空间异面直线的距离直接套模板。
求交点：求出两条直线的公共法向量，其中一条直线与法向量构成的平面 与 另一条直线 的交点即可。还是套模板o(╯□╰)o
1.不会有两条线平行的情况。
2.两条直线可能相交
#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;};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;}/************以上模板*************/void solved( Line3 A, Line3 B ){Point3 normal;double dis = LineToLine( A, B, normal );printf( "%.6f\n", dis );plane3 pla;pla = plane3( A.a, A.b, A.a + normal );Point3 u = Intersection( B, pla );pla = plane3( B.a, B.b, B.a + normal );Point3 v = Intersection( A, pla );printf("%.6f %.6f %.6f %.6f %.6f %.6f\n", v.x, v.y, v.z, u.x, u.y, u.z );return;}int main(){int T;scanf( "%d", &T );while ( T-- ){Line3 A, B;scanf("%lf%lf%lf", &A.a.x, &A.a.y, &A.a.z );scanf("%lf%lf%lf", &A.b.x, &A.b.y, &A.b.z );scanf("%lf%lf%lf", &B.a.x, &B.a.y, &B.a.z );scanf("%lf%lf%lf", &B.b.x, &B.b.y, &B.b.z );solved( A, B );}return 0;}
