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[Efi Fogel <>]

Hi Nicklas,

I'm not sure which issue you exactly refer to...

There are several ways to handle those numbers, for example:

Given a rational center c and the square of a radius, you can find a  point with rational coordinates (x,y) exactly on the circle that approximates the exact point p in direction d = (dx, dy) from c, within a certain bound.

There are infinitely many such rational points...

Look at CGAL::rational_rotation_approximation().

If you have an arc of a circle, it would be more efficient in general to use it when constructing an arrangement and using the arrangement for further operations, than constructing an arrangement of segments that approximate the arc.

So I would recommend using the Arr_circle_segment_traits_2. This traits class uses an algebraic number type called CGAL::Sqrt_extension< NT, Root, DifferentExtensionComparable, FilterPredicates >.

It is more efficient than a general algebraic number (e.g., provided by Core) but it is limited. You can try to learn to use it for your needs.

Finally, the (regularized) operations on polygons depend on the 2D Arrangement package. 

More precisely, when performing a Boolean-set operation an arrangement is constructed and manipulated behind the scene.

If you use the Polygon_set_2 construct, you can obtain this arrangement. (Naturally, if you want to change this arrangement, obtain it by value...)

Efi

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On Tue, 8 Jul 2025 at 15:08, Nicklas SB Karlsson <> wrote:

I already solved it and provided some kind of example to show how I did it.

If you want I could provide my code as an example?

It is complemented with pdf file written more or less in the form of a scientific article describing the problem. In short it is intended to calculate paths for control of CNC machine following a more or less arbitrary surface described with lines or cirular arcs with constant tool angle engagement. While simple to calculate tool engamenent following a linear surface it become a little bit more tricky following a circular surface and did not find closed form solution then there is intersections between different shapes. As there is no need for high accuracy until desired shape is reached I therefore decided to use iterative calculations with polygons and follow "exactly" then desired shape is reached.

It is still work in progress since calculation is rather slow and I therefore postponed it until I maybe in future get more time for this. Guess it would be a very nice algotithm to have to calculate tool paths for CNC machines.

Nicklas Karlsson

tis 2025-07-01 klockan 10:10 +0300 skrev Efi Fogel:

Hi Nicklas,

Before we can solve something, we need to know whether there is something to solve and if so, we need to know what to solve.

A minimal program that can be used to reproduce the problem is what we need.

The exact input data can help too.

Efi

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On Mon, 30 Jun 2025 at 23:15, Nicklas SB Karlsson <> wrote:

In attached files I do this for polygon. Have complete program that compile and run if you need?

Did not find any examples so had to struggle a while before I figured how it should be done so guess maybe this help you how to solve your problem.

Nicklas Karlsson

sön 2025-06-22 klockan 17:45 +0800 skrev ж��:

I submitted three straight lines and one circular arc to the CGAL Arrangement, as shown in the left figure. The final calculation result, shown in the right figure, is incorrect. However, if I discretize the arc into line segments, the result becomes correct. so how to do .

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卸甲

 

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