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["Vu, Khuong" <>]

That's nice :).

Khuong
________________________________________
From: clemen 
[]
Sent: Monday, June 14, 2010 8:23 AM
To: 

Subject: Re: AW: [cgal-discuss] shortest line between two lines in 3d

Ok, thanks again. it turned out that khuong's way is pretty straightforward
to implement in cgal:

// get plane p1 that contains l1 and is parallel to l2
Plane_3 p1( l1, l1.point(0) + l2.to_vector() );

// get plane p2 that contains l1 and is perpendicular to p1
Plane_3 p2( l1, l1.point(0) + p1.orthogonal_vector() );

// get intersection i1 between p2 and l2
Point_3 i1;
CGAL::Object result = CGAL::intersection( p2, l2 );
if( !assign( i1, result ) ) {
        Line_3 il;
        if( assign( il, result ) )
                std::cout << "intersection between plane and line is a line 
--> l1 and l2
are parallel!" << std::endl;
        return -1.0;
}

// get intersection i2 on l1
Point_3 i2 = l1.projection( i1 );

// final point is (i1+i2)/2
Point_3 f((i1.x() + i2.x()) / 2.0, (i1.y() + i2.y()) / 2.0, (i1.z() +
i2.z()) / 2.0);

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