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cgal/AABB_tree/include/CGAL/AABB_traits_2.h

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// 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_2_H_
#define CGAL_AABB_TRAITS_2_H_
#include <CGAL/license/AABB_tree.h>
#include <CGAL/disable_warnings.h>
#include <CGAL/Bbox_2.h>
#include <CGAL/Default.h>
#include <CGAL/intersections.h>
#include <CGAL/AABB_tree/internal/AABB_traits_base.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/AABB_tree/internal/Remove_optional.h>
#include <CGAL/Filtered_predicate.h>
#include <CGAL/Filtered_kernel/internal/Static_filters/Static_filter_error.h>
#include <CGAL/Filtered_kernel/internal/Static_filters/tools.h>
#include <CGAL/Kernel_23/internal/Has_boolean_tags.h>
#include <CGAL/Search_traits_2.h>
#include <optional>
/// \file AABB_traits_2.h
namespace CGAL {
namespace internal{ namespace AABB_tree {
// AABB_traits_intersection_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_2<GeomTraits>::value>
struct AABB_traits_intersection_base_2;
template <typename GeomTraits>
struct AABB_traits_intersection_base_2<GeomTraits,false>{};
template <typename GeomTraits>
struct AABB_traits_intersection_base_2<GeomTraits,true>{
template<typename AABBTree, typename SkipFunctor>
friend class AABB_ray_intersection;
private:
typedef typename GeomTraits::FT FT;
typedef typename GeomTraits::Point_2 Point;
typedef typename GeomTraits::Cartesian_const_iterator_2 Cartesian_const_iterator;
typedef typename GeomTraits::Construct_cartesian_const_iterator_2 Construct_cartesian_const_iterator;
static Construct_cartesian_const_iterator construct_cartesian_const_iterator_object() {
return GeomTraits().construct_cartesian_const_iterator_2_object();
}
public:
typedef typename GeomTraits::Ray_2 Ray;
typedef typename GeomTraits::Vector_2 Vector;
typedef typename GeomTraits::Construct_source_2 Construct_source;
typedef typename GeomTraits::Construct_vector_2 Construct_vector;
static Construct_source construct_source_object() {
return GeomTraits().construct_source_2_object();
}
static Construct_vector construct_vector_object() {
return GeomTraits().construct_vector_2_object();
}
// Defining Bounding_box and other types from the full AABB_traits_2
// here 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_2 Bounding_box;
struct Intersection_distance {
std::optional<FT> operator()(const Ray& 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 construct_cartesian_const_iterator_2
= GeomTraits().construct_cartesian_const_iterator_2_object();
const Construct_source construct_source_2 = GeomTraits().construct_source_2_object();
const Construct_vector construct_vector_2 = GeomTraits().construct_vector_2_object();
const Point source = construct_source_2(ray);
const Vector direction = construct_vector_2(ray);
Cartesian_const_iterator source_iter = construct_cartesian_const_iterator_2(source);
Cartesian_const_iterator direction_iter = construct_cartesian_const_iterator_2(direction);
for(int i = 0; i < 2; ++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(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(); }
};
template<typename GeomTraits>
class Compare_distance {
typedef typename GeomTraits::Point_2 Point;
typedef typename GeomTraits::FT FT;
/// Bounding box type.
typedef typename CGAL::Bbox_2 Bounding_box;
public:
CGAL::Comparison_result operator()(const Point& p, const Bounding_box& bb, const Point& bound) const
{
return do_intersect_circle_iso_rectangle_2
(GeomTraits().construct_circle_2_object()
(p, GeomTraits().compute_squared_distance_2_object()(p, bound)), bb) ?
CGAL::SMALLER : CGAL::LARGER;
}
template <class Solid>
CGAL::Comparison_result operator()(const Point& p, const Solid& pr, const Point& bound) const
{
return GeomTraits().do_intersect_2_object()
(GeomTraits().construct_circle_2_object()
(p, GeomTraits().compute_squared_distance_2_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_2_object()
(GeomTraits().construct_circle_2_object()(p, sq_distance),
pr) ?
CGAL::SMALLER :
CGAL::LARGER;
}
typename GeomTraits::Boolean do_intersect_circle_iso_rectangle_2(const typename GeomTraits::Circle_2& circle,
const typename GeomTraits::Iso_rectangle_2& rec) const
{
typedef typename GeomTraits::FT FT;
typedef typename GeomTraits::Point_2 Point;
Point center = circle.center();
// Check that the minimum distance to the box is smaller than the radius, otherwise there is
// no intersection. `distance` stays at 0 if the center is inside or on `rec`.
FT distance = FT(0);
if (center.x() < rec.xmin())
{
FT d = rec.xmin() - center.x();
distance += d * d;
}
else if (center.x() > rec.xmax())
{
FT d = center.x() - rec.xmax();
distance += d * d;
}
if (center.y() < rec.ymin())
{
FT d = rec.ymin() - center.y();
distance += d * d;
}
else if (center.y() > rec.ymax())
{
FT d = center.y() - rec.ymax();
distance += d * d;
}
if (distance <= circle.squared_radius())
return true;
return false;
}
};
template <typename GeomTraits, bool Has_filtered_predicates = internal::Has_filtered_predicates<GeomTraits>::value, bool Has_static_filters = internal::Has_static_filters<GeomTraits>::value>
class Compare_distance_getter_2 {};
template <typename GeomTraits>
class Compare_distance_getter_2<GeomTraits, false, false> {
// this class is in charge of checking what K provides (i.e., can we use filtered predicates, can we use statically filtered predicates, etc.)
// depending on that it defines
public:
typedef Compare_distance<GeomTraits> type;
static Compare_distance<GeomTraits> compare_distance_object() {
return Compare_distance<GeomTraits>();
}
};
template <typename GeomTraits>
class Compare_distance_getter_2<GeomTraits, true, false> {
// this class is in charge of checking what K provides (i.e., can we use filtered predicates, can we use statically filtered predicates, etc.)
// depending on that it defines
typedef GeomTraits Kernel;
typedef typename Kernel::Exact_kernel EKernel;
typedef typename Kernel::Approximate_kernel AKernel;
typedef typename Kernel::C2E C2E;
typedef typename Kernel::C2F C2F;
typedef Compare_distance<EKernel> Exact_functor;
typedef Compare_distance<AKernel> Filtered_functor;
public:
typedef Filtered_predicate<Exact_functor, Filtered_functor,
C2E, C2F> Compare_distance_pred;
typedef Compare_distance_pred type;
static Compare_distance_pred compare_distance_object() {
return Compare_distance_pred(Exact_functor(), Filtered_functor());
}
};
template <typename GeomTraits>
class Compare_distance_getter_2<GeomTraits, true, true> {
// this class is in charge of checking what K provides (i.e., can we use filtered predicates, can we use statically filtered predicates, etc.)
// depending on that it defines
class Statically_filtered_compare_distance {
public:
typedef typename GeomTraits::Point_2 Point;
typedef typename GeomTraits::FT FT;
typedef typename GeomTraits::Circle_2 Circle_2;
/// Bounding box type.
typedef CGAL::Bbox_2 Bounding_box;
template <class Solid>
CGAL::Comparison_result operator()(const Point& p, const Solid& pr, const Point& bound) const {
return Compare_distance_getter_2<GeomTraits, true, false>::compare_distance_object()(p, pr, bound);
}
template <class Solid>
CGAL::Comparison_result operator()(const Point& p, const Solid& pr, const FT& sq_distance) const {
return Compare_distance_getter_2<GeomTraits, true, false>::compare_distance_object()(p, pr, sq_distance);
}
Comparison_result operator()(const Point& p, const Bounding_box& b, const Point& bound) const {
Circle_2 s = GeomTraits().construct_circle_2_object()(p, GeomTraits().compute_squared_distance_2_object()(p, bound));
CGAL_BRANCH_PROFILER_3(std::string("semi-static failures/attempts/calls to : ") +
std::string(CGAL_PRETTY_FUNCTION), tmp);
internal::Static_filters_predicates::Get_approx<Point> get_approx; // Identity functor for all points
const Point& c = s.center();
double scx, scy, ssr;
double bxmin = b.xmin(), bymin = b.ymin(),
bxmax = b.xmax(), bymax = b.ymax();
if (internal::fit_in_double(get_approx(c).x(), scx) &&
internal::fit_in_double(get_approx(c).y(), scy) &&
internal::fit_in_double(s.squared_radius(), ssr))
{
CGAL_BRANCH_PROFILER_BRANCH_1(tmp);
if ((ssr < 1.11261183279326254436e-293) || (ssr > 2.80889552322236673473e+306)) {
CGAL_BRANCH_PROFILER_BRANCH_2(tmp);
return Compare_distance_getter_2<GeomTraits, true, false>::compare_distance_object()(p, b, bound);
}
double distance = 0;
double max1 = 0;
double double_tmp_result = 0;
double eps = 0;
if (scx < bxmin)
{
double bxmin_scx = bxmin - scx;
max1 = bxmin_scx;
distance = square(bxmin_scx);
double_tmp_result = (distance - ssr);
if ((max1 < 3.33558365626356687717e-147) || (max1 > 1.67597599124282407923e+153))
return CGAL::SMALLER;
eps = 1.99986535548615598560e-15 * (std::max)(ssr, square(max1));
if (double_tmp_result > eps)
return CGAL::LARGER;
}
else if (scx > bxmax)
{
double scx_bxmax = scx - bxmax;
max1 = scx_bxmax;
distance = square(scx_bxmax);
double_tmp_result = (distance - ssr);
if ((max1 < 3.33558365626356687717e-147) || (max1 > 1.67597599124282407923e+153))
return CGAL::SMALLER;
eps = 1.99986535548615598560e-15 * (std::max)(ssr, square(max1));
if (double_tmp_result > eps)
return CGAL::LARGER;
}
if (scy < bymin)
{
double bymin_scy = bymin - scy;
if (max1 < bymin_scy) {
max1 = bymin_scy;
}
distance += square(bymin_scy);
double_tmp_result = (distance - ssr);
if ((max1 < 3.33558365626356687717e-147) || ((max1 > 1.67597599124282407923e+153)))
return CGAL::SMALLER;
eps = 1.99986535548615598560e-15 * (std::max)(ssr, square(max1));
if (double_tmp_result > eps) {
return CGAL::LARGER;
}
}
else if (scy > bymax)
{
double scy_bymax = scy - bymax;
if (max1 < scy_bymax) {
max1 = scy_bymax;
}
distance += square(scy_bymax);
double_tmp_result = (distance - ssr);
if (((max1 < 3.33558365626356687717e-147)) || ((max1 > 1.67597599124282407923e+153)))
return CGAL::SMALLER;
eps = 1.99986535548615598560e-15 * (std::max)(ssr, square(max1));
if (double_tmp_result > eps)
return CGAL::LARGER;
}
// double_tmp_result and eps were growing all the time
// no need to test for > eps as done earlier in at least one case
return CGAL::SMALLER;
}
return Compare_distance_getter_2<GeomTraits, true, false>::compare_distance_object()(p, b, bound);
}
};
public:
typedef Statically_filtered_compare_distance type;
static Statically_filtered_compare_distance compare_distance_object() {
return Statically_filtered_compare_distance();
}
};
} } //end of namespace internal::AABB_tree
/// \addtogroup PkgAABBTreeRef
/// @{
// forward declaration
template< typename AABBTraits>
class AABB_tree;
template<typename GeomTraits, typename AABBPrimitive, typename BboxMap = Default>
class AABB_traits_2
#ifndef DOXYGEN_RUNNING
: public internal::AABB_tree::AABB_traits_base<AABBPrimitive>,
public internal::AABB_tree::AABB_traits_intersection_base_2<GeomTraits>,
public Search_traits_2<GeomTraits>
#endif
{
typedef typename CGAL::Object Object;
typedef GeomTraits Geom_traits;
public:
typedef AABB_traits_2<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_2, 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_2::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_2>()(
std::declval<Query>(),
std::declval<typename Primitive::Datum>())) Intersection_type;
typedef std::pair<
typename internal::Remove_optional<Intersection_type>::type,
typename Primitive::Id > Type;
};
// types for search tree
/// \name Types
/// @{
/// <summary>
/// point type
/// </summary>
typedef typename GeomTraits::Point_2 Point;
/// 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_rectangle_2 Iso_rectangle_2;
/// Bounding box type.
typedef typename CGAL::Bbox_2 Bounding_box;
/// @}
typedef typename GeomTraits::Circle_2 Circle_2;
typedef typename GeomTraits::Cartesian_const_iterator_2 Cartesian_const_iterator_2;
typedef typename GeomTraits::Construct_cartesian_const_iterator_2 Construct_cartesian_const_iterator_2;
typedef typename GeomTraits::Construct_center_2 Construct_center_2;
typedef typename GeomTraits::Compute_squared_radius_2 Compute_squared_radius_2;
typedef typename GeomTraits::Construct_min_vertex_2 Construct_min_vertex_2;
typedef typename GeomTraits::Construct_max_vertex_2 Construct_max_vertex_2;
typedef typename GeomTraits::Construct_iso_rectangle_2 Construct_iso_rectangle_2;
BboxMap bbm;
/// Default constructor.
AABB_traits_2() { }
AABB_traits_2(BboxMap bbm)
: bbm(bbm)
{}
typedef typename GeomTraits::Compute_squared_distance_2 Squared_distance;
Squared_distance squared_distance_object() const { return GeomTraits().compute_squared_distance_2_object(); }
typedef typename GeomTraits::Equal_2 Equal;
Equal equal_object() const { return GeomTraits().equal_2_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_2<GeomTraits,AABBPrimitive,BboxMap> Traits;
const Traits& m_traits;
public:
Split_primitives(const AABB_traits_2<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;
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_2<GeomTraits,AABBPrimitive, BboxMap>& m_traits;
public:
Compute_bbox(const AABB_traits_2<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_2<GeomTraits,AABBPrimitive, BboxMap>& m_traits;
public:
Do_intersect(const AABB_traits_2<GeomTraits,AABBPrimitive, BboxMap>& traits)
:m_traits(traits) {}
template<typename Query>
bool operator()(const Query& q, const Bounding_box& bbox) const
{
return GeomTraits().do_intersect_2_object()(q, bbox);
}
template<typename Query>
bool operator()(const Query& q, const Primitive& pr) const
{
return GeomTraits().do_intersect_2_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_2<GeomTraits,AABBPrimitive,BboxMap>& m_traits;
public:
Intersection(const AABB_traits_2<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_2_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 Point;
typedef typename AT::Primitive Primitive;
const AABB_traits_2<GeomTraits,AABBPrimitive, BboxMap>& m_traits;
public:
Closest_point(const AABB_traits_2<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_2_object()(
internal::Primitive_helper<AT>::get_datum(pr,m_traits), p);
return (geom_traits.compare_distance_2_object()(p, closest_point, bound) == LARGER) ?
bound : closest_point;
}
};
typedef typename internal::AABB_tree::Compare_distance_getter_2<GeomTraits>::type Compare_distance;
Closest_point closest_point_object() const { return Closest_point(*this); }
Compare_distance compare_distance_object() const { return internal::AABB_tree::Compare_distance_getter_2<GeomTraits>::compare_distance_object(); }
typedef enum { CGAL_AXIS_X = 0,
CGAL_AXIS_Y = 1} 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 GeomTraits().construct_bbox_2_object()(internal::Primitive_helper<AT>::get_datum(pr, *this));
}
/// Comparison functions
static bool less_x(const Primitive& pr1, const Primitive& pr2,const AABB_traits_2<GeomTraits,AABBPrimitive, BboxMap>& traits)
{
return GeomTraits().less_x_2_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_2<GeomTraits,AABBPrimitive, BboxMap>& traits)
{
return GeomTraits().less_y_2_object()( internal::Primitive_helper<AT>::get_reference_point(pr1,traits),
internal::Primitive_helper<AT>::get_reference_point(pr2,traits) );
}
}; // end class AABB_traits_2
//-------------------------------------------------------
// Private methods
//-------------------------------------------------------
template<typename GT, typename P, typename B>
typename AABB_traits_2<GT,P,B>::Axis
AABB_traits_2<GT,P,B>::longest_axis(const Bounding_box& bbox)
{
const double dx = bbox.xmax() - bbox.xmin();
const double dy = bbox.ymax() - bbox.ymin();
if(dx>=dy)
{
return CGAL_AXIS_X;
}
else
{
return CGAL_AXIS_Y;
}
}
} // end namespace CGAL
#include <CGAL/enable_warnings.h>
#endif // CGAL_AABB_TRAITS_2_H_
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