UVa 10897 - Travelling Distance

题目：给你地球上两点的经度和纬度，计算球面最近距离。

分析：计算几何、大地坐标系。利用公式计算连点间距离，再转化成弧长即可。

d = r*sqrt(2-2*(cos(lat1)*cos(lat2)*cos(lon1-lon2)+sin(lat1)*sin(lat2))) （推导见11817）

弧长：s =2*asin(d/(2*r))*r

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

int main()
{
	double r = 6371.01;
	double p = acos(-1.0);
	
	int    n;
	char   ch;
	double a,b,c,A1,B1,A2,B2;
	while ( scanf("%d",&n) != EOF )
	while ( n -- ) {
		scanf("%lf%lf%lf %c",&a,&b,&c,&ch);
		A1 = a+b/60.0+c/3600.0;
		if ( ch == 'S' ) A1 *= -1;
		A1 *= p/180.0;
		
		scanf("%lf%lf%lf %c",&a,&b,&c,&ch);
		B1 = a+b/60.0+c/3600.0;
		if ( ch == 'W' ) B1 *= -1;
		B1 *= p/180.0;
		
		scanf("%lf%lf%lf %c",&a,&b,&c,&ch);
		A2 = a+b/60.0+c/3600.0;
		if ( ch == 'S' ) A2 *= -1;
		A2 *= p/180.0;
		
		scanf("%lf%lf%lf %c",&a,&b,&c,&ch);
		B2 = a+b/60.0+c/3600.0;
		if ( ch == 'W' ) B2 *= -1;
		B2 *= p/180.0;
		
		double d = r*sqrt(2-2*(cos(A1)*cos(A2)*cos(B1-B2)+sin(A1)*sin(A2)));
		printf("%.2lf\n",2*asin(d/(2*r))*r);
	}
	return 0;
}