CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

Take a kernel with exact constructions (like 
CGAL::Exact_predicates_exact_constructions_kernel).

Construct you lines with this kernel.
compute the vector orthogonal to those two lines (using cross_product
on their director vectors)
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Kernel_23_ref/Function_cross_product.html

Assume the vector is not 0 and take any a point on Line_1
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Kernel_23_ref/Class_Line_3.html
and construct the plane containing this line and having the computed
vector as orthogonal vector.
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Kernel_23_ref/Class_Plane_3.html

Take two points on Line_2 and project then on the plane. Construct the
line passing through the projected points and intersect it with Line_1
to get the first point.
http://www.cgal.org/Manual/latest/doc_html/cgal_manual/Kernel_23_ref/Function_intersection.html
To get the second point construct the line containing the first point
with direction the computed vector. Intersect this line with Line_2 and
you will get the second point.

I agree that a closest_point method would be nice to have in CGAL.

Sebastien.

updog wrote:
>  I just find CGAL::squared_distance() would be useful. 
>
> However, is there a way to get the locations of the very pair of points
> achieving the minimal squared distance?
>
> --
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