start updating the AABB-tree to work in both 2D and 3D

This commit is contained in:
Sébastien Loriot 2024-03-04 12:54:59 +01:00
parent d68ef56d8d
commit 006d46b1d4
10 changed files with 596 additions and 559 deletions

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@ -3,8 +3,8 @@
\ingroup PkgAABBTreeConcepts
\cgalConcept
The concept `AABBGeomTraits` defines the requirements for the first template parameter of the class
`CGAL::AABB_traits<AABBGeomTraits, AABBPrimitive>`. It provides predicates and constructors to detect
The concept `AABBGeomTraits_3` defines the requirements for the first template parameter of the class
`CGAL::AABB_traits<AABBGeomTraits_3, AABBPrimitive>`. It provides predicates and constructors to detect
and compute intersections between query objects and the primitives stored in the AABB tree.
In addition, it contains predicates and constructors to compute distances between a point query
and the primitives stored in the AABB tree.
@ -15,13 +15,13 @@ and the primitives stored in the AABB tree.
\cgalHasModelsBare{All models of the concept `Kernel`}
\cgalHasModelsEnd
\sa `CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>`
\sa `CGAL::AABB_traits<AABBGeomTraits_3,AABBPrimitive>`
\sa `CGAL::AABB_tree<AABBTraits>`
\sa `AABBPrimitive`
*/
class AABBGeomTraits {
class AABBGeomTraits_3 {
public:
/// \name Types
@ -199,5 +199,5 @@ Equal_3 equal_3_object();
/// @}
}; /* end AABBGeomTraits */
}; /* end AABBGeomTraits_3 */

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@ -21,46 +21,48 @@ define the Intersection_distance functor.
class AABBRayIntersectionGeomTraits {
public:
/*!
Type of a 3D ray.
Type of a ray.
*/
typedef unspecified_type Ray_3;
typedef unspecified_type Ray;
/*!
Type of a 3D vector.
Type of a vector.
*/
typedef unspecified_type Vector_3;
typedef unspecified_type Vector;
/*!
A functor object to construct the source point of a ray. Provides the operator:
`Point_3 operator()(const Ray_3&);`
`Point operator()(const Ray&);`
*/
typedef unspecified_type Construct_source_3;
typedef unspecified_type Construct_source;
/*!
*/
Construct_source_3 construct_source_3_object();
Construct_source construct_source_object();
/*!
@todo update me
A model of `CartesianConstIterator3`.
*/
typedef unspecified_type Cartesian_const_iterator_3;
typedef unspecified_type Cartesian_const_iterator;
/*!
@todo update me
A model of `ConstructCartesianConstIterator3`.
*/
typedef unspecified_type Construct_cartesian_const_iterator_3;
typedef unspecified_type Construct_cartesian_const_iterator;
/*!
*/
Construct_source_3 construct_cartesian_const_iterator_3_object();
Construct_source construct_cartesian_const_iterator_object();
/*!
A functor object to construct a vector giving the direction of a ray. Provides the operator:
`Vector_3 operator()(const Ray_3&);`
`Vector operator()(const Ray&);`
*/
typedef unspecified_type Construct_vector_3;
typedef unspecified_type Construct_vector;
/*!
*/
Construct_source_3 construct_vector_3_object();
Construct_source construct_vector_object();
};

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@ -9,7 +9,7 @@ The concept `AABBTraits` provides the geometric primitive types and methods for
\cgalHasModels{CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>}
\cgalHasModelsEnd
\cgalRefines{SearchGeomTraits_3}
\cgalRefines{SearchTraits}
\sa `CGAL::AABB_traits<AABBGeomTraits,AABBPrimitive>`
\sa `CGAL::AABB_tree<AABBTraits>`
@ -30,7 +30,7 @@ typedef unspecified_type FT;
/*!
Type of a 3D point.
*/
typedef unspecified_type Point_3;
typedef unspecified_type Point;
/*!
Type of primitive.
@ -43,19 +43,10 @@ Bounding box type.
*/
typedef unspecified_type Bounding_box;
/*!
enum required for axis selection
*/
enum Axis {
CGAL_X_AXIS,
CGAL_Y_AXIS,
CGAL_Z_AXIS
};
/*!
3D Point and Primitive Id type
*/
typedef std::pair<Point_3, Primitive::Id> Point_and_primitive_id;
typedef std::pair<Point, Primitive::Id> Point_and_primitive_id;
/*!
\deprecated
@ -145,21 +136,21 @@ typedef unspecified_type Compare_distance;
/*!
A functor object to compute closest point from the query on a primitive. Provides the operator:
`Point_3 operator()(const Query& query, const Primitive& primitive, const Point_3 & closest);` which returns the closest point to `query`, among `closest` and all points of the primitive.
`Point operator()(const Query& query, const Primitive& primitive, const Point & closest);` which returns the closest point to `query`, among `closest` and all points of the primitive.
*/
typedef unspecified_type Closest_point;
/*!
A functor object to compute the squared distance between two points. Provides the operator:
`FT operator()(const Point& query, const Point_3 & p);` which returns the squared distance between `p` and `q`.
`FT operator()(const Point& query, const Point & p);` which returns the squared distance between `p` and `q`.
*/
typedef unspecified_type Squared_distance;
/*!
A functor object to compare two points. Provides the operator:
`bool operator()(const Point_3& p, const Point_3& q);}` which returns `true` if `p` is equal to `q`.
`bool operator()(const Point& p, const Point& q);}` which returns `true` if `p` is equal to `q`.
*/
typedef unspecified_type Equal_3;
typedef unspecified_type Equal;
/// @}
/// \name Operations
@ -203,7 +194,7 @@ Squared_distance squared_distance_object();
/*!
returns the equal functor.
*/
Equal_3 equal_3_object();
Equal equal_object();
/// @}

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@ -5,12 +5,12 @@
/*!
\addtogroup PkgAABBTreeRef
\cgalPkgDescriptionBegin{3D Fast Intersection and Distance Computation,PkgAABBTree}
\cgalPkgDescriptionBegin{Fast Intersection and Distance Computation,PkgAABBTree}
\cgalPkgPicture{aabb-teaser-thumb.png}
\cgalPkgSummaryBegin
\cgalPkgAuthors{Pierre Alliez, Stéphane Tayeb, and Camille Wormser}
\cgalPkgDesc{The AABB (axis-aligned bounding box) tree component offers a static data structure and algorithms to perform efficient intersection and distance queries on sets of finite 3D geometric objects.}
\cgalPkgManuals{Chapter_3D_Fast_Intersection_and_Distance_Computation,PkgAABBTreeRef}
\cgalPkgManuals{Chapter_Fast_Intersection_and_Distance_Computation,PkgAABBTreeRef}
\cgalPkgSummaryEnd
\cgalPkgShortInfoBegin
\cgalPkgSince{3.5}
@ -25,18 +25,23 @@
\cgalCRPSection{Concepts}
- `AABBPrimitive`
- `AABBPrimitiveWithSharedData`
- `AABBGeomTraits`
- `AABBGeomTraits_2`
- `AABBGeomTraits_3`
- `AABBTraits`
- `AABBRayIntersectionGeomTraits`
- `AABBRayIntersectionGeomTraits_2`
- `AABBRayIntersectionGeomTraits_3`
- `AABBRayIntersectionTraits`
\cgalCRPSection{Classes}
- `CGAL::AABB_traits<GeomTraits,Primitive>`
- `CGAL::AABB_traits_2<GeomTraits,Primitive>`
- `CGAL::AABB_traits_3<GeomTraits,Primitive>`
- `CGAL::AABB_tree<AT>`
\cgalCRPSection{Primitives}
- `CGAL::AABB_triangle_primitive<GeomTraits, Iterator, CacheDatum>`
- `CGAL::AABB_segment_primitive<GeomTraits, Iterator, CacheDatum>`
- `CGAL::AABB_triangle_primitive_2<GeomTraits, Iterator, CacheDatum>`
- `CGAL::AABB_segment_primitive_2<GeomTraits, Iterator, CacheDatum>`
- `CGAL::AABB_triangle_primitive_3<GeomTraits, Iterator, CacheDatum>`
- `CGAL::AABB_segment_primitive_3<GeomTraits, Iterator, CacheDatum>`
- `CGAL::AABB_primitive<Id,ObjectPropertyMap,PointPropertyMap,ExternalPropertyMaps,CacheDatum>`
- `CGAL::AABB_halfedge_graph_segment_primitive<HalfedgeGraph,Vpm,OneHalfedgeGraphPerTree,CacheDatum>`
- `CGAL::AABB_face_graph_triangle_primitive<FaceGraph,Vpm,OneFaceGraphPerTree,CacheDatum>`

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@ -3,7 +3,7 @@ namespace CGAL {
/*!
\mainpage User Manual
\anchor Chapter_3D_Fast_Intersection_and_Distance_Computation
\anchor Chapter_Fast_Intersection_and_Distance_Computation
\cgalAutoToc
\authors Pierre Alliez, Stephane Tayeb, and Camille Wormser

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@ -1,4 +1,4 @@
// Copyright (c) 2009 INRIA Sophia-Antipolis (France).
// Copyright (c) 2024 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
@ -14,524 +14,24 @@
#ifndef CGAL_AABB_TRAITS_H_
#define CGAL_AABB_TRAITS_H_
#define CGAL_DEPRECATED_HEADER "<CGAL/AABB_traits.h>"
#define CGAL_REPLACEMENT_HEADER "<CGAL/AABB_traits_3.h>"
#include <CGAL/Installation/internal/deprecation_warning.h>
#ifndef CGAL_NO_DEPRECATED_CODE
#include <CGAL/license/AABB_tree.h>
#include <CGAL/disable_warnings.h>
#include <CGAL/AABB_traits_3.h>
#include <CGAL/Bbox_3.h>
#include <CGAL/Default.h>
#include <CGAL/intersections.h>
#include <CGAL/AABB_tree/internal/Has_nested_type_Shared_data.h>
#include <CGAL/AABB_tree/internal/Is_ray_intersection_geomtraits.h>
#include <CGAL/AABB_tree/internal/Primitive_helper.h>
#include <CGAL/Kernel_23/internal/Has_boolean_tags.h>
#include <optional>
/// \file AABB_traits.h
namespace CGAL {
namespace internal{ namespace AABB_tree {
template <class T>
struct Remove_optional { typedef T type; };
template <class T>
struct Remove_optional< ::std::optional<T> > { typedef T type; };
//helper controlling whether extra data should be stored in the AABB_tree traits class
template <class Primitive, bool has_shared_data=Has_nested_type_Shared_data<Primitive>::value>
struct AABB_traits_base;
template <class Primitive>
struct AABB_traits_base<Primitive,false>{};
template <class Primitive>
struct AABB_traits_base<Primitive,true>{
typename Primitive::Shared_data m_primitive_data;
template <typename ... T>
void set_shared_data(T&& ... t){
m_primitive_data=Primitive::construct_shared_data(std::forward<T>(t)...);
}
const typename Primitive::Shared_data& shared_data() const {return m_primitive_data;}
};
// AABB_traits_base_2 brings in the Intersection_distance predicate,
// if GeomTraits is a model RayIntersectionGeomTraits.
template <typename GeomTraits, bool ray_intersection_geom_traits=Is_ray_intersection_geomtraits<GeomTraits>::value>
struct AABB_traits_base_2;
template <typename GeomTraits>
struct AABB_traits_base_2<GeomTraits,false>{};
template <typename GeomTraits>
struct AABB_traits_base_2<GeomTraits,true>{
typedef typename GeomTraits::Ray_3 Ray_3;
typedef typename GeomTraits::Point_3 Point_3;
typedef typename GeomTraits::Vector_3 Vector_3;
typedef typename GeomTraits::FT FT;
typedef typename GeomTraits::Cartesian_const_iterator_3 Cartesian_const_iterator_3;
typedef typename GeomTraits::Construct_cartesian_const_iterator_3 Construct_cartesian_const_iterator_3;
typedef typename GeomTraits::Construct_source_3 Construct_source_3;
typedef typename GeomTraits::Construct_vector_3 Construct_vector_3;
// Defining Bounding_box and other types from the full AABB_traits
// here is might seem strange, but otherwise we would need to use
// CRTP to get access to the derived class, which would bloat the
// code more.
typedef typename CGAL::Bbox_3 Bounding_box;
struct Intersection_distance {
std::optional<FT> operator()(const Ray_3& ray, const Bounding_box& bbox) const {
FT t_near = -DBL_MAX; // std::numeric_limits<FT>::lowest(); C++1903
FT t_far = DBL_MAX;
const Construct_cartesian_const_iterator_3 construct_cartesian_const_iterator_3
= GeomTraits().construct_cartesian_const_iterator_3_object();
const Construct_source_3 construct_source_3 = GeomTraits().construct_source_3_object();
const Construct_vector_3 construct_vector_3 = GeomTraits().construct_vector_3_object();
const Point_3 source = construct_source_3(ray);
const Vector_3 direction = construct_vector_3(ray);
Cartesian_const_iterator_3 source_iter = construct_cartesian_const_iterator_3(source);
Cartesian_const_iterator_3 direction_iter = construct_cartesian_const_iterator_3(direction);
for(int i = 0; i < 3; ++i, ++source_iter, ++direction_iter) {
if(*direction_iter == 0) {
if((*source_iter < (bbox.min)(i)) || (*source_iter > (bbox.max)(i))) {
return std::nullopt;
}
} else {
FT t1 = ((bbox.min)(i) - *source_iter) / *direction_iter;
FT t2 = ((bbox.max)(i) - *source_iter) / *direction_iter;
t_near = (std::max)(t_near, (std::min)(t1, t2));
t_far = (std::min)(t_far, (std::max)(t1, t2));
// if(t1 > t2)
// std::swap(t1, t2);
// if(t1 > t_near)
// t_near = t1;
// if(t2 < t_far)
// t_far = t2;
if(t_near > t_far || t_far < FT(0.))
return std::nullopt;
}
}
if(t_near < FT(0.))
return FT(0.);
else
return t_near;
}
};
Intersection_distance intersection_distance_object() const { return Intersection_distance(); }
};
} } //end of namespace internal::AABB_tree
/// \addtogroup PkgAABBTreeRef
/// @{
// forward declaration
template< typename AABBTraits>
class AABB_tree;
/// This traits class handles any type of 3D geometric
/// primitives provided that the proper intersection tests and
/// constructions are implemented. It handles points, rays, lines and
/// segments as query types for intersection detection and
/// computations, and it handles points as query type for distance
/// queries.
///
/// \cgalModels{AABBTraits,AABBRayIntersectionTraits}
///
/// \tparam GeomTraits must be a model of the concept \ref AABBGeomTraits,
/// and provide the geometric types as well as the intersection tests and computations.
/// \tparam Primitive provide the type of primitives stored in the AABB_tree.
/// It is a model of the concept `AABBPrimitive` or `AABBPrimitiveWithSharedData`.
///
/// \tparam BboxMap must be a model of `ReadablePropertyMap` that has as key type a primitive id,
/// and as value type a `Bounding_box`.
/// If the type is `Default` the `Datum` must have the
/// member function `bbox()` that returns the bounding box of the primitive.
///
/// If the argument `GeomTraits` is a model of the concept \ref
/// AABBRayIntersectionGeomTraits, this class is also a model of \ref
/// AABBRayIntersectionTraits.
///
/// \sa `AABBTraits`
/// \sa `AABB_tree`
/// \sa `AABBPrimitive`
/// \sa `AABBPrimitiveWithSharedData`
template<typename GeomTraits, typename AABBPrimitive, typename BboxMap = Default>
class AABB_traits
#ifndef DOXYGEN_RUNNING
: public internal::AABB_tree::AABB_traits_base<AABBPrimitive>,
public internal::AABB_tree::AABB_traits_base_2<GeomTraits>
#endif
namespace CGAL
{
typedef typename CGAL::Object Object;
public:
typedef GeomTraits Geom_traits;
typedef AABB_traits<GeomTraits, AABBPrimitive, BboxMap> AT;
// AABBTraits concept types
typedef typename GeomTraits::FT FT;
typedef AABBPrimitive Primitive;
template<typename GeomTraits, typename AABBPrimitive, typename BboxMap = Default>
using AABB_traits = AABB_traits_3<GeomTraits, AABBPrimitive, BboxMap>;
typedef typename std::pair<Object,typename Primitive::Id> Object_and_primitive_id;
} // namespace CGAL
typedef typename std::pair<typename GeomTraits::Point_3, typename Primitive::Id> Point_and_primitive_id;
/// `Intersection_and_primitive_id<Query>::%Type::first_type` is found according to
/// the result type of `GeomTraits::Intersect_3::operator()`. If it is
/// `std::optional<T>` then it is `T`, and the result type otherwise.
template<typename Query>
struct Intersection_and_primitive_id {
typedef decltype(
std::declval<typename GeomTraits::Intersect_3>()(
std::declval<Query>(),
std::declval<typename Primitive::Datum>())) Intersection_type;
typedef std::pair<
typename internal::AABB_tree::Remove_optional<Intersection_type>::type,
typename Primitive::Id > Type;
};
// types for search tree
/// \name Types
/// @{
/// Point query type.
typedef typename GeomTraits::Point_3 Point_3;
/// additional types for the search tree, required by the RangeSearchTraits concept
/// \bug This is not documented for now in the AABBTraits concept.
typedef typename GeomTraits::Iso_cuboid_3 Iso_cuboid_3;
/// Bounding box type.
typedef typename CGAL::Bbox_3 Bounding_box;
/// @}
typedef typename GeomTraits::Sphere_3 Sphere_3;
typedef typename GeomTraits::Cartesian_const_iterator_3 Cartesian_const_iterator_3;
typedef typename GeomTraits::Construct_cartesian_const_iterator_3 Construct_cartesian_const_iterator_3;
typedef typename GeomTraits::Construct_center_3 Construct_center_3;
typedef typename GeomTraits::Compute_squared_radius_3 Compute_squared_radius_3;
typedef typename GeomTraits::Construct_min_vertex_3 Construct_min_vertex_3;
typedef typename GeomTraits::Construct_max_vertex_3 Construct_max_vertex_3;
typedef typename GeomTraits::Construct_iso_cuboid_3 Construct_iso_cuboid_3;
BboxMap bbm;
/// Default constructor.
AABB_traits() { }
AABB_traits(BboxMap bbm)
: bbm(bbm)
{}
typedef typename GeomTraits::Compute_squared_distance_3 Squared_distance;
Squared_distance squared_distance_object() const { return GeomTraits().compute_squared_distance_3_object(); }
typedef typename GeomTraits::Equal_3 Equal_3;
Equal_3 equal_3_object() const { return GeomTraits().equal_3_object(); }
/**
* @internal
* @brief Sorts [first,beyond[
* @param first iterator on first element
* @param beyond iterator on beyond element
* @param bbox the bounding box of [first,beyond[
*
* Sorts the range defined by [first,beyond[. Sort is achieved on bbox longest
* axis, using the comparison function `<dim>_less_than` (dim in {x,y,z})
*/
class Split_primitives
{
typedef AABB_traits<GeomTraits,AABBPrimitive,BboxMap> Traits;
const Traits& m_traits;
public:
Split_primitives(const AABB_traits<GeomTraits,AABBPrimitive,BboxMap>& traits)
: m_traits(traits) {}
typedef void result_type;
template<typename PrimitiveIterator>
void operator()(PrimitiveIterator first,
PrimitiveIterator beyond,
const typename AT::Bounding_box& bbox) const
{
PrimitiveIterator middle = first + (beyond - first)/2;
switch(Traits::longest_axis(bbox))
{
case AT::CGAL_AXIS_X: // sort along x
std::nth_element(first, middle, beyond, [this](const Primitive& p1, const Primitive& p2){ return Traits::less_x(p1, p2, this->m_traits); });
break;
case AT::CGAL_AXIS_Y: // sort along y
std::nth_element(first, middle, beyond, [this](const Primitive& p1, const Primitive& p2){ return Traits::less_y(p1, p2, this->m_traits); });
break;
case AT::CGAL_AXIS_Z: // sort along z
std::nth_element(first, middle, beyond, [this](const Primitive& p1, const Primitive& p2){ return Traits::less_z(p1, p2, this->m_traits); });
break;
default:
CGAL_error();
}
}
};
Split_primitives split_primitives_object() const {return Split_primitives(*this);}
/*
* Computes the bounding box of a set of primitives
* @param first an iterator on the first primitive
* @param beyond an iterator on the past-the-end primitive
* @return the bounding box of the primitives of the iterator range
*/
class Compute_bbox {
const AABB_traits<GeomTraits,AABBPrimitive, BboxMap>& m_traits;
public:
Compute_bbox(const AABB_traits<GeomTraits,AABBPrimitive, BboxMap>& traits)
:m_traits (traits) {}
template<typename ConstPrimitiveIterator>
typename AT::Bounding_box operator()(ConstPrimitiveIterator first,
ConstPrimitiveIterator beyond) const
{
typename AT::Bounding_box bbox = m_traits.compute_bbox(*first,m_traits.bbm);
for(++first; first != beyond; ++first)
{
bbox = bbox + m_traits.compute_bbox(*first,m_traits.bbm);
}
return bbox;
}
};
Compute_bbox compute_bbox_object() const {return Compute_bbox(*this);}
/// \brief Function object using `GeomTraits::Do_intersect`.
/// In the case the query is a `CGAL::AABB_tree`, the `do_intersect()`
/// function of this tree is used.
class Do_intersect {
const AABB_traits<GeomTraits,AABBPrimitive, BboxMap>& m_traits;
public:
Do_intersect(const AABB_traits<GeomTraits,AABBPrimitive, BboxMap>& traits)
:m_traits(traits) {}
template<typename Query>
bool operator()(const Query& q, const Bounding_box& bbox) const
{
return GeomTraits().do_intersect_3_object()(q, bbox);
}
template<typename Query>
bool operator()(const Query& q, const Primitive& pr) const
{
return GeomTraits().do_intersect_3_object()(q, internal::Primitive_helper<AT>::get_datum(pr,m_traits));
}
// intersection with AABB-tree
template<typename AABBTraits>
bool operator()(const CGAL::AABB_tree<AABBTraits>& other_tree, const Primitive& pr) const
{
return other_tree.do_intersect( internal::Primitive_helper<AT>::get_datum(pr,m_traits) );
}
template<typename AABBTraits>
bool operator()(const CGAL::AABB_tree<AABBTraits>& other_tree, const Bounding_box& bbox) const
{
return other_tree.do_intersect(bbox);
}
};
Do_intersect do_intersect_object() const {return Do_intersect(*this);}
class Intersection {
const AABB_traits<GeomTraits,AABBPrimitive,BboxMap>& m_traits;
public:
Intersection(const AABB_traits<GeomTraits,AABBPrimitive,BboxMap>& traits)
:m_traits(traits) {}
template<typename Query>
std::optional< typename Intersection_and_primitive_id<Query>::Type >
operator()(const Query& query, const typename AT::Primitive& primitive) const {
auto inter_res = GeomTraits().intersect_3_object()(query, internal::Primitive_helper<AT>::get_datum(primitive,m_traits));
if (!inter_res)
return std::nullopt;
return std::make_optional( std::make_pair(*inter_res, primitive.id()) );
}
};
Intersection intersection_object() const {return Intersection(*this);}
// This should go down to the GeomTraits, i.e. the kernel
class Closest_point {
typedef typename AT::Point_3 Point;
typedef typename AT::Primitive Primitive;
const AABB_traits<GeomTraits,AABBPrimitive, BboxMap>& m_traits;
public:
Closest_point(const AABB_traits<GeomTraits,AABBPrimitive, BboxMap>& traits)
: m_traits(traits) {}
Point operator()(const Point& p, const Primitive& pr, const Point& bound) const
{
GeomTraits geom_traits;
Point closest_point = geom_traits.construct_projected_point_3_object()(
internal::Primitive_helper<AT>::get_datum(pr,m_traits), p);
return (geom_traits.compare_distance_3_object()(p, closest_point, bound) == LARGER) ?
bound : closest_point;
}
};
// This should go down to the GeomTraits, i.e. the kernel
// and the internal implementation should change its name from
// do_intersect to something like does_contain (this is what we compute,
// this is not the same do_intersect as the spherical kernel)
class Compare_distance {
typedef typename AT::Point_3 Point;
typedef typename AT::FT FT;
typedef typename AT::Primitive Primitive;
public:
CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound, Tag_true) const
{
return GeomTraits().do_intersect_3_object()
(GeomTraits().construct_sphere_3_object()
(p, GeomTraits().compute_squared_distance_3_object()(p, bound)), bb,true)?
CGAL::SMALLER : CGAL::LARGER;
}
CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound, Tag_false) const
{
return GeomTraits().do_intersect_3_object()
(GeomTraits().construct_sphere_3_object()
(p, GeomTraits().compute_squared_distance_3_object()(p, bound)), bb)?
CGAL::SMALLER : CGAL::LARGER;
}
CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound) const
{
return (*this)(p, bb, bound, Boolean_tag<internal::Has_static_filters<GeomTraits>::value>());
}
// The following functions seem unused...?
template <class Solid>
CGAL::Comparison_result operator()(const Point& p, const Solid& pr, const Point& bound) const
{
return GeomTraits().do_intersect_3_object()
(GeomTraits().construct_sphere_3_object()
(p, GeomTraits().compute_squared_distance_3_object()(p, bound)), pr)?
CGAL::SMALLER : CGAL::LARGER;
}
template <class Solid>
CGAL::Comparison_result operator()(const Point& p, const Solid& pr, const FT& sq_distance) const
{
return GeomTraits().do_intersect_3_object()
(GeomTraits().construct_sphere_3_object()(p, sq_distance),
pr) ?
CGAL::SMALLER :
CGAL::LARGER;
}
};
Closest_point closest_point_object() const {return Closest_point(*this);}
Compare_distance compare_distance_object() const {return Compare_distance();}
typedef enum { CGAL_AXIS_X = 0,
CGAL_AXIS_Y = 1,
CGAL_AXIS_Z = 2} Axis;
static Axis longest_axis(const Bounding_box& bbox);
private:
/**
* @brief Computes bounding box of one primitive
* @param pr the primitive
* @return the bounding box of the primitive \c pr
*/
template <typename PM>
Bounding_box compute_bbox(const Primitive& pr, const PM&)const
{
return get(bbm, pr.id());
}
Bounding_box compute_bbox(const Primitive& pr, const Default&)const
{
return internal::Primitive_helper<AT>::get_datum(pr,*this).bbox();
}
/// Comparison functions
static bool less_x(const Primitive& pr1, const Primitive& pr2,const AABB_traits<GeomTraits,AABBPrimitive, BboxMap>& traits)
{
return GeomTraits().less_x_3_object()( internal::Primitive_helper<AT>::get_reference_point(pr1,traits),
internal::Primitive_helper<AT>::get_reference_point(pr2,traits) );
}
static bool less_y(const Primitive& pr1, const Primitive& pr2,const AABB_traits<GeomTraits,AABBPrimitive, BboxMap>& traits)
{
return GeomTraits().less_y_3_object()( internal::Primitive_helper<AT>::get_reference_point(pr1,traits),
internal::Primitive_helper<AT>::get_reference_point(pr2,traits) );
}
static bool less_z(const Primitive& pr1, const Primitive& pr2,const AABB_traits<GeomTraits,AABBPrimitive, BboxMap>& traits)
{
return GeomTraits().less_z_3_object()( internal::Primitive_helper<AT>::get_reference_point(pr1,traits),
internal::Primitive_helper<AT>::get_reference_point(pr2,traits) );
}
}; // end class AABB_traits
//-------------------------------------------------------
// Private methods
//-------------------------------------------------------
template<typename GT, typename P, typename B>
typename AABB_traits<GT,P,B>::Axis
AABB_traits<GT,P,B>::longest_axis(const Bounding_box& bbox)
{
const double dx = bbox.xmax() - bbox.xmin();
const double dy = bbox.ymax() - bbox.ymin();
const double dz = bbox.zmax() - bbox.zmin();
if(dx>=dy)
{
if(dx>=dz)
{
return CGAL_AXIS_X;
}
else // dz>dx and dx>=dy
{
return CGAL_AXIS_Z;
}
}
else // dy>dx
{
if(dy>=dz)
{
return CGAL_AXIS_Y;
}
else // dz>dy and dy>dx
{
return CGAL_AXIS_Z;
}
}
}
/// @}
} // end namespace CGAL
#include <CGAL/enable_warnings.h>
#endif // CGAL_NO_DEPRECATED_CODE
#endif // CGAL_AABB_TRAITS_H_

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@ -0,0 +1,539 @@
// Copyright (c) 2009 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL$
// $Id$
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Stéphane Tayeb, Pierre Alliez, Camille Wormser
//
#ifndef CGAL_AABB_TRAITS_3_H_
#define CGAL_AABB_TRAITS_3_H_
#include <CGAL/license/AABB_tree.h>
#include <CGAL/disable_warnings.h>
#include <CGAL/Bbox_3.h>
#include <CGAL/Default.h>
#include <CGAL/intersections.h>
#include <CGAL/AABB_tree/internal/Has_nested_type_Shared_data.h>
#include <CGAL/AABB_tree/internal/Is_ray_intersection_geomtraits.h>
#include <CGAL/AABB_tree/internal/Primitive_helper.h>
#include <CGAL/Kernel_23/internal/Has_boolean_tags.h>
#include <optional>
/// \file AABB_traits_3.h
namespace CGAL {
namespace internal{ namespace AABB_tree {
template <class T>
struct Remove_optional { typedef T type; };
template <class T>
struct Remove_optional< ::std::optional<T> > { typedef T type; };
//helper controlling whether extra data should be stored in the AABB_tree traits class
template <class Primitive, bool has_shared_data=Has_nested_type_Shared_data<Primitive>::value>
struct AABB_traits_base;
template <class Primitive>
struct AABB_traits_base<Primitive,false>{};
template <class Primitive>
struct AABB_traits_base<Primitive,true>{
typename Primitive::Shared_data m_primitive_data;
template <typename ... T>
void set_shared_data(T&& ... t){
m_primitive_data=Primitive::construct_shared_data(std::forward<T>(t)...);
}
const typename Primitive::Shared_data& shared_data() const {return m_primitive_data;}
};
// AABB_traits_intersection_base brings in the Intersection_distance predicate,
// if GeomTraits is a model RayIntersectionGeomTraits.
template <typename GeomTraits, bool ray_intersection_geom_traits=Is_ray_intersection_geomtraits<GeomTraits>::value>
struct AABB_traits_intersection_base;
template <typename GeomTraits>
struct AABB_traits_intersection_base<GeomTraits,false>{};
template <typename GeomTraits>
struct AABB_traits_intersection_base<GeomTraits,true>{
typedef typename GeomTraits::Ray_3 Ray_3;
typedef typename GeomTraits::Point_3 Point_3;
typedef typename GeomTraits::Point_3 Point;
typedef typename GeomTraits::Point_3 Ray;
typedef typename GeomTraits::Vector_3 Vector_3;
typedef typename GeomTraits::FT FT;
typedef typename GeomTraits::Cartesian_const_iterator_3 Cartesian_const_iterator_3;
typedef typename GeomTraits::Construct_cartesian_const_iterator_3 Construct_cartesian_const_iterator_3;
typedef typename GeomTraits::Construct_source_3 Construct_source_3;
typedef typename GeomTraits::Construct_vector_3 Construct_vector_3;
// Defining Bounding_box and other types from the full AABB_traits_3
// here is might seem strange, but otherwise we would need to use
// CRTP to get access to the derived class, which would bloat the
// code more.
typedef typename CGAL::Bbox_3 Bounding_box;
struct Intersection_distance {
std::optional<FT> operator()(const Ray_3& ray, const Bounding_box& bbox) const {
FT t_near = -DBL_MAX; // std::numeric_limits<FT>::lowest(); C++1903
FT t_far = DBL_MAX;
const Construct_cartesian_const_iterator_3 construct_cartesian_const_iterator_3
= GeomTraits().construct_cartesian_const_iterator_3_object();
const Construct_source_3 construct_source_3 = GeomTraits().construct_source_3_object();
const Construct_vector_3 construct_vector_3 = GeomTraits().construct_vector_3_object();
const Point_3 source = construct_source_3(ray);
const Vector_3 direction = construct_vector_3(ray);
Cartesian_const_iterator_3 source_iter = construct_cartesian_const_iterator_3(source);
Cartesian_const_iterator_3 direction_iter = construct_cartesian_const_iterator_3(direction);
for(int i = 0; i < 3; ++i, ++source_iter, ++direction_iter) {
if(*direction_iter == 0) {
if((*source_iter < (bbox.min)(i)) || (*source_iter > (bbox.max)(i))) {
return std::nullopt;
}
} else {
FT t1 = ((bbox.min)(i) - *source_iter) / *direction_iter;
FT t2 = ((bbox.max)(i) - *source_iter) / *direction_iter;
t_near = (std::max)(t_near, (std::min)(t1, t2));
t_far = (std::min)(t_far, (std::max)(t1, t2));
// if(t1 > t2)
// std::swap(t1, t2);
// if(t1 > t_near)
// t_near = t1;
// if(t2 < t_far)
// t_far = t2;
if(t_near > t_far || t_far < FT(0.))
return std::nullopt;
}
}
if(t_near < FT(0.))
return FT(0.);
else
return t_near;
}
};
Intersection_distance intersection_distance_object() const { return Intersection_distance(); }
};
} } //end of namespace internal::AABB_tree
/// \addtogroup PkgAABBTreeRef
/// @{
// forward declaration
template< typename AABBTraits>
class AABB_tree;
/// This traits class handles any type of 3D geometric
/// primitives provided that the proper intersection tests and
/// constructions are implemented. It handles points, rays, lines and
/// segments as query types for intersection detection and
/// computations, and it handles points as query type for distance
/// queries.
///
/// \cgalModels{AABBTraits,AABBRayIntersectionTraits}
///
/// \tparam GeomTraits must be a model of the concept \ref AABBGeomTraits_3,
/// and provide the geometric types as well as the intersection tests and computations.
/// \tparam Primitive provide the type of primitives stored in the AABB_tree.
/// It is a model of the concept `AABBPrimitive` or `AABBPrimitiveWithSharedData`.
///
/// \tparam BboxMap must be a model of `ReadablePropertyMap` that has as key type a primitive id,
/// and as value type a `Bounding_box`.
/// If the type is `Default` the `Datum` must have the
/// member function `bbox()` that returns the bounding box of the primitive.
///
/// If the argument `GeomTraits` is a model of the concept \ref
/// AABBRayIntersectionGeomTraits, this class is also a model of \ref
/// AABBRayIntersectionTraits.
///
/// \sa `AABBTraits`
/// \sa `AABB_tree`
/// \sa `AABBPrimitive`
/// \sa `AABBPrimitiveWithSharedData`
template<typename GeomTraits, typename AABBPrimitive, typename BboxMap = Default>
class AABB_traits_3
#ifndef DOXYGEN_RUNNING
: public internal::AABB_tree::AABB_traits_base<AABBPrimitive>,
public internal::AABB_tree::AABB_traits_intersection_base<GeomTraits>
#endif
{
typedef typename CGAL::Object Object;
public:
typedef GeomTraits Geom_traits;
typedef AABB_traits_3<GeomTraits, AABBPrimitive, BboxMap> AT;
// AABBTraits concept types
typedef typename GeomTraits::FT FT;
typedef AABBPrimitive Primitive;
typedef typename std::pair<Object,typename Primitive::Id> Object_and_primitive_id;
typedef typename std::pair<typename GeomTraits::Point_3, typename Primitive::Id> Point_and_primitive_id;
/// `Intersection_and_primitive_id<Query>::%Type::first_type` is found according to
/// the result type of `GeomTraits::Intersect_3::operator()`. If it is
/// `std::optional<T>` then it is `T`, and the result type otherwise.
template<typename Query>
struct Intersection_and_primitive_id {
typedef decltype(
std::declval<typename GeomTraits::Intersect_3>()(
std::declval<Query>(),
std::declval<typename Primitive::Datum>())) Intersection_type;
typedef std::pair<
typename internal::AABB_tree::Remove_optional<Intersection_type>::type,
typename Primitive::Id > Type;
};
// types for search tree
/// \name Types
/// @{
/// Point query type.
typedef typename GeomTraits::Point_3 Point_3;
/// additional types for the search tree, required by the RangeSearchTraits concept
/// \bug This is not documented for now in the AABBTraits concept.
typedef typename GeomTraits::Iso_cuboid_3 Iso_cuboid_3;
/// Bounding box type.
typedef typename CGAL::Bbox_3 Bounding_box;
/// @}
typedef typename GeomTraits::Sphere_3 Sphere_3;
typedef typename GeomTraits::Cartesian_const_iterator_3 Cartesian_const_iterator_3;
typedef typename GeomTraits::Construct_cartesian_const_iterator_3 Construct_cartesian_const_iterator_3;
typedef typename GeomTraits::Construct_center_3 Construct_center_3;
typedef typename GeomTraits::Compute_squared_radius_3 Compute_squared_radius_3;
typedef typename GeomTraits::Construct_min_vertex_3 Construct_min_vertex_3;
typedef typename GeomTraits::Construct_max_vertex_3 Construct_max_vertex_3;
typedef typename GeomTraits::Construct_iso_cuboid_3 Construct_iso_cuboid_3;
BboxMap bbm;
/// Default constructor.
AABB_traits_3() { }
AABB_traits_3(BboxMap bbm)
: bbm(bbm)
{}
typedef typename GeomTraits::Compute_squared_distance_3 Squared_distance;
Squared_distance squared_distance_object() const { return GeomTraits().compute_squared_distance_3_object(); }
typedef typename GeomTraits::Equal_3 Equal_3;
Equal_3 equal_3_object() const { return GeomTraits().equal_3_object(); }
/**
* @internal
* @brief Sorts [first,beyond[
* @param first iterator on first element
* @param beyond iterator on beyond element
* @param bbox the bounding box of [first,beyond[
*
* Sorts the range defined by [first,beyond[. Sort is achieved on bbox longest
* axis, using the comparison function `<dim>_less_than` (dim in {x,y,z})
*/
class Split_primitives
{
typedef AABB_traits_3<GeomTraits,AABBPrimitive,BboxMap> Traits;
const Traits& m_traits;
public:
Split_primitives(const AABB_traits_3<GeomTraits,AABBPrimitive,BboxMap>& traits)
: m_traits(traits) {}
typedef void result_type;
template<typename PrimitiveIterator>
void operator()(PrimitiveIterator first,
PrimitiveIterator beyond,
const typename AT::Bounding_box& bbox) const
{
PrimitiveIterator middle = first + (beyond - first)/2;
switch(Traits::longest_axis(bbox))
{
case AT::CGAL_AXIS_X: // sort along x
std::nth_element(first, middle, beyond, [this](const Primitive& p1, const Primitive& p2){ return Traits::less_x(p1, p2, this->m_traits); });
break;
case AT::CGAL_AXIS_Y: // sort along y
std::nth_element(first, middle, beyond, [this](const Primitive& p1, const Primitive& p2){ return Traits::less_y(p1, p2, this->m_traits); });
break;
case AT::CGAL_AXIS_Z: // sort along z
std::nth_element(first, middle, beyond, [this](const Primitive& p1, const Primitive& p2){ return Traits::less_z(p1, p2, this->m_traits); });
break;
default:
CGAL_error();
}
}
};
Split_primitives split_primitives_object() const {return Split_primitives(*this);}
/*
* Computes the bounding box of a set of primitives
* @param first an iterator on the first primitive
* @param beyond an iterator on the past-the-end primitive
* @return the bounding box of the primitives of the iterator range
*/
class Compute_bbox {
const AABB_traits_3<GeomTraits,AABBPrimitive, BboxMap>& m_traits;
public:
Compute_bbox(const AABB_traits_3<GeomTraits,AABBPrimitive, BboxMap>& traits)
:m_traits (traits) {}
template<typename ConstPrimitiveIterator>
typename AT::Bounding_box operator()(ConstPrimitiveIterator first,
ConstPrimitiveIterator beyond) const
{
typename AT::Bounding_box bbox = m_traits.compute_bbox(*first,m_traits.bbm);
for(++first; first != beyond; ++first)
{
bbox = bbox + m_traits.compute_bbox(*first,m_traits.bbm);
}
return bbox;
}
};
Compute_bbox compute_bbox_object() const {return Compute_bbox(*this);}
/// \brief Function object using `GeomTraits::Do_intersect`.
/// In the case the query is a `CGAL::AABB_tree`, the `do_intersect()`
/// function of this tree is used.
class Do_intersect {
const AABB_traits_3<GeomTraits,AABBPrimitive, BboxMap>& m_traits;
public:
Do_intersect(const AABB_traits_3<GeomTraits,AABBPrimitive, BboxMap>& traits)
:m_traits(traits) {}
template<typename Query>
bool operator()(const Query& q, const Bounding_box& bbox) const
{
return GeomTraits().do_intersect_3_object()(q, bbox);
}
template<typename Query>
bool operator()(const Query& q, const Primitive& pr) const
{
return GeomTraits().do_intersect_3_object()(q, internal::Primitive_helper<AT>::get_datum(pr,m_traits));
}
// intersection with AABB-tree
template<typename AABBTraits>
bool operator()(const CGAL::AABB_tree<AABBTraits>& other_tree, const Primitive& pr) const
{
return other_tree.do_intersect( internal::Primitive_helper<AT>::get_datum(pr,m_traits) );
}
template<typename AABBTraits>
bool operator()(const CGAL::AABB_tree<AABBTraits>& other_tree, const Bounding_box& bbox) const
{
return other_tree.do_intersect(bbox);
}
};
Do_intersect do_intersect_object() const {return Do_intersect(*this);}
class Intersection {
const AABB_traits_3<GeomTraits,AABBPrimitive,BboxMap>& m_traits;
public:
Intersection(const AABB_traits_3<GeomTraits,AABBPrimitive,BboxMap>& traits)
:m_traits(traits) {}
template<typename Query>
std::optional< typename Intersection_and_primitive_id<Query>::Type >
operator()(const Query& query, const typename AT::Primitive& primitive) const {
auto inter_res = GeomTraits().intersect_3_object()(query, internal::Primitive_helper<AT>::get_datum(primitive,m_traits));
if (!inter_res)
return std::nullopt;
return std::make_optional( std::make_pair(*inter_res, primitive.id()) );
}
};
Intersection intersection_object() const {return Intersection(*this);}
// This should go down to the GeomTraits, i.e. the kernel
class Closest_point {
typedef typename AT::Point_3 Point;
typedef typename AT::Primitive Primitive;
const AABB_traits_3<GeomTraits,AABBPrimitive, BboxMap>& m_traits;
public:
Closest_point(const AABB_traits_3<GeomTraits,AABBPrimitive, BboxMap>& traits)
: m_traits(traits) {}
Point operator()(const Point& p, const Primitive& pr, const Point& bound) const
{
GeomTraits geom_traits;
Point closest_point = geom_traits.construct_projected_point_3_object()(
internal::Primitive_helper<AT>::get_datum(pr,m_traits), p);
return (geom_traits.compare_distance_3_object()(p, closest_point, bound) == LARGER) ?
bound : closest_point;
}
};
// This should go down to the GeomTraits, i.e. the kernel
// and the internal implementation should change its name from
// do_intersect to something like does_contain (this is what we compute,
// this is not the same do_intersect as the spherical kernel)
class Compare_distance {
typedef typename AT::Point_3 Point;
typedef typename AT::FT FT;
typedef typename AT::Primitive Primitive;
public:
CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound, Tag_true) const
{
return GeomTraits().do_intersect_3_object()
(GeomTraits().construct_sphere_3_object()
(p, GeomTraits().compute_squared_distance_3_object()(p, bound)), bb,true)?
CGAL::SMALLER : CGAL::LARGER;
}
CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound, Tag_false) const
{
return GeomTraits().do_intersect_3_object()
(GeomTraits().construct_sphere_3_object()
(p, GeomTraits().compute_squared_distance_3_object()(p, bound)), bb)?
CGAL::SMALLER : CGAL::LARGER;
}
CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound) const
{
return (*this)(p, bb, bound, Boolean_tag<internal::Has_static_filters<GeomTraits>::value>());
}
// The following functions seem unused...?
template <class Solid>
CGAL::Comparison_result operator()(const Point& p, const Solid& pr, const Point& bound) const
{
return GeomTraits().do_intersect_3_object()
(GeomTraits().construct_sphere_3_object()
(p, GeomTraits().compute_squared_distance_3_object()(p, bound)), pr)?
CGAL::SMALLER : CGAL::LARGER;
}
template <class Solid>
CGAL::Comparison_result operator()(const Point& p, const Solid& pr, const FT& sq_distance) const
{
return GeomTraits().do_intersect_3_object()
(GeomTraits().construct_sphere_3_object()(p, sq_distance),
pr) ?
CGAL::SMALLER :
CGAL::LARGER;
}
};
Closest_point closest_point_object() const {return Closest_point(*this);}
Compare_distance compare_distance_object() const {return Compare_distance();}
typedef enum { CGAL_AXIS_X = 0,
CGAL_AXIS_Y = 1,
CGAL_AXIS_Z = 2} Axis;
static Axis longest_axis(const Bounding_box& bbox);
private:
/**
* @brief Computes bounding box of one primitive
* @param pr the primitive
* @return the bounding box of the primitive \c pr
*/
template <typename PM>
Bounding_box compute_bbox(const Primitive& pr, const PM&)const
{
return get(bbm, pr.id());
}
Bounding_box compute_bbox(const Primitive& pr, const Default&)const
{
return internal::Primitive_helper<AT>::get_datum(pr,*this).bbox();
}
/// Comparison functions
static bool less_x(const Primitive& pr1, const Primitive& pr2,const AABB_traits_3<GeomTraits,AABBPrimitive, BboxMap>& traits)
{
return GeomTraits().less_x_3_object()( internal::Primitive_helper<AT>::get_reference_point(pr1,traits),
internal::Primitive_helper<AT>::get_reference_point(pr2,traits) );
}
static bool less_y(const Primitive& pr1, const Primitive& pr2,const AABB_traits_3<GeomTraits,AABBPrimitive, BboxMap>& traits)
{
return GeomTraits().less_y_3_object()( internal::Primitive_helper<AT>::get_reference_point(pr1,traits),
internal::Primitive_helper<AT>::get_reference_point(pr2,traits) );
}
static bool less_z(const Primitive& pr1, const Primitive& pr2,const AABB_traits_3<GeomTraits,AABBPrimitive, BboxMap>& traits)
{
return GeomTraits().less_z_3_object()( internal::Primitive_helper<AT>::get_reference_point(pr1,traits),
internal::Primitive_helper<AT>::get_reference_point(pr2,traits) );
}
}; // end class AABB_traits_3
//-------------------------------------------------------
// Private methods
//-------------------------------------------------------
template<typename GT, typename P, typename B>
typename AABB_traits_3<GT,P,B>::Axis
AABB_traits_3<GT,P,B>::longest_axis(const Bounding_box& bbox)
{
const double dx = bbox.xmax() - bbox.xmin();
const double dy = bbox.ymax() - bbox.ymin();
const double dz = bbox.zmax() - bbox.zmin();
if(dx>=dy)
{
if(dx>=dz)
{
return CGAL_AXIS_X;
}
else // dz>dx and dx>=dy
{
return CGAL_AXIS_Z;
}
}
else // dy>dx
{
if(dy>=dz)
{
return CGAL_AXIS_Y;
}
else // dz>dy and dy>dx
{
return CGAL_AXIS_Z;
}
}
}
/// @}
} // end namespace CGAL
#include <CGAL/enable_warnings.h>
#endif // CGAL_AABB_TRAITS_3_H_

View File

@ -76,7 +76,7 @@ namespace CGAL {
/// Type of 3D point.
typedef typename AABBTraits::Point_3 Point;
typedef typename AABBTraits::Point Point;
/// Type of input primitive.
typedef typename AABBTraits::Primitive Primitive;
@ -300,7 +300,7 @@ public:
/// returns the intersection and primitive id closest to the source point of the ray
/// query.
/// \tparam Ray must be the same as `AABBTraits::Ray_3` and
/// \tparam Ray must be the same as `AABBTraits::Ray` and
/// `do_intersect` predicates and intersections for it must be
/// defined.
/// \tparam Skip a functor with an operator
@ -331,7 +331,7 @@ public:
/// returns the primitive id closest to the source point of the ray
/// query.
/// \tparam Ray must be the same as `AABBTraits::Ray_3` and
/// \tparam Ray must be the same as `AABBTraits::Ray` and
/// `do_intersect` predicates and intersections for it must be
/// defined.
/// \tparam Skip a functor with an operator