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// Copyright (c) 2019-2022 Google LLC (USA).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Alpha_wrap_3/include/CGAL/Alpha_wrap_3/internal/offset_intersection.h $
// $Id: include/CGAL/Alpha_wrap_3/internal/offset_intersection.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s) : Pierre Alliez
// Cedric Portaneri,
// Mael Rouxel-Labbé
// Andreas Fabri
// Michael Hemmer
//
#ifndef CGAL_ALPHA_WRAP_3_INTERNAL_OFFSET_INTERSECTION_H
#define CGAL_ALPHA_WRAP_3_INTERNAL_OFFSET_INTERSECTION_H
#include <CGAL/license/Alpha_wrap_3.h>
#include <CGAL/number_utils.h>
#include <boost/algorithm/clamp.hpp>
namespace CGAL {
namespace Alpha_wraps_3 {
namespace internal {
template <typename AABBTree,
typename AABBTraversalTraits>
struct AABB_tree_oracle_helper;
template <typename AABBTree, typename AABBTraversalTraits>
struct AABB_distance_oracle
{
using FT = typename AABBTree::FT;
using Point_3 = typename AABBTree::Point;
using AABB_helper = AABB_tree_oracle_helper<AABBTree, AABBTraversalTraits>;
AABB_distance_oracle(const AABBTree& tree) : tree(tree) { }
FT operator()(const Point_3& p) const
{
return approximate_sqrt(AABB_helper::squared_distance(p, tree));
}
private:
const AABBTree& tree;
};
// @todo even with EPECK, the precision cannot be 0 (otherwise it will not converge),
// thus exactness is pointless. Might as well use a cheap kernel (e.g. SC<double>), as long
// as there exists a mechanism to catch when the cheap kernel fails to converge (iterations?
// see also Tr_3::locate() or Mesh_3::Robust_intersection_traits_3.h)
template <class Kernel, class DistanceOracle>
class Offset_intersection
{
using FT = typename Kernel::FT;
using Point_2 = typename Kernel::Point_2;
using Point_3 = typename Kernel::Point_3;
using Vector_3 = typename Kernel::Vector_3;
public:
Offset_intersection(const DistanceOracle& oracle,
const FT& off,
const FT& prec,
const FT& lip)
: dist_oracle(oracle), offset(off), precision(prec), lipschitz(lip)
{ }
bool first_intersection(const Point_3& s,
const Point_3& t,
Point_3& output_pt)
{
source = s;
target = t;
seg_length = approximate_sqrt(squared_distance(s, t));
seg_unit_v = (t - s) / seg_length;
const Point_2 p0 { 0, dist_oracle(source) };
const Point_2 p1 { seg_length, dist_oracle(target) };
return recursive_dichotomic_search(p0, p1, output_pt);
}
private:
Point_3 source;
Point_3 target;
FT seg_length;
Vector_3 seg_unit_v;
DistanceOracle dist_oracle;
FT offset;
FT precision;
FT lipschitz;
template <class Point>
bool recursive_dichotomic_search(const Point_2& s, const Point_2& t,
Point& output_pt)
{
if(CGAL::abs(s.x() - t.x()) < precision)
{
if(CGAL::abs(s.y() - offset) < precision)
{
const FT x_clamp = boost::algorithm::clamp<FT>(s.x(), FT{0}, seg_length);
output_pt = source + (seg_unit_v * x_clamp);
return true;
}
return false;
}
const bool sign_s = (s.y() > offset);
const bool sign_t = (t.y() > offset);
const FT gs_a = (sign_s) ? -lipschitz : lipschitz;
const FT gs_b = s.y() - (gs_a * s.x());
const FT gt_a = (sign_t) ? lipschitz : -lipschitz;
const FT gt_b = t.y() - (gt_a * t.x());
FT ms = (offset - gs_b) / gs_a;
FT mt = (offset - gt_b) / gt_a;
// early exit if there is no intersection
if(sign_s == sign_t)
{
FT ui = (gt_b - gs_b) / (gs_a - gt_a);
const FT gs_ui = (gs_a * ui) + gs_b;
if((sign_s && (gs_ui > offset)) || (!sign_s && (gs_ui < offset)))
{
if(CGAL::abs(s.y() - offset) < precision)
{
const FT x_clamp = boost::algorithm::clamp<FT>(s.x(), FT{0}, seg_length);
output_pt = source + (seg_unit_v * x_clamp);
return true;
}
else if(CGAL::abs(t.y() - offset) < precision)
{
const FT x_clamp = boost::algorithm::clamp<FT>(t.x(), FT{0}, seg_length);
output_pt = source + (seg_unit_v * x_clamp);
return true;
}
return false;
}
else
{
ms = boost::algorithm::clamp<FT>(ms, FT{0}, seg_length);
ui = boost::algorithm::clamp<FT>(ui, FT{0}, seg_length);
mt = boost::algorithm::clamp<FT>(mt, FT{0}, seg_length);
const Point_2 ms_pt { ms, dist_oracle(source + (seg_unit_v * ms)) };
const Point_2 ui_pt { ui, dist_oracle(source + (seg_unit_v * ui)) };
const Point_2 mt_pt { mt, dist_oracle(source + (seg_unit_v * mt)) };
if(CGAL::abs(ms_pt.y() - offset) < precision)
{
const FT x_clamp = boost::algorithm::clamp<FT>(ms_pt.x(), FT{0}, seg_length);
output_pt = source + (seg_unit_v * x_clamp);
return true;
}
else if(CGAL::abs(ui_pt.y() - offset) < precision)
{
const FT x_clamp = boost::algorithm::clamp<FT>(ui_pt.x(), FT{0}, seg_length);
output_pt = source + (seg_unit_v * x_clamp);
return true;
}
else if(CGAL::abs(mt_pt.y() - offset) < precision)
{
const FT x_clamp = boost::algorithm::clamp<FT>(mt_pt.x(), FT{0}, seg_length);
output_pt = source + (seg_unit_v * x_clamp);
return true;
}
return (recursive_dichotomic_search(ms_pt, ui_pt, output_pt) ||
recursive_dichotomic_search(ui_pt, mt_pt, output_pt));
}
}
else // there is an intersection
{
if(CGAL::abs(mt - ms) <= precision) // linear approximation
{
const FT fsft_a = (t.y() - s.y()) / (t.x() - s.x());
const FT fsft_b = s.y() - fsft_a * s.x();
FT m_fsft;
if(fsft_a == FT{0})
{
if(CGAL::abs(s.y() - offset) < precision)
m_fsft = s.x();
else
return false;
}
else
{
m_fsft = (offset - fsft_b) / fsft_a;
}
m_fsft = boost::algorithm::clamp<FT>(m_fsft, FT{0}, seg_length);
output_pt = source + (seg_unit_v * m_fsft);
return true;
}
else
{
FT m = (ms + mt) / FT{2};
ms = boost::algorithm::clamp<FT>(ms, FT{0}, seg_length);
m = boost::algorithm::clamp<FT>(m, FT{0}, seg_length);
mt = boost::algorithm::clamp<FT>(mt, FT{0}, seg_length);
const Point_2 ms_pt { ms, dist_oracle(source + (seg_unit_v * ms)) };
const Point_2 m_pt { m, dist_oracle(source + (seg_unit_v * m)) };
const Point_2 mt_pt { mt, dist_oracle(source + (seg_unit_v * mt)) };
return (recursive_dichotomic_search(ms_pt, m_pt, output_pt) ||
recursive_dichotomic_search(m_pt, mt_pt, output_pt));
}
}
}
};
} // namespace internal
} // namespace Alpha_wraps_3
} // namespace CGAL
#endif // CGAL_ALPHA_WRAP_3_INTERNAL_OFFSET_INTERSECTION_H
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