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[Philipp Blanke <>]

Hello Monique & Sebastien ,

as I understand the incremental algorithm, if a tetrahedron T is marked degenerated and a point would be inserted into its circumsphere, T would be destroyed and the hole re-triangulated. The newly constructed tets would not automatically inherit the "degenerate" flag from T.

You suggest that a marked tetrahedron could lose its degenerate status, since there could be an insertion of a point, so that there are not >4 points cospherical anymore. But such a point would have to be inserted inside T's circumsphere.

Was there an email from Laurent regarding this topic on the list?! I did not find one. But Monique's email has pointed me into the right direction. Thank you!

Best regards!

Philipp

On Tue, Mar 19, 2013 at 9:34 AM, Sebastien Loriot (GeometryFactory) <> wrote:

I think if you proceed like this, since the algorithm is incremental, you can end up with tetrahedra marked that are no longer degenerated.

I think the method Laurent proposed you is the best.

Sebastien.

On 03/19/2013 09:07 AM, Philipp Blanke wrote:

Hello!

I'd like to construct a Delaunay complex for a point set that contains
several degenerate cases, i. e., >4 cospherical points. The doc says
that the  Delaunay_triangulation_3 code solves the local disambiguity by
using a perturbation scheme.

If the tetrahedra that were constructed using this scheme would be
marked, I could merge them in a preprocessing step to get a Delaunay
complex consisting of convex polyhedra.

Where in the code is the perturbation scheme used to select a possible
tetrahedrization? I did not find this.

Best regards,
Philipp

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