CGAL users discussion list

[Bernd Gaertner <>]

You can also use the Quadratic programming solver whenever you need to 
compute the minimum squared distance between two objects, each of which 
can be described by linear equations and inequalities (lines, segments, 
boxes, points,...):

http://www.cgal.org/Manual/latest/doc_html/cgal_manual/QP_solver/Chapter_main.html


Best,
Bernd.



Sebastien Loriot (GeometryFactory) wrote:
> 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?
> >
> > --
> > View this message in context: 
> > http://cgal-discuss.949826.n4.nabble.com/how-to-find-closest-point-on-a-segment-rectangle-to-a-given-point-tp3618761p3618911.html 
> >
> > Sent from the cgal-discuss mailing list archive at Nabble.com.