CGAL users discussion list

["Sebastien Loriot (GeometryFactory)" <>]

On 2/28/20 10:34 AM, Marc Alexa wrote:
> Dear Sebastien,
>
> your last paragraph sounds like you had code for triangulating planar 3D 
> polygons. If you have a constrained Delaunay triangulation for planar 
> polygons in 3D avoiding the projection into the plane I think this would be 
> very useful addition to CGAL. And I would be interested in the code in any 
> case.


That's indeed the case and when I find time I will integrate it into
CGAL. But for now the code is not clean enough to be publicly
distributed and I want to know with who I'm sharing it.

Best,

Sebastien.

> Best,
> Marc
>
>
>
>
>
> > On 26. Feb 2020, at 13:31, Sebastien Loriot (GeometryFactory) 
> > <>
> >  wrote:
> >
> > In such a case the best way to proceed is to identify the set of faces
> > that defines an almost coplanar patch of faces and retriangulate it
> > directly.
> >
> > You can achieve this by first find a plane for the fitting of the
> > patch boundary [1], then project the patch boundary points in 2D [2]
> > while keeping the relationship with the input vertices [3]. Then You can
> > triangulate that polygon [4], remove the patch faces [5] from the mesh
> > and refit the new one extracted from the 2D triangulation [6].
> >
> > For the projection step you should use a kernel with exact
> > constructions such as CGAL::Exact_predicates_inexact_constructions_kernel. 
> > More precisely,
> > the Plane_3 should be from that Kernel and input points provided to
> > the to_2d() member function can be converted on the fly using
> > Cartesian_converter [7].
> >
> > I have a more complicated version of that code that does not use any explicit 
> > projection but it is not yet ready to be publicly distributed.
> > If you contact me in private and can share your affiliation and some
> > details of your usage scenario, we'll see how we can get you a copy.
> >
> > Best regards,
> >
> > Sebastien.
> >
> > [1] 
> > https://doc.cgal.org/latest/Principal_component_analysis/index.html#Chapter_Principal_Component_Analysis
> > [2] 
> > https://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Plane__3.html#a24c55e9e8c0250c70f377cba0d66f330
> > [3] 
> > https://doc.cgal.org/latest/Triangulation_2/Triangulation_2_2info_insert_with_pair_iterator_2_8cpp-example.html
> > [4] 
> > https://doc.cgal.org/latest/Triangulation_2/Triangulation_2_2polygon_triangulation_8cpp-example.html
> > [5] 
> > https://doc.cgal.org/latest/BGL/group__PkgBGLEulerOperations.html#gacfae7ff8e782da55b941e4487e86c738
> > [6] 
> > https://doc.cgal.org/latest/BGL/group__PkgBGLEulerOperations.html#gaa386d0cdef3b5d6ef43d6b503392dbcd
> > [7] 
> > https://doc.cgal.org/latest/Kernel_23/classCGAL_1_1Cartesian__converter.html
> >
> > On 2/24/20 8:03 PM, one_eyed_cat wrote:
> > > Hello everyone,
> > > I would like to reduce a model's complexity as much as possible by merging
> > > adjacent, (nearly for an ε) coplanar faces. The model's surfaces can be
> > > closed or contain holes. Currently. I am using a Polyhedron with plane
> > > equations (like here
> > > https://doc.cgal.org/latest/Polyhedron/Polyhedron_2polyhedron_prog_planes_8cpp-example.html
> > > <https://doc.cgal.org/latest/Polyhedron/Polyhedron_2polyhedron_prog_planes_8cpp-example.html>
> > > ), iteratively iterating the halfedges and calling `join_facet`when needed
> > > until there's nothing left to merge. However, I encounter problems like
> > > antennas for more than one overlapping edge for adjacent facets or
> > > overlapping edges in the same facet, ending up trying to merge with itself
> > > in the merging process which makes me doubt my approach (examples appened).
> > > I get the feeling I would have to consider a lot of factors and edge cases
> > > if I am staying with `join_facet`. So I wonder if Polyhedron is really the
> > > right class to use regarding the joining of any faces and not having exactly
> > > coplanar surfaces.
> > > If you could help a newcomer out with your experience, that would make my
> > > day :)
> > > Best regards
> > > <http://cgal-discuss.949826.n4.nabble.com/file/t376194/resulting_antenna.jpg>
> > > <http://cgal-discuss.949826.n4.nabble.com/file/t376194/overlapping.png>
> > > --
> > > Sent from: http://cgal-discuss.949826.n4.nabble.com/
> >
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