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["????" <>]

"Thank you very much, although I have already solved this problem.

I looked through the official help documentation, but I never managed to find how to handle precision issues. It only explains the principles, but I couldn't find any solutions or practical examples on how to deal with it.

Straight lines are manageable, but for arcs or circles, in the official examples, the endpoint coordinates appear to use rational numbers. Even the radii seem to have specific requirements; they aren't given directly as floating-point numbers. I feel this is almost impossible to achieve in real-world projects, where floating-point numbers are generally used. Yet, I couldn't find any information on how to properly handle this.

In the end, I approximated the arcs and circles with line segments. Working with straight lines in CGAL Arrangements seems to be reliable and error-free in calculations."

using Kernel = CGAL::Exact_predicates_exact_constructions_kernel;

using Segment_traits = CGAL::Arr_segment_traits_2<Kernel>;

using Traits = CGAL::Arr_polyline_traits_2<Segment_traits>;

using Point = Traits::Point_2;

using Segment = Segment_traits::Segment_2;

using My_polyline = Traits::Curve_2;

using X_monotone_curve = Traits::X_monotone_curve_2;

using Arrangement = CGAL::Arrangement_2<Traits>;

My_polyline CircularArc::toCurve() const {

        

        

        

        Kernel kernel;

        

        

        Kernel::Circle_2 supporting_circle(m_source, m_point_on_arc, m_target);

        Point center = supporting_circle.center();

        double radius = std::sqrt(CGAL::to_double(supporting_circle.squared_radius()));

        

       

        CGAL::Orientation orient = CGAL::orientation(m_source, m_point_on_arc, m_target);

        

        

        double start_angle = std::atan2(CGAL::to_double(m_source.y() - center.y()), 

                                       CGAL::to_double(m_source.x() - center.x()));

        double end_angle = std::atan2(CGAL::to_double(m_target.y() - center.y()), 

                                     CGAL::to_double(m_target.x() - center.x()));

        

        

        if (orient == CGAL::COUNTERCLOCKWISE) {

            if (end_angle <= start_angle) end_angle += 2 * CGAL_PI;

        } else {

            if (start_angle <= end_angle) start_angle += 2 * CGAL_PI;

        }

        

       

        const int num_segments = 32;

        std::vector<Segment> segments;

        segments.reserve(num_segments);

        

        double angle_step;

        if (orient == CGAL::COUNTERCLOCKWISE) {

            angle_step = (end_angle - start_angle) / num_segments;

        } else {

            angle_step = (start_angle - end_angle) / num_segments;

        }

        

        Point prev_point = m_source;

        for (int i = 1; i <= num_segments; ++i) {

            double curr_angle;

            if (orient == CGAL::COUNTERCLOCKWISE) {

                curr_angle = start_angle + i * angle_step;

            } else {

                curr_angle = start_angle - i * angle_step;

            }

            

            

            double x = CGAL::to_double(center.x()) + radius * std::cos(curr_angle);

            double y = CGAL::to_double(center.y()) + radius * std::sin(curr_angle);

            Point curr_point(x, y);

            

            

            if (i == num_segments) {

                curr_point = m_target;

            }

            

            

            segments.push_back(Segment(prev_point, curr_point));

            prev_point = curr_point;

        }

        

        

        Traits traits;

        return traits.construct_curve_2_object()(segments.begin(), segments.end());

    }

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??????: "cgal-discuss" <>;

????????: 2025??7??1??(??????) ????4:15

??????: "cgal-discuss"<>;

????: Re: [cgal-discuss] about arc in cgal arrangement

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

s?0?2n 2025-06-22 klockan 17:45 +0800 skrev ???1?7?1?7:

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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????

 

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