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[houes <>]

Dear Efi,

Hello. I basically want to do the halfplane intersection either in 2D or 3D
(in 2D, I have a set of oriented lines, in 3D, I have a set of oriented
planes).

In 3D, I have used CGAL::halfspace_intersection_3() to do halfplane
intersections of a set of planes(all planes pass through the Origin and I
add a cap plane to get a closed polyhedra).

My problem can be also solved in 2D: I intersect each of my 3D planes with
one fixed plane Z=1, and I get a set of oriented 2D line, each of these line
define a halfplane. And the halfplanes intersection of these lines give the
result I want: a convex polyhedon.

The problem is no matter I do 2D or 3D, the polyhedron or polyhedra resulted
from halfplane intersection is not necessarily closed: unbounded either in
2D or 3D. Thus the CGAL::halfspace_intersection_3() will throw exception: no
intersection found. After some research, I found the Nef_polyhedron is the
solution: it deal with polyhegon that can be open. Therefore, I want to
convert my lines/planes to Nef_polyhegron::Line or Nef_polyhegron::Plane to
do the intersection, which is equivalently the halfplane intersectin.

The problem I found with Nef_polyhegron is that there is no documentation
that tell me how to use Real number type instead of integer. All my data is
stored in Epick and use double coordinates. Therefore, if would be great if
you can provide me with some clue on this so I can utilize Nef_polyhedron
either in 2D or 3D using the data from Epick. 

The solution provided by Adrien Lefieux works for me, but I have problem
converting data from Epick to Nef_polyhedron::Point or Nef_polyhedron::Line,
do you have a solution?

Thank you very much.

houes



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