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[Kevin Morgan <>]

Hi Ahmed, Efi,

Thanks for your reply. 

I'll take a look at Arr_algebraic_segment_traits_2. I can't tell yet, but it might be what I need.

I'm aware that the intersection of two beziers is not necessarily rational. It seems like an odd design choice to me that the bezier_traits_adapter would only take rational control points, yet would add algebraic vertices to the arrangement that cannot be connected via an edge to any other vertex. Especially since the intersection itself is a vertex that connects via monotone edges to other vertices.

I have looked at the code, and I do understand the underlying exact representation, and the issues around it, but wonder if there might not be some way to support algebraic vertices in such an arrangement, or at least to connect those vertices to each other or to other rational vertices.

Anyway, thanks for your help.

Kevin

On Mon, Nov 29, 2021 at 8:56 AM Efi Fogel <> wrote:

I, of course, second Ahmed's explanation.

Let me add and say that the Arr_algebraic_segment_traits_2 geometry traits does support algebraic coordinates and so you may want to consider it as an alternative.

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On Mon, 29 Nov 2021 at 15:02, Ahmed Essam <> wrote:

Hi,

As stated in the error message, the intersection point of the Bezier curves does not have rational coordinates (but rather algebraic). Bezier curves in the Arrangement package require that their control points be rational, and hence you can't use these points as control points.

This is to be expected since the intersection point is the solution of two non linear equations representing the curves.

Best,

Ahmed.

On Mon, Nov 29, 2021, 8:17 AM Kevin Morgan <> wrote:

Hi,

I'm using a CGAL::Arrangment and am trying to connect edges to the intersection of Beziers.

In the application, I'm getting a precondition violation, complaining that the intersection is not rational.

I tried to construct a synthetic example to reproduce the problem, which I've posted on stackoverflow, and it gets a segfault.

https://stackoverflow.com/questions/70107781/cgal-how-can-i-construct-an-edge-between-a-vertex-and-the-intersections-of-two-b

But, assuming the segfault is just a bug, my question is really about the intended API for Beziers. Is it possible to connect an edge to a vertex which is the intersection of two Bezier curves? If so, what's the mechanism I'm supposed to use to avoid the precondition violation?

Thanks in advance for your help.

Kevin

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