我的目标是使用CGAL计算一组3D点的静态凸包。我在the proper CGAL documentation page上阅读了这篇文章，并实现了第一个算法，在该算法中，我从先前转换为Polyhedron_3结构的3D点集中获得了Kernel::Point_3（凸包）。可以。
然后，我尝试将算法直接应用于原始点即，而不将转换应用于Kernel::Point_3结构。从上面提到的文档中，我了解到，实现此目的的方法是实现一种新的Traits类，该类定义了算法使用的几何图元。因此，我遵循了ConvexHullTraits_3 Concept Reference，并通过查看 Convex_hull_traits_3.h CGAL文件，生成了以下代码：
#include <iostream>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/convex_hull_3.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/Convex_hull_traits_3.h>
#include <CGAL/internal/Projection_traits_3.h>
#include <CGAL/predicates/kernel_ftC3.h>
#include <CGAL/Kernel/global_functions_2.h>
#include <CGAL/Surface_mesh.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel My_kernel;
class My_point_3
{
private:
typedef My_kernel::Point_3 Point_3;
Point_3 point; //!< coordinates of the point
int index; //!< additional info about the point
public:
//constructors
My_point_3() : index(-1), point() {};
My_point_3(const double x, const double y, const double z, int i = -1) : index(i), point(x, y, z) {};
My_point_3(Point_3& point, int i = -1) : index(i), point(point) {};
My_point_3(Point_3 point, int i = -1) : index(i), point(point) {};
//access to members for reading
const int & Index() const { return index; }
const Point_3 & Point()const { return point; }
//access to members for writing
int & Index() { return index; }
Point_3 & Point() { return point; }
//operators
bool operator==(const My_point_3 &p) const
{
return (point == p.Point());
}
bool operator!=(const My_point_3 &p) const
{
return !(*this == p);
}
//see §5.3 of https://doc.cgal.org/latest/Kernel_23/index.html#sectionextensiblekernel
const double & x() const { return point.x(); }
const double & y() const { return point.y(); }
const double & z() const { return point.z(); }
};
//projection traits implemented to satisfy https://doc.cgal.org/latest/Convex_hull_2/group__PkgConvexHull2Functions.html#gac13b4efbc337c7a8d5ad418521edcd4f
template <int dim>
class My_projection_traits_3
{
public:
//Point_2
typedef My_point_3 Point_2;
//Less_signed_distance_to_line_2
typedef CGAL::internal::Less_signed_distance_to_line_projected_3<My_kernel, dim> Default_less_signed_distance_to_line_2;
template <int d>
class Less_signed_distance_to_line_projected_3
{
public:
typedef My_point_3 Point_3;
typedef My_kernel::Point_2 Point_2;
My_kernel::FT x(const My_kernel::Point_3 &p) const { return CGAL::internal::Projector<My_kernel, d>::x(p); }
My_kernel::FT y(const My_kernel::Point_3 &p) const { return CGAL::internal::Projector<My_kernel, d>::y(p); }
Point_2 project(const Point_3& p) const
{
return Point_2(x(p.Point()), y(p.Point()));
}
bool operator()(const Point_3& p, const Point_3& q, const Point_3& r, const Point_3& s) const
{
Default_less_signed_distance_to_line_2 predicate;
return predicate(project(p), project(q), project(r), project(s));
}
typedef bool result_type;
};
typedef Less_signed_distance_to_line_projected_3<dim> Less_signed_distance_to_line_2;
Less_signed_distance_to_line_2 less_signed_distance_to_line_2_object() const
{
return Less_signed_distance_to_line_2();
}
//Orientation_2
template <int d>
class Orientation_projected_3
{
public:
typedef My_point_3 Point_3;
typedef My_kernel::Point_2 Point_2;
My_kernel::FT x(const My_kernel::Point_3 &p) const { return CGAL::internal::Projector<My_kernel, d>::x(p); }
My_kernel::FT y(const My_kernel::Point_3 &p) const { return CGAL::internal::Projector<My_kernel, d>::y(p); }
Point_2 project(const Point_3& p) const
{
return Point_2(x(p.Point()), y(p.Point()));
}
CGAL::Orientation operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
return CGAL::orientation(project(p), project(q), project(r));
}
typedef CGAL::Orientation result_type;
};
typedef Orientation_projected_3<dim> Orientation_2;
Orientation_2 orientation_2_object() const
{
return Orientation_2();
}
//Left_turn_2
struct Left_turn_2
{
public:
bool operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
Orientation_2 predicate;
return (predicate(p, q, r) == CGAL::LEFT_TURN);
}
typedef bool result_type;
};
Left_turn_2 left_turn_2_object() const
{
return Left_turn_2();
}
//Less_xy_2
typedef typename CGAL::internal::Projector<My_kernel, dim>::Compare_x_2 Compare_x_2;
typedef typename CGAL::internal::Projector<My_kernel, dim>::Less_y_2 Less_y_2;
struct Less_xy_2
{
public:
bool operator()(const Point_2& p, const Point_2& q) const
{
Compare_x_2 predicate1;
CGAL::Comparison_result crx = predicate1(p.Point(), q.Point());
if (crx == CGAL::SMALLER) { return true; }
if (crx == CGAL::LARGER) { return false; }
Less_y_2 predicate2;
return predicate2(p.Point(), q.Point());
}
typedef bool result_type;
};
Less_xy_2 less_xy_2_object() const
{
return Less_xy_2();
}
//Less_yx_2
typedef typename CGAL::internal::Projector<My_kernel, dim>::Compare_y_2 Compare_y_2;
typedef typename CGAL::internal::Projector<My_kernel, dim>::Less_x_2 Less_x_2;
struct Less_yx_2
{
public:
bool operator()(const Point_2& p, const Point_2& q) const
{
Compare_y_2 predicate1;
CGAL::Comparison_result cry = predicate1(p.Point(), q.Point());
if (cry == CGAL::SMALLER) { return true; }
if (cry == CGAL::LARGER) { return false; }
Less_x_2 predicate2;
return predicate2(p.Point(), q.Point());
}
typedef bool result_type;
};
Less_yx_2 less_yx_2_object() const
{
return Less_yx_2();
}
//Equal_2
typedef typename CGAL::internal::Projector<My_kernel, dim>::Equal_x_2 Equal_x_2;
typedef typename CGAL::internal::Projector<My_kernel, dim>::Equal_y_2 Equal_y_2;
struct Equal_2
{
public:
bool operator()(const Point_2& p, const Point_2& q) const
{
Equal_x_2 predicate1;
Equal_y_2 predicate2;
return predicate1(p.Point(), q.Point()) & predicate2(p.Point(), q.Point());
}
typedef bool result_type;
};
Equal_2 equal_2_object() const
{
return Equal_2();
}
};
class Point_triple
{
protected:
typedef My_kernel::FT FT;
typedef My_kernel::Point_3 Point_3;
typedef My_kernel::Vector_3 Vector_3;
Point_3 p_, q_, r_;
public:
Point_triple() {}
Point_triple(const Point_3 &p, const Point_3 &q, const Point_3 &r): p_(p), q_(q), r_(r) {}
const Point_3& p() const { return p_; }
const Point_3& q() const { return q_; }
const Point_3& r() const { return r_; }
};
typedef CGAL::Convex_hull_traits_3<My_kernel> Default_traits;
class My_traits
{
public:
typedef My_point_3 Point_3;
typedef My_kernel::Segment_3 Segment_3;
typedef My_kernel::Triangle_3 Triangle_3;
typedef Point_triple Plane_3;
class Construct_segment_3
{
public:
Segment_3 operator ()(const Point_3& p, const Point_3& q) const
{
Default_traits::Construct_segment_3 object;
return object(p.Point(), q.Point());
}
typedef Segment_3 result_type;
};
class Construct_plane_3
{
public:
Plane_3 operator ()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
CGAL::Convex_hull_traits_3<My_kernel>::Construct_plane_3 object;
CGAL::Point_triple<My_kernel> plane = object(p.Point(), q.Point(), r.Point());
return Point_triple(plane.p(), plane.q(), plane.r());
}
typedef Plane_3 result_type;
};
class Construct_triangle_3
{
public:
Triangle_3 operator ()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
Default_traits::Construct_triangle_3 object;
return object(p.Point(), q.Point(), r.Point());
}
typedef Triangle_3 result_type;
};
class Equal_3
{
public:
bool operator ()(const Point_3& p, const Point_3& q) const
{
Default_traits::Equal_3 predicate;
return predicate(p.Point(), q.Point());
}
typedef bool result_type;
};
class Collinear_3
{
public:
bool operator ()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
Default_traits::Collinear_3 predicate;
return predicate(p.Point(), q.Point(), r.Point());
}
typedef bool result_type;
};
class Coplanar_3
{
public:
bool operator ()(const Point_3& p, const Point_3& q, const Point_3& r, const Point_3& s) const
{
Default_traits::Coplanar_3 predicate;
return predicate(p.Point(), q.Point(), r.Point(), s.Point());
}
typedef bool result_type;
};
class Has_on_positive_side_3
{
public:
bool operator()(const Plane_3& pl, const Point_3& p) const
{
Default_traits::Orientation_3 predicate;
return (predicate(pl.p(), pl.q(), pl.r(), p.Point()) == CGAL::POSITIVE);
}
typedef bool result_type;
};
class Less_distance_to_point_3
{
public:
bool operator ()(const Point_3 & p, const Point_3 & q, const Point_3 & r) const
{
Default_traits::Less_distance_to_point_3 predicate;
return predicate(p.Point(), q.Point(), r.Point());
}
typedef bool result_type;
};
class Less_signed_distance_to_plane_3
{
public:
bool operator()(const Plane_3 & h, const Point_3 & p, const Point_3 & q) const
{
const My_kernel::Point_3 & hp = h.p();
const My_kernel::Point_3 & hq = h.q();
const My_kernel::Point_3 & hr = h.r();
return CGAL::has_smaller_signed_dist_to_planeC3(
hp.x(), hp.y(), hp.z(),
hq.x(), hq.y(), hq.z(),
hr.x(), hr.y(), hr.z(),
p.Point().x(), p.Point().y(),
p.Point().z(), q.Point().x(),
q.Point().y(), q.Point().z()
);
}
typedef bool result_type;
};
typedef My_projection_traits_3<2> Traits_xy_3;
typedef My_projection_traits_3<0> Traits_yz_3;
typedef My_projection_traits_3<1> Traits_xz_3;
Construct_segment_3 construct_segment_3_object() const
{
return Construct_segment_3();
}
Construct_plane_3 construct_plane_3_object() const
{
return Construct_plane_3();
}
Construct_triangle_3 construct_triangle_3_object() const
{
return Construct_triangle_3();
}
Collinear_3 collinear_3_object() const
{
return Collinear_3();
}
Coplanar_3 coplanar_3_object() const
{
return Coplanar_3();
}
Less_distance_to_point_3 less_distance_to_point_3_object() const
{
return Less_distance_to_point_3();
}
Has_on_positive_side_3 has_on_positive_side_3_object() const
{
return Has_on_positive_side_3();
}
Equal_3 equal_3_object() const
{
return Equal_3();
}
Less_signed_distance_to_plane_3 less_signed_distance_to_plane_3_object() const
{
return Less_signed_distance_to_plane_3();
}
Traits_xy_3 construct_traits_xy_3_object() const
{
return Traits_xy_3();
}
Traits_yz_3 construct_traits_yz_3_object() const
{
return Traits_yz_3();
}
Traits_xz_3 construct_traits_xz_3_object() const
{
return Traits_xz_3();
}
};
typedef My_kernel::Point_3 Point_3;
typedef CGAL::Surface_mesh<My_point_3> Surface_mesh;
int main()
{
std::vector<My_point_3> input_points;
input_points.push_back(My_point_3(Point_3(0, 0, 0), 1));
input_points.push_back(My_point_3(Point_3(1, 0, 0), 2));
input_points.push_back(My_point_3(Point_3(0, 1, 0), 3));
input_points.push_back(My_point_3(Point_3(0, 0, 1), 4));
input_points.push_back(My_point_3(Point_3(0.5, 0.5, 0.5), 5));
Surface_mesh mesh;
CGAL::convex_hull_3(input_points.begin(), input_points.end(), mesh, My_traits());
Surface_mesh::Vertex_iterator v;
for (v = mesh.vertices_begin(); v != mesh.vertices_end(); v++)
{
std::cout << input_points[*v].Index() << " (" << input_points[*v].Point() << ")" << std::endl;
}
return 0;
}
但是，当我尝试编译时，它给了我以下错误：[...] （ Edit ：通过将CGAL从4.12更新为4.13和其他一些更正---有关详细信息，请参见下面的编辑历史记录和注释）。
代码会编译；但是，在一个最小示例中，当我在凸包的顶点上进行迭代时（请参见上面的 main 函数），也会打印不在凸包上的顶点。
问题是：我的代码在做什么错？缺少什么？