Question about Steiner point location in CGAL Constrained Delaunay Triangulation 3D

[ImperatorS79]

In the documentation, it seems the Steiner points are only added on the constrained facets and edges specified by the user. However during my tests of the package, I sometimes encounter the problem where the Steiner point is not added on the constrained surface.

Let's say I have a cloud of points and some constraints from which I want to generate a constrained tetrahedralization. What would happen if:

• the constrained surface is not closed ?
• the constrained surface is closed ?
• the constrained surface is closed, with another (not closed) constrained surface inside it ?

[lrineau]

In the documentation, it seems the Steiner points are only added on the constrained facets and edges specified by the user. However during my tests of the package, I sometimes encounter the problem where the Steiner point is not added on the constrained surface.

Hi, that is strange: Steiner vertices are indeed supposed to be added on constrained facets (or edges) only? Do you a way to share the code and input data so that we can reproduce?

Let's say I have a cloud of points and some constraints from which I want to generate a constrained tetrahedralization. What would happen if:

• the constrained surface is not closed ?
• the constrained surface is closed ?
• the constrained surface is closed, with another (not closed) constrained surface inside it ?

The code of CGAL Constrained Delaunay Triangulation 3D does not really change behavior depending on the surface being closed or not. What do you expect as difference between those three cases?

[ImperatorS79]

Regarding the problem of point not located on the surface, it was a bug in the library I used to locate the point. So there is no problem anymore.

If the surface is closed, you could add the Steiner points not on the surface but in the volume in order to preserve the surface (like TetGen can do, as far as I understand), so I was wondering if CGAL might did this. Anyway, there is actually no problem on CGAL side.

[lrineau]

Regarding the problem of point not located on the surface, it was a bug in the library I used to locate the point. So there is no problem anymore.

Thanks for letting us know.

If the surface is closed, you could add the Steiner points not on the surface but in the volume in order to preserve the surface (like TetGen can do, as far as I understand), so I was wondering if CGAL might did this. Anyway, there is actually no problem on CGAL side.

That is on our TODO-list. We wanted to publish a first version of CDT_3 without that possibility, and add it afterward.