hdu 4741 Save Labman No.004（2013杭州网络赛）

http://blog.sina.com.cn/s/blog_a401a1ea0101ij9z.html

 空间两直线上最近点对。

这个博客上给出了很好的点法式公式了。。。其实没有那么多的tricky。。。不知到别人怎么错的。。。

 

//#pragma comment(linker, "/STACK:1024000000,1024000000")

#include<algorithm>

#include<iostream>

#include<cstring>

#include<fstream>

#include<sstream>

#include<vector>

#include<string>

#include<cstdio>

#include<bitset>

#include<queue>

#include<stack>

#include<cmath>

#include<map>

#include<set>

#define FF(i, a, b) for(int i=a; i<b; i++)

#define FD(i, a, b) for(int i=a; i>=b; i--)

#define REP(i, n) for(int i=0; i<n; i++)

#define CLR(a, b) memset(a, b, sizeof(a))

#define debug puts("**debug**")

#define LL long long

#define PB push_back

#define MP make_pair

#define eps 1e-10

using namespace std;



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 - (Vector a, Vector 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); }



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)); }

Vector Cross(Point a, Point b)

{

    return Vector(a.y*b.z-a.z*b.y, a.z*b.x-a.x*b.z, a.x*b.y-a.y*b.x);

}



Point a1, b1, a2, b2;

int main()

{

    int n;

    scanf("%d", &n);

    while(n--)

    {

        scanf("%lf%lf%lf", &a1.x, &a1.y, &a1.z);

        scanf("%lf%lf%lf", &b1.x, &b1.y, &b1.z);

        scanf("%lf%lf%lf", &a2.x, &a2.y, &a2.z);

        scanf("%lf%lf%lf", &b2.x, &b2.y, &b2.z);

        Vector v1 = (a1-b1), v2 = (a2-b2);

        Vector N = Cross(v1, v2);

        Vector ab = (a1-a2);

        double ans = Dot(N, ab) / Length(N);

        Point p1 = a1, p2 = a2;

        Vector d1 = b1-a1, d2 = b2-a2;

        Point ans1, ans2;

        double t1, t2;

        t1 = Dot((Cross(p2-p1, d2)), Cross(d1, d2));

        t2 = Dot((Cross(p2-p1, d1)), Cross(d1, d2));

        double dd = Length((Cross(d1, d2)));

        t1 /= dd*dd;

        t2 /= dd*dd;

        ans1 = (a1 + (b1-a1)*t1);

        ans2 = (a2 + (b2-a2)*t2);

        printf("%.6f\n", fabs(ans));

        printf("%.6f %.6f %.6f ", ans1.x, ans1.y, ans1.z);

        printf("%.6f %.6f %.6f\n", ans2.x, ans2.y, ans2.z);

    }

    return 0;

}