POJ 4741 Save Labman No.004

题目链接:Save Labman No.004

解题思路:给你两条直线，异面的空间直线，求直线间最短距离，并且求出最短距离的这两个点。下面是模板，先求出公垂线的法向量，在构造两个平面分别是两条直线各自跟公垂线的平面，会与另一条直线有交点，这两个交点就是所求的点。

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <cmath>using namespace std;const double EPS = 1e-9;
const int MAXN = 40;struct Point3  //空间点
{double x, y, z;Point3( double x=0, double y=0, double z=0 ): x(x), y(y), z(z) { }Point3( const Point3& a ){x = a.x;y = a.y;z = a.z;return;}void showP(){printf("%f %f %f \n", x, y, z);}Point3 operator+( Point3& rhs ){return Point3( x+rhs.x, y+rhs.y, z+rhs.z );}
};struct Line3   //空间直线
{Point3 a, b;Line3 (){}Line3 (Point3 x, Point3 y){a = x, b = y;}
};struct plane3   //空间平面
{Point3 a, b, c;plane3() {}plane3( Point3 a, Point3 b, Point3 c ):a(a), b(b), c(c) { }void showPlane(){a.showP();b.showP();c.showP();return;}
};double dcmp( double a )
{if ( fabs( a ) < EPS ) return 0;return a < 0 ? -1 : 1;
}//三维叉积
Point3 Cross3( Point3 u, Point3 v )
{Point3 ret;ret.x = u.y * v.z - v.y * u.z;ret.y = u.z * v.x - u.x * v.z;ret.z = u.x * v.y - u.y * v.x;return ret;
}//三维点积
double Dot3( Point3 u, Point3 v )
{return u.x * v.x + u.y * v.y + u.z * v.z;
}//矢量差
Point3 Subt( Point3 u, Point3 v )
{Point3 ret;ret.x = u.x - v.x;ret.y = u.y - v.y;ret.z = u.z - v.z;return ret;
}//两点距离
double TwoPointDistance( Point3 p1, Point3 p2 )
{return sqrt( (p1.x - p2.x)*(p1.x - p2.x) + (p1.y - p2.y)*(p1.y - p2.y) + (p1.z - p2.z)*(p1.z - p2.z) );
}//向量的模
double VectorLenth( Point3 p )
{return sqrt( p.x*p.x + p.y*p.y + p.z*p.z );
}//空间直线距离
double LineToLine( Line3 u, Line3 v, Point3& tmp )
{tmp = Cross3( Subt( u.a, u.b ), Subt( v.a, v.b ) );return fabs( Dot3( Subt(u.a, v.a), tmp ) ) / VectorLenth(tmp);
}//取平面法向量
Point3 pvec( plane3 s )
{return Cross3( Subt( s.a, s.b ), Subt( s.b, s.c ) );
}//空间平面与直线的交点
Point3 Intersection( Line3 l, plane3 s )
{Point3 ret = pvec(s);double t = ( ret.x*(s.a.x-l.a.x)+ret.y*(s.a.y-l.a.y)+ret.z*(s.a.z-l.a.z) )/( ret.x*(l.b.x-l.a.x)+ret.y*(l.b.y-l.a.y)+ret.z*(l.b.z-l.a.z) );ret.x = l.a.x + ( l.b.x - l.a.x ) * t;ret.y = l.a.y + ( l.b.y - l.a.y ) * t;ret.z = l.a.z + ( l.b.z - l.a.z ) * t;return ret;
}int main(){int t;Point3 a, b, c, d, tem;Point3 u, v, n;plane3 o, p;scanf("%d", &t);while(t--){scanf("%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf%lf", &a.x, &a.y, &a.z, &b.x, &b.y, &b.z, &c.x, &c.y, &c.z, &d.x, &d.y, &d.z);double dis = LineToLine(Line3(a, b), Line3(c, d), tem);printf("%lf\n", dis);u = Subt(a, b), v = Subt(c, d);n = Cross3(u, v);o = plane3(a, b, Point3(a.x + n.x, a.y + n.y, a.z + n.z));p = plane3(c, d, Point3(c.x + n.x, c.y + n.y, c.z + n.z));u = Intersection(Line3(a, b), p);v = Intersection(Line3(c, d), o);printf("%.6lf %.6lf %.6lf %.6lf %.6lf %.6lf\n", u.x, u.y, u.z, v.x, v.y, v.z);}return 0;
}

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