CGAL users discussion list

[Efi Fogel <>]

Yes, of course Monique is right. As a matter of fact, there is more to the story.

The approximate version, uses the Arr_circle_segment_traits_2 geometry traits model, which uses a certain number type called Sqrt_extension. This number type also represents algebraic numbers of degree 2, but has some constrains, which increases the efficiency of the supported operations. These constraints, naturally, limits its usages.

The exact version uses code that can handle conic arcs, so as far as number types are concerned (and as far as I can tell), it should suffice also for computing the offset of generalized polygons that comprise linear segments and circular arcs.

The bottom line doesn't change---the input must be a (linear) polygon.

However, perhaps with some limited effort, at least the exact version, can be extended to handle the desired generalized polygons.

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On Thu, Mar 31, 2016 at 3:00 PM, Monique Teillaud <> wrote:

On 31 Mar 2016, at 08:08, Efi Fogel <> wrote:

What you describe may end up with a generalized polygon that have consecutive arcs. Representing the vertices requires a higher order algebraic number.

Hi,

A quick comment only on this specific aspect. Intersecting two circles should not require higher degree than intersecting a circle and a line. In both cases, it is degree 2. 

Best,

--

Monique Teillaud 
http://www.loria.fr/~teillaud/ 
INRIA Nancy - Grand Est, LORIA 
Institut National de Recherche en Informatique et Automatique