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[Bear <>]

Hi Sebastien,

 

Thanks. But I do not know how to cut cube with a plane and/or several planes into several cells. It seems the linear_cell_complex does not have those functions.

 

Best

 

From: Sebastien Loriot (GeometryFactory) [via cgal-discuss] [mailto:ml-node+[hidden email]]
Sent: Friday, August 28, 2015 7:33 AM
To: Xiong, B (ITC) <[hidden email]>
Subject: Re: 3D Arrangement of planes using Nef Polyhedra

 

On 08/25/2015 08:42 PM, Bear wrote:

> Hello,
>
> I want to have 3D arrangement of planes using Nef_Polyhedron_3. For example,
> I want to cross one plane with one 3D cubic, then the cubic will be
> partitioned into two volumes, and all volumes can be visited. One possible
> way is intersection the cubic Nef_Polyhedron with the plane. See following
> example. I have tried all three Intersection_mode, CLOSED_HALFSPACE,
> OPEN_HALFSPACE, PLANE_ONLY. However, the intersection results are all the
> same, the same one with the input cubic Nef_polyhedron.
>

I don't think it's possible to do what you want.
 From here:
http://doc.cgal.org/latest/Nef_3/classCGAL_1_1Nef__polyhedron__3.html

"A 3D Nef polyhedron is a subset of the 3-dimensional space that is the
result of forming complements and intersections starting from a finite
set H of 3-dimensional halfspaces."

In you case you are looking for a decomposition of the 3D space. Maybe
you should have a look at the linear complex to see whether it can fit
you needs (in particular you won't be able to have infinite cells):
http://doc.cgal.org/latest/Linear_cell_complex/index.html

Sebastien.

> Another option is to construct half plane Nef_Polyhedron to do intersection.
> However, the three Boolean operation, intersection, difference, and union,
> can only result in one volume.
>
> See attachments for codes. Please help me to do 3D arrangement of planes.
> Maybe there is some other ways to do that. Or I need to add more Boolean
> operations to Nef_Polyhedron. If so, please give me some suggestions to how
> to improve codes.
>
> Thanks in advance.
> test_nef_intersection_nef.cpp
> <http://cgal-discuss.949826.n4.nabble.com/file/n4661101/test_nef_intersection_nef.cpp>
>
> test_nef_intersection_plane.cpp
> <http://cgal-discuss.949826.n4.nabble.com/file/n4661101/test_nef_intersection_plane.cpp>
>
>
>
>
> --
> View this message in context: http://cgal-discuss.949826.n4.nabble.com/3D-Arrangement-of-planes-using-Nef-Polyhedra-tp4661103.html
> Sent from the cgal-discuss mailing list archive at Nabble.com.
>

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