UVA 11817 Tunnelling the Earth

最新推荐文章于 2020-11-16 19:05:59 发布

lfj200411

最新推荐文章于 2020-11-16 19:05:59 发布

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分类专栏：三维计算几何

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本文介绍了一种计算两点间沿地球表面行走与直线穿越地球内部距离之差的方法。使用C++编程实现，通过经纬度坐标转换为三维坐标，进而计算两点间球面距离及直线距离，并给出具体代码实例。

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题意：

给起点经纬度和终点经纬度

求沿地球表面走和钻隧道走直线的距离差

#include <vector>
#include <cstdio>
#include <algorithm>
#include <cmath>
using namespace std;
const double eps=1e-10;//精度
const int INF=1<<29;
const double PI=acos(-1);
int dcmp(double x){//判断double等于0或。。。
	if(fabs(x)<eps)return 0;else return x<0?-1:1;
}
struct Point{
	double x,y,z;
	Point(double x=0,double y=0,double z=0):x(x),y(y),z(z){}
};
typedef Point Vector;
Vector operator+(Vector a,Vector b){return Vector(a.x+b.x,a.y+b.y,a.z+b.z);}
Vector operator-(Point a,Point b){return Vector(a.x-b.x,a.y-b.y,a.z-b.z);}
Vector operator*(Vector a,double p){return Vector(a.x*p,a.y*p,a.z*p);}
Vector operator/(Vector a,double p){return Vector(a.x/p,a.y/p,a.z/p);}
bool operator==(Point a,Point b){return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0&&dcmp(a.z-b.z)==0;}
double Dot(Vector a,Vector b){return a.x*b.x+a.y*b.y+a.z*b.z;}
double Length(Vector a){return sqrt(Dot(a,a));}
double Angle(Vector a,Vector b){return acos(Dot(a,b)/Length(a)/Length(b));}
double torad(double deg){return deg/180*PI;}
void getcoord(double R,double lat ,double lng,double& x,double& y,double& z){
	lat=torad(lat);lng=torad(lng);
	x=R*cos(lat)*cos(lng);
	y=R*cos(lat)*sin(lng);
	z=R*sin(lat);
}

const double r=6371009;
int main(){
	int T;
	scanf("%d",&T);
	while(T--){
		double lata,lnga,latb,lngb;
		scanf("%lf%lf%lf%lf",&lata,&lnga,&latb,&lngb);
		Point a,b;
		getcoord(r,lata,lnga,a.x,a.y,a.z);
		getcoord(r,latb,lngb,b.x,b.y,b.z);
		double dis=Length(a-b)/2;
		double angle=asin(dis/r);
		double ans=r*angle-dis;
		printf("%.0lf\n",ans*2);
	}
	return 0;
}