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I am trying to project a Polyhedron on the xy plane with CGAL, which should result in a (2D) polygon.

I wonder, if there is an elegant way to achieve it?

Of course, I can iterate over all surfaces and build 2D-Segments from the 3D-Segments by throwing away the z coordinate and then reassemble the polgon cycles.

But I feel, that somehow using Projection_traits_xy_3 it should be possible to solve that task more elegant, however, I couldn't find a way. Is this possible?

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A possible way to do this is tracing the silhouette edges of the polyhedron and projecting them to a 2d polygon only at the end of the process.

A silhouette edge (in your context) is defined by its neighboring facets having one upwards and one downwards normal (i.e., one positive normal z-coordinate and one negative). This can be checked using Polyhedron_traits_with_normals_3 or you can compute the normals yourself on-the-fly.

If you only need the outside polygon, you can start with an extreme vertex (e.g., the one with minimal x-coordinate), circulate over its incident halfedges (using Halfedge_around_vertex_circulator), take the one that is a silhouette edge and continue tracing with its next vertex until you close the cycle.

If you also need inside (hole) polygons, a possible solution can be to gather the silhouette edges from all the polyhedron, and trace the cycles from this set.

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