LineSegment.h

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#pragma once
 
#ifdef OGDF_INCLUDE_CGAL
 
#   ifndef OGDF_GEOMETRIC_INEXACT_NUMBER_TYPE
#       define OGDF_GEOMETRIC_INEXACT_NUMBER_TYPE false
#   endif
 
#   include <ogdf/geometric/cr_min/geometry/objects/Line.h>
#   include <ogdf/geometric/cr_min/geometry/objects/Point.h>
#   include <ogdf/geometric/cr_min/geometry/objects/Ray.h>
#   include <ogdf/geometric/cr_min/geometry/objects/Vector.h>
#   include <ogdf/geometric/cr_min/tools/math.h>
 
#   include <iomanip>
#   include <limits>
 
#   include <CGAL/Segment_2.h>
 
namespace ogdf {
namespace internal {
namespace gcm {
namespace geometry {
using namespace tools;
 
template<typename kernel>
using LineSegment_t = CGAL::Segment_2<kernel>;
 
/* computes angle between this segment and @ls
    * @ls line segment
    * @return angle in [0, \Pi]
    * */
template<typename kernel>
inline typename kernel::FT angle(const LineSegment_t<kernel>& l1, const LineSegment_t<kernel>& l2) {
    OGDF_ASSERT(l1.to_vector().squared_length() > 0);
    OGDF_ASSERT(l2.to_vector().squared_length() > 0);
    return geometry::angle(l1.to_vector(), l2.to_vector());
}
 
/* compute the full angle between this segment and @ls  counterclockwise order
    * @ls line segment
    * @return angle in [0, 2 * \Pi]
    * */
template<typename kernel>
inline typename kernel::FT full_angle(const LineSegment_t<kernel>& l1,
        const LineSegment_t<kernel>& l2) {
    OGDF_ASSERT(l1.to_vector().squared_length() > 0);
    OGDF_ASSERT(l2.to_vector().squared_length() > 0);
    return full_angle(l1.to_vector(), l2.to_vector());
}
 
template<typename kernel>
inline bool turn(const LineSegment_t<kernel>& ls, const Line_t<kernel>& l) {
    return turn(ls.to_vector(), l.to_vector());
}
 
template<typename kernel>
inline bool left_turn(const LineSegment_t<kernel>& ls, const LineSegment_t<kernel>& l) {
    return left_turn(ls.to_vector(), l.to_vector());
}
 
template<typename kernel>
inline bool right_turn(const LineSegment_t<kernel>& ls, const LineSegment_t<kernel>& l) {
    return right_turn(ls.to_vector(), l.to_vector());
}
 
template<typename kernel>
inline bool turn(const LineSegment_t<kernel>& ls, const Point_t<kernel>& p) {
    return turn(ls.supporting_line(), p);
}
 
template<typename kernel>
inline bool left_turn(const LineSegment_t<kernel>& ls, const Point_t<kernel>& p) {
    return left_turn(ls.supporting_line(), p);
}
 
template<typename kernel>
inline bool right_turn(const LineSegment_t<kernel>& ls, const Point_t<kernel>& p) {
    return right_turn(ls.supporting_line(), p);
}
 
template<typename kernel>
inline typename kernel::FT squared_convex_parameter_directed(const LineSegment_t<kernel>& ls,
        const Point_t<kernel>& p) {
    OGDF_ASSERT(ls.has_on(p));
    return (ls.source() - p).squared_length() / ls.to_vector().squared_length();
}
 
template<typename kernel>
inline typename kernel::FT squared_convex_parameter(const LineSegment_t<kernel>& ls,
        const Point_t<kernel>& point) {
    OGDF_ASSERT(ls.has_on(point));
    return std::max(squared_convex_parameter_directed(ls, point),
            squared_convex_parameter_directed(ls.opposite(), point));
}
 
template<typename kernel>
inline Point_t<kernel> rel_point_at(const LineSegment_t<kernel>& ls, const typename kernel::FT l) {
    OGDF_ASSERT(0 <= l && l <= 1.0);
    return ls.source() + (ls.to_vector() * l);
}
 
template<typename kernel>
inline typename kernel::FT value_at(const LineSegment_t<kernel>& ls, const typename kernel::FT x) {
    if (ls.supporting_line().is_vertical()) {
        return std::numeric_limits<typename kernel::FT>::infinity();
    } else {
        return ls.supporting_line().y_at_x(x);
    }
}
 
template<typename kernel>
inline typename kernel::FT value_at(const LineSegment_t<kernel>& ls, const Point_t<kernel>& p) {
    if (ls.supporting_line().is_vertical()) {
        return p.y();
    } else {
        return ls.supporting_line().y_at_x(p.x());
    }
}
 
template<bool closed, typename kernel>
inline bool is_on(const LineSegment_t<kernel>& ls, const Point_t<kernel>& point) {
    if (!closed) {
        return ls.has_on(point) && ls.target() != point;
    } else {
        return ls.has_on(point);
    }
}
 
template<typename kernel>
inline bool is_on(const LineSegment_t<kernel>& ls, const Point_t<kernel>& point) {
    return is_on<false>(ls, point);
}
 
template<typename kernel>
inline bool overlapping(const LineSegment_t<kernel>& l1, const LineSegment_t<kernel>& l2) {
    const bool parallel = CGAL::parallel(l1.supporting_line(), l2.supporting_line());
    const bool on_l1 = is_on<true>(l1, l2.source()) || is_on<true>(l1, l2.target());
    const bool on_l2 = is_on<true>(l2, l1.source()) || is_on<true>(l2, l1.target());
    return (on_l1 || on_l2) && parallel;
}
 
template<typename kernel>
inline bool overlapping(const LineSegment_t<kernel>& ls, const Line_t<kernel>& line) {
    const bool parallel = parallel(ls.supporting_line(), line);
    // if both segments are parallel, then it would be sufficient to check wheather base or end is on the line
    // to be a little more robust, check if one of both is on the line. therefore small error are overseen
    const bool on_line = line.has_on(ls.source()) || line.has_on(ls.target());
    return on_line && parallel;
}
 
template<typename kernel>
inline bool do_intersect_wo_targets(const LineSegment_t<kernel>& l1, const LineSegment_t<kernel>& l2) {
    return CGAL::do_intersect(l1, l2) && !l1.has_on(l2.target()) && !l2.has_on(l1.target());
}
 
template<typename kernel>
inline bool do_intersect_open(const LineSegment_t<kernel>& l1, const LineSegment_t<kernel>& l2) {
    return CGAL::do_intersect(l1, l2) && !l1.has_on(l2.target()) && !l2.has_on(l1.target())
            && !l1.has_on(l2.source()) && !l2.has_on(l1.source());
}
 
template<typename kernel>
inline bool do_intersect_wo_target(const LineSegment_t<kernel>& l1, const Line_t<kernel>& l) {
    return CGAL::do_intersect(l1, l) && !l.has_on(l1.target());
}
 
template<typename kernel>
inline bool do_intersect_wo_target(const Line_t<kernel>& l, const LineSegment_t<kernel>& l1) {
    return geometry::do_intersect_wo_target(l1, l);
}
 
template<typename kernel>
inline bool do_intersect_wo_target(const LineSegment_t<kernel>& l1, const Ray_t<kernel>& r) {
    return CGAL::do_intersect(l1, r) && !r.has_on(l1.target());
}
 
template<typename kernel>
inline bool do_intersect_wo_target(const Ray_t<kernel>& r, const LineSegment_t<kernel>& l1) {
    return geometry::do_intersect_wo_target(l1, r);
}
 
template<typename kernel>
inline bool have_common_endpoints(const LineSegment_t<kernel>& l1, const LineSegment_t<kernel>& l2) {
    return l1.source() == l2.source() || l1.source() == l2.target() || l1.target() == l1.source()
            || l1.target() == l2.target();
}
 
template<typename kernel>
inline Point_t<kernel> get_common_endpoint(const LineSegment_t<kernel>& l1,
        const LineSegment_t<kernel>& l2) {
    OGDF_ASSERT(have_common_endpoints(l1, l2));
 
    if (l1.source() == l2.source() || l1.source() == l2.target()) {
        return l1.source();
    } else {
        return l1.target();
    }
}
 
template<typename kernel>
inline Point_t<kernel> intersect(const LineSegment_t<kernel>& l1, const LineSegment_t<kernel>& l2) {
    OGDF_ASSERT(!l1.is_degenerate());
    OGDF_ASSERT(!l2.is_degenerate());
 
    auto result = CGAL::intersection(l1, l2);
    if (!result) {
        return Point_t<kernel>(std::numeric_limits<double>::max(),
                std::numeric_limits<double>::max());
    }
 
    Point_t<kernel> intersection;
    if (boost::get<LineSegment_t<kernel>>(&*result)) {
        auto s = boost::get<LineSegment_t<kernel>>(&*result);
        intersection = s->source();
    } else if (boost::get<Point_t<kernel>>(&*result)) {
        intersection = *boost::get<Point_t<kernel>>(&*result);
    }
    //TODO
    //OGDF_ASSERT(is_on<true>(l1, intersection));
    //OGDF_ASSERT(is_on<true>(l2, intersection));
    return intersection;
}
 
template<typename kernel>
inline Point_t<kernel> intersect(const LineSegment_t<kernel>& l1, const Line_t<kernel>& l2) {
    OGDF_ASSERT(!l1.is_degenerate());
    OGDF_ASSERT(!l2.is_degenerate());
    auto result = CGAL::intersection(l1, l2);
    if (!result) {
        return Point_t<kernel>(std::numeric_limits<unsigned int>::max(),
                std::numeric_limits<unsigned int>::max());
    }
 
    Point_t<kernel> intersection;
    if (boost::get<LineSegment_t<kernel>>(&*result)) {
        auto s = boost::get<LineSegment_t<kernel>>(&*result);
        intersection = s->source();
    } else {
        intersection = *boost::get<Point_t<kernel>>(&*result);
    }
    OGDF_ASSERT(is_on<true>(l1, intersection));
    OGDF_ASSERT(l2.has_on(intersection));
    return intersection;
}
 
template<typename kernel>
inline Point_t<kernel> intersect(const Line_t<kernel>& l1, const LineSegment_t<kernel>& l2) {
    return intersect(l2, l1);
}
 
template<typename kernel>
inline Point_t<kernel> intersect(const LineSegment_t<kernel>& l1, const Ray_t<kernel>& r) {
    OGDF_ASSERT(!l1.is_degenerate());
    OGDF_ASSERT(!r.is_degenerate());
 
    auto result = CGAL::intersection(l1, r);
    if (!result) {
        return Point_t<kernel>(std::numeric_limits<unsigned int>::max(),
                std::numeric_limits<unsigned int>::max());
    }
 
 
    Point_t<kernel> intersection;
    if (boost::get<LineSegment_t<kernel>>(&*result)) {
        auto s = boost::get<LineSegment_t<kernel>>(&*result);
        intersection = s->source();
    } else {
        intersection = *boost::get<Point_t<kernel>>(&*result);
    }
    OGDF_ASSERT(OGDF_GEOMETRIC_INEXACT_NUMBER_TYPE || is_on<true>(l1, intersection));
    OGDF_ASSERT(OGDF_GEOMETRIC_INEXACT_NUMBER_TYPE || r.has_on(intersection));
    return intersection;
}
 
template<typename kernel>
inline Point_t<kernel> intersect(const Ray_t<kernel>& l1, const LineSegment_t<kernel>& l2) {
    return intersect(l2, l1);
}
 
template<typename kernel>
inline typename kernel::FT order_along_seg(const LineSegment_t<kernel>& reference
 
        ,
        const LineSegment_t<kernel>& l_1, const LineSegment_t<kernel>& l_2) {
    auto cross = [&](const Vector_t<kernel>& v_1, const Vector_t<kernel>& v_2) {
        return v_1.x() * v_2.y() - v_1.y() * v_2.x();
    };
 
    auto s = reference.target() - reference.source();
    auto r_1 = l_1.target() - l_1.source();
    auto r_2 = l_2.target() - l_2.source();
 
    auto c_1 = cross(reference.source() - l_1.source(), s);
    auto c_2 = cross(reference.source() - l_2.source(), s);
 
    auto d_1 = cross(r_1, s);
    auto d_2 = cross(r_2, s);
 
    return c_1 * d_2 - c_2 * d_1;
}
 
template<typename kernel>
void serialize(const LineSegment_t<kernel>& ls, std::ostream& os) {
    serialize(ls.source(), os);
    serialize(ls.target(), os);
}
 
template<typename kernel>
inline bool operator<(const LineSegment_t<kernel>& l1, const LineSegment_t<kernel>& l2) {
    return l1.source() < l2.source() || (l1.source() == l2.source() && l1.target() < l2.target());
}
 
template<typename Kernel, typename T>
LineSegment_t<Kernel> cast(const LineSegment_t<T>& segment) {
    return {cast<Kernel>(segment.source()), cast<Kernel>(segment.target())};
}
 
} //namespace
}
}
}
 
#endif