CGAL users discussion list

[Phil Weir <>]

A very late follow on, but just wanted to ping the list to express 
thanks for Laurent's input on 3D meshing in discussion at the FEniCS 
workshop last year (Paris). For a number of reasons, we have only just 
finished incorporating his suggestion today, but have noticed a 
significant improvement.

In summary: as part of the Go-Smart EU-FP7 project, we are doing 
polyhedral meshing prior to Elmer simulation - this may be relevant to a 
couple of earlier posts this week, e.g. 'Best approach to create 
Mesh_Domain_3 from multiple Polyhedral_3' and 3D-mesh creation 
(Mesh_complex_3_in_triangulation_3) from *multiple* polyhedral surface 
meshes...'. It sounds like Jane's suggestion has covered the use-case 
there, but if intersection is required, such as in our case, I think 
Polyhedral_mesh_domain_3 would need some wrapping, at least (if I 
understand the documentation and remember previous experience correctly?).

Originally, we loaded STLs as Polyhedra, converted to Nef Polyhedra and 
performed a series of Boolean operations, before converting back to a 
domain Polyhedron and meshing. However, this was very slow and the 
polyhedra requirements are quite restrictive, especially for converting 
a Nef Polyhedron to the final domain polyhedron. Instead, we switched to 
a Labeled_mesh_domain_3, using Point_in_polyhedron calls - this was much 
faster, flexible and more robust, providing subdomain labelling (for MSH 
output), effectively free.

However, labelling output boundaries by the original STL was harder - 
Laurent's tip to re-use surface patches, which are actually filled by 
the domain oracle (as I hadn't spotted!), made it far more efficient. We 
combine this with a subclass (Signed_mesh_domain_3) that simply 
overrides the Is_in_domain struct, allowing the labelling function to 
return negative indices for external points. Negative return values are 
preserved in the surface patch for future reference (at MSH output 
time). The simulation component of this project is being open sourced 
(including the CGAL-based meshing tool), although the tools are being 
finished, tidied and documented over the course of this year (and are 
still based on CGAL-4.3/4) - nonetheless, I hope this provides some 
useful feedback for the moment.

Comments welcome.

Best wishes,

Phil Weir

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Phil Weir | NUMA Engineering Services Ltd.
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