CGAL users discussion list

[Bruno Rammon <>]

Hello, 

For my dissertation, I have a problem that I need to compute intersections
between two meshes. I have already successfully computed the intersections
regions between meshes using CGAL features, specifically those to create
Constrained Delaunay Triangulations. Until here everything seems ok. 
But after the computation of intersections, it's still necessary to create a
map that relates each intersection with two elements finite (one from each
mesh). This last procedure, which does not lead directly with CGAL, is
making the most of the time. I would like to know if exists some way to do
that with CGAL. Also, I accept any suggestions to improve the efficiency of
my code.

My code is  here
<http://cgal-discuss.949826.n4.nabble.com/file/t376297/intersection.cpp>  .
Unfortunately, it's not possible to run it. I divided it into three basic
sections: the first one creates a 2D Arrangement from the element finite
edges of two different meshes of the same problem provided, let's say, by
the user. The second section creates the Constrained Delaunay Triangulations
(CDT) from the 2D Arrangement previously created. In the last section, for
each facet of the CDT is searched the finite element associated with this
facet (in the two meshes) verifying if the central point of the facet relies
on the finite element. This last section is the slowest one because of the
several calls to the function "pointLiesInsideElement". I am wondering if
it's not possible to make this search procedure with some of the CGAL
features or use some information provided by CGAL objects to help this
procedure be more efficient. Others suggestions are also welcome.

Example of intersection computation:
Finite element mesh 1:
<http://cgal-discuss.949826.n4.nabble.com/file/t376297/Screenshot_from_2021-05-18_09-55-32.png>
 
Finite element mesh 2:
<http://cgal-discuss.949826.n4.nabble.com/file/t376297/Screenshot_from_2021-05-18_09-56-24.png>
 
Constrained Delaunay Triangulations computed by CGAL features:
<http://cgal-discuss.949826.n4.nabble.com/file/t376297/Screenshot_from_2021-05-18_09-57-11.png>
 

After the creation of the CDT is still necessary to compute the mapping of
finite elements associated with the facets of CDT as explained before, that
is, the third figure is associated with the first and second ones. This
search procedure is taking most of the time. Basically, the CDT is necessary
because it will be used to perform a numerical integration in the
intersection regions between finite elements of the two meshes.

Thanks for any suggestions,

Bruno



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