CGAL users discussion list

[Marc Alexa <>]

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.

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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