（方法详见《算法竞赛入门经典——训练指南》P257）

代码：

#include<cstdio>
#include<cstring>
#include<iostream>
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 - (Point A,Point 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);}
double operator ^ (Vector A,Vector B){return A.x*B.y-A.y*B.x;}
double operator * (Vector A,Vector B){return A.x*B.x+A.y*B.y;}
int N;
bool Point_on_Line(Point P,Vector v,Point Q){
	return ((Q-P)^v)==0;
}
Point Line_Intersection(Point P,Vector v,Point Q,Vector w){
	static Vector u; static double t1;
	u=P-Q;
	t1=(w^u)/(v^w);
	return P+v*t1;
}
int main(){
	Vector v,w;
	Point P,_P,Q,_Q,D;
	scanf("%d",&N);
	printf("INTERSECTING LINES OUTPUT\n");
	while(N--){
		scanf("%lf%lf%lf%lf%lf%lf%lf%lf",&P.x,&P.y,&_P.x,&_P.y,&Q.x,&Q.y,&_Q.x,&_Q.y);
		v=_P-P;	w=_Q-Q;
		if((v^w)==0){//向量共线
			if(Point_on_Line(P,v,Q)) printf("LINE");
			else printf("NONE");
		}
		else{
			D=Line_Intersection(P,v,Q,w);
			printf("POINT %.2lf %.2lf",D.x,D.y);
		}
		printf("\n");
	}
	printf("END OF OUTPUT\n");
	return 0;
}