CGAL中用球面测地线构造Polycurve的问题与方案咨询

我尝试在CGAL中基于球面测地线构造polycurve。类模板CGAL::Arr_polycurve_traits_2<SubcurveTraits_2>要求SubcurveTraits_2必须是ArrangementTraits_2和ArrangementDirectionalXMonotoneTraits_2概念的模型。我使用CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel>（属于球面圆弧子集）作为子特征类，但它仅满足ArrangementTraits_2，不满足ArrangementDirectionalXMonotoneTraits_2，导致编译错误。

测试代码 #

#include <iostream>

#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Arr_geodesic_arc_on_sphere_traits_2.h>
#include <CGAL/Arr_spherical_topology_traits_2.h>
#include <CGAL/Surface_sweep_2_algorithms.h>
#include <CGAL/point_generators_3.h>
#include <CGAL/Arr_spherical_topology_traits_2.h>
#include <CGAL/Arrangement_on_surface_2.h>
#include <Eigen/Core>
#include <CGAL/Arr_polycurve_traits_2.h>

using Kernel = CGAL::Exact_predicates_exact_constructions_kernel;
using Geom_traits = CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel>;
using Point = Geom_traits::Point_2;
using X_monotone_curve = Geom_traits::X_monotone_curve_2;
using Curve = Geom_traits::Curve_2;
using Polycurve = CGAL::Arr_polycurve_traits_2<Geom_traits>;

int main()
{
    Geom_traits traits;
    Polycurve polycurve_trait;
    auto ctr_pnt = traits.construct_point_2_object();
    auto ctr_cv = traits.construct_curve_2_object();
    auto ctr_poly = polycurve_trait.push_back_2_object();

    Eigen::MatrixXd curve(4, 3);
    curve << -0.962746937823763, 0.1741138079042976, -0.2068881717451065,
        -0.9602600833963838, 0.178977377213232, -0.2141673893977384,
        -0.9595444292144757, 0.1833686986933843, -0.21365956262934,
        -0.9602511343581622, 0.1870351558488714, -0.2072090959404319;

  int num_curves = curve.rows();

  Polycurve::Curve_2 polycurve;

  Eigen::MatrixXd extended_curve = curve;
  for (std::size_t i = 0; i < curve.rows(); i++)
  {
      auto p1 = curve.row(i);
      auto p2 = curve.row((i + 1) % num_curves);
      auto cv = ctr_cv(ctr_pnt(p1.x(), p1.y(), p1.z()), ctr_pnt(p2.x(), p2.y(), p2.z()));
      ctr_poly(polycurve, cv);
  }

 std::vector<Point> pts;
 CGAL::compute_intersection_points(polycurve.begin(), polycurve.end(),
     std::back_inserter(pts), true, polycurve_trait); // 我也尝试过用Geom_trait替换这里的polycurve_trait
}

错误信息 #

Severity    Code    Description Project File    Line    Suppression State   Details
Error   C3889   call to object of class type 
'CGAL::Arr_polycurve_traits_2<Geom_traits>::Make_x_monotone_2': no matching call operator found 
bem_curve_network   C:\...\CGAL\Surface_sweep_2\Surface_sweep_2_utils.h 61       

疑问 #

作为CGAL新手，我想确认是否误用了模板，或是遗漏了某些步骤；如果不是，是否需要实现可拆分为X单调段的自定义Polycurve特征类？理论上，相连的X单调段组成的曲线应保持X单调，因此构造此类Polycurve应具备可行性。

内容的提问来源于stack exchange，提问作者Cedric Martens