segment.hpp

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#pragma once
 
#include "implementation/orientation.hpp"

 
#include <array>
#include <cassert>
#include <cmath>
#include <concepts>
#include <cstddef>
#include <functional>
#include <ostream>
#include <type_traits>
#include <utility>
#include <variant>
#include <vector>
#include <optional>
 
 
namespace pgl {
 
template <class PointType = Point<>, class Label>
struct Segment;
 
Segment() -> Segment<Point<>, NoLabel>;
 
template <class PointType>
Segment(PointType, PointType) -> Segment<PointType, NoLabel>;
 
template <class PointType, class A>
Segment(PointType, PointType, A) -> Segment<PointType, std::decay_t<A>>;
 
template <class Number>
Segment(Number, Number, Number, Number) -> Segment<Point<Number>, NoLabel>;

template <class TPoint, class TLabel>
struct Segment {
    using PointType = TPoint;
    using NumberType = PointType::NumberType;
    using LabelType = TLabel;
 
    static_assert(detail::is_point_v<PointType>, "Segment requires pgl::Point endpoints");

    constexpr Segment() = default;

    constexpr Segment(PointType first, PointType second) {
        if (second < first) {
            std::swap(first, second);
        }
        points_[0] = std::move(first);
        points_[1] = std::move(second);
    }

    constexpr Segment(NumberType x1, NumberType y1, NumberType x2, NumberType y2)
        : Segment(PointType(x1, y1), PointType(x2, y2)) {}

    template <class A>
        requires(detail::has_label_v<LabelType> && std::constructible_from<LabelType, A&&>)
    constexpr Segment(PointType first, PointType second, A&& label)
        : Segment(std::move(first), std::move(second)) {
        label_ = std::forward<A>(label);
    }

    template <class A>
        requires(detail::has_label_v<LabelType> && std::constructible_from<LabelType, A&&>)
    constexpr Segment(NumberType x1, NumberType y1, NumberType x2, NumberType y2, A&& label)
        : Segment(PointType(x1, y1), PointType(x2, y2), std::forward<A>(label)) {}

    template<PointConcept OtherPointType, class OtherLabelType>
        requires(std::constructible_from<PointType, const OtherPointType&>)
    constexpr Segment(const Segment<OtherPointType, OtherLabelType>& other)
        : Segment(PointType(other.min()), PointType(other.max())) {
        label_ = detail::copyLabel<LabelType>(other);
    }

    template<PointConcept OtherPointType, class OtherLabelType>
        requires(std::constructible_from<PointType, const OtherPointType&>)
    constexpr Segment& operator=(const Segment<OtherPointType, OtherLabelType>& other) {
        points_[0] = PointType(other.min());
        points_[1] = PointType(other.max());
        label_ = detail::copyLabel<LabelType>(other);
        return *this;
    }

    constexpr const PointType& operator[](std::size_t index) const {
        assert(index < size());
        return points_[index];
    }

    static constexpr std::size_t size() {
        return 2;
    }

    constexpr const PointType& get(std::ptrdiff_t index) const {
        const std::ptrdiff_t n = static_cast<std::ptrdiff_t>(size());
        return (*this)[static_cast<std::size_t>(((index % n) + n) % n)];
    }

    constexpr std::ptrdiff_t index(const PointType& point) const {
        for (std::ptrdiff_t i = 0; i < static_cast<std::ptrdiff_t>(size()); ++i) {
            if ((*this)[static_cast<std::size_t>(i)] == point) {
                return i;
            }
        }
        return -1;
    }

    constexpr const PointType& min() const {
        return points_[0];
    }

    constexpr const PointType& max() const {
        return points_[1];
    }

    constexpr auto begin() const {
        return points_.cbegin();
    }

    constexpr auto cbegin() const {
        return points_.cbegin();
    }

    constexpr auto end() const {
        return points_.cend();
    }

    constexpr auto cend() const {
        return points_.cend();
    }

    constexpr bool operator==(const Segment& other) const {
        return points_ == other.points_;
    }

    template<AnyShapeConcept OtherShape>
    [[nodiscard]] constexpr bool samePointSet(const OtherShape& other) const;

    constexpr auto operator<=>(const Segment& other) const {
        return points_ <=> other.points_;
    }

    template <class A = LabelType>
        requires(detail::has_label_v<A>)
    constexpr A& label() const {
        return label_;
    }

    [[nodiscard]] constexpr explicit operator Line<PointType>() const;

    [[nodiscard]] constexpr Line<PointType> asLine() const {
        return static_cast<Line<PointType>>(*this);
    }

    [[nodiscard]] constexpr HalfplaneIntersection<PointType> asHalfplaneIntersection() const {
        return HalfplaneIntersection<PointType>(*this);
    }

    [[nodiscard]] constexpr Segment rotated90(int k = 1) const;

    constexpr void rotate90(int k = 1);

    template <class OtherNumber>
    [[nodiscard]] constexpr Segment scaledUpX(const OtherNumber scalar) const;

    template <class OtherNumber>
    constexpr void scaleUpX(const OtherNumber scalar);

    template <class OtherNumber>
    [[nodiscard]] constexpr Segment scaledUpY(const OtherNumber scalar) const;

    template <class OtherNumber>
    constexpr void scaleUpY(const OtherNumber scalar);

    template <class OtherNumber>
    [[nodiscard]] constexpr Segment scaledDownX(const OtherNumber scalar) const;

    template <class OtherNumber>
    constexpr void scaleDownX(const OtherNumber scalar);

    template <class OtherNumber>
    [[nodiscard]] constexpr Segment scaledDownY(const OtherNumber scalar) const;

    template <class OtherNumber>
    constexpr void scaleDownY(const OtherNumber scalar);
 

    [[nodiscard]] constexpr bool isDegenerate() const;

    [[nodiscard]] constexpr bool isPoint() const;

    [[nodiscard]] constexpr std::optional<PointType> getIfPoint() const;

    [[nodiscard]] constexpr bool isUndefined() const;

    [[nodiscard]] constexpr bool isVertical() const;

    [[nodiscard]] constexpr bool isHorizontal() const;

    template <class ResultNumber = NumberType>
    [[nodiscard]] constexpr ResultNumber area() const;

    [[nodiscard]] constexpr NumberType twiceArea() const;

    [[nodiscard]] constexpr auto squaredLength() const;

    template <class ApproximateNumber = double>
    [[nodiscard]] ApproximateNumber length() const;

    [[nodiscard]] constexpr auto lengthL1() const;

    [[nodiscard]] constexpr auto lengthLInf() const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool verticesContain(const OtherPoint& point) const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool containsEndpoint(const OtherPoint& point) const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool boundaryContains(const OtherPoint& point) const;

    // The boundary of a segment is exactly its two endpoints, a finite point
    // set, so it contains no positive-length or two-dimensional shape.
    template<SegmentConcept OtherSegment>
    [[nodiscard]] constexpr bool boundaryContains(const OtherSegment& other) const {
        return detail::reduceDegenerateToPoint(
            other, [this](const auto& vertex) { return this->boundaryContains(vertex); });
    }

    template<OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr bool boundaryContains(const OtherOrientedSegment& other) const {
        return detail::reduceDegenerateToPoint(
            other, [this](const auto& vertex) { return this->boundaryContains(vertex); });
    }

    template<LineConcept OtherLine>
    [[nodiscard]] constexpr bool boundaryContains(const OtherLine&) const { return false; }
    template<OrientedLineConcept OtherOrientedLine>
    [[nodiscard]] constexpr bool boundaryContains(const OtherOrientedLine&) const { return false; }
    template<RayConcept OtherRay>
    [[nodiscard]] constexpr bool boundaryContains(const OtherRay&) const { return false; }
    template<HalfplaneConcept OtherHalfplane>
    [[nodiscard]] constexpr bool boundaryContains(const OtherHalfplane&) const { return false; }
    template<RectangleConcept OtherRectangle>
    [[nodiscard]] constexpr bool boundaryContains(const OtherRectangle& other) const {
        return detail::reduceDegenerateToPoint(
            other, [this](const auto& vertex) { return this->boundaryContains(vertex); });
    }

    template<TriangleConcept OtherTriangle>
    [[nodiscard]] constexpr bool boundaryContains(const OtherTriangle& other) const {
        return detail::reduceDegenerateToPoint(
            other, [this](const auto& vertex) { return this->boundaryContains(vertex); });
    }

    template<ConvexConcept OtherConvex>
    [[nodiscard]] constexpr bool boundaryContains(const OtherConvex& other) const {
        return detail::reduceDegenerateToPoint(
            other, [this](const auto& vertex) { return this->boundaryContains(vertex); });
    }

    template<PolygonConcept OtherPolygon>
    [[nodiscard]] constexpr bool boundaryContains(const OtherPolygon& other) const {
        return detail::reduceDegenerateToPoint(
            other, [this](const auto& vertex) { return this->boundaryContains(vertex); });
    }

    template<DiskConcept OtherDisk>
    [[nodiscard]] constexpr bool boundaryContains(const OtherDisk& other) const {
        return detail::reduceDegenerateToPoint(
            other, [this](const auto& vertex) { return this->boundaryContains(vertex); });
    }

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool containsCollinear(const OtherPoint& point) const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool contains(const OtherPoint& point) const;

    template<SegmentConcept OtherSegment>
    [[nodiscard]] constexpr bool contains(const OtherSegment& other) const;

    template<OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr bool contains(const OtherOrientedSegment& other) const;

    template<LineConcept OtherLine>
    [[nodiscard]] constexpr bool contains(const OtherLine& other) const;

    template<OrientedLineConcept OtherOrientedLine>
    [[nodiscard]] constexpr bool contains(const OtherOrientedLine& other) const;

    template<RayConcept OtherRay>
    [[nodiscard]] constexpr bool contains(const OtherRay& other) const;

    template<HalfplaneConcept OtherHalfplane>
    [[nodiscard]] constexpr bool contains(const OtherHalfplane& other) const;

    template<RectangleConcept OtherRectangle>
    [[nodiscard]] constexpr bool contains(const OtherRectangle& other) const;

    template<TriangleConcept OtherTriangle>
    [[nodiscard]] constexpr bool contains(const OtherTriangle& other) const;

    template<ConvexConcept OtherConvex>
    [[nodiscard]] constexpr bool contains(const OtherConvex& other) const;

    template<PolygonConcept OtherPolygon>
    [[nodiscard]] constexpr bool contains(const OtherPolygon& other) const;

    template<DiskConcept OtherDisk>
    [[nodiscard]] constexpr bool contains(const OtherDisk& other) const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool contains(const Shape<OtherPoint>& other) const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool boundaryContains(const Shape<OtherPoint>& other) const;
 
    // The empty set is a subset of every shape (contained in all of them) and
    // disjoint from all of them, so containment is true while separation is
    // false. These overloads let an EmptyShape flow through Shape's variant
    // dispatch without special-casing.
    template <class EmptyPoint>
    [[nodiscard]] constexpr bool contains(const EmptyShape<EmptyPoint>&) const {
        return true;
    }

    template <class EmptyPoint>
    [[nodiscard]] constexpr bool boundaryContains(const EmptyShape<EmptyPoint>&) const {
        return true;
    }

    template <class EmptyPoint>
    [[nodiscard]] constexpr bool interiorContains(const EmptyShape<EmptyPoint>&) const {
        return true;
    }

    template <class EmptyPoint>
    [[nodiscard]] constexpr bool separates(const EmptyShape<EmptyPoint>&) const {
        return false;
    }

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool interiorContains(const OtherPoint& point) const;

    template<SegmentConcept OtherSegment>
    [[nodiscard]] constexpr bool interiorContains(const OtherSegment& other) const;

    template<OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr bool interiorContains(const OtherOrientedSegment& other) const;

    template<TriangleConcept OtherTriangle>
    [[nodiscard]] constexpr bool interiorContains(const OtherTriangle& other) const;
 
    // A segment is one-dimensional: its interior is the open segment, which
    // cannot contain any unbounded or two-dimensional shape.
    template<LineConcept OtherLine>
    [[nodiscard]] constexpr bool interiorContains(const OtherLine&) const { return false; }
    template<OrientedLineConcept OtherOrientedLine>
    [[nodiscard]] constexpr bool interiorContains(const OtherOrientedLine&) const { return false; }
    template<RayConcept OtherRay>
    [[nodiscard]] constexpr bool interiorContains(const OtherRay&) const { return false; }
    template<HalfplaneConcept OtherHalfplane>
    [[nodiscard]] constexpr bool interiorContains(const OtherHalfplane&) const { return false; }
    template<RectangleConcept OtherRectangle>
    [[nodiscard]] constexpr bool interiorContains(const OtherRectangle& other) const {
        return detail::reduceDegenerateGuarded(
            other, [this](const auto& carrier) { return this->interiorContains(carrier); });
    }

    template<ConvexConcept OtherConvex>
    [[nodiscard]] constexpr bool interiorContains(const OtherConvex& other) const {
        return detail::reduceDegenerateGuarded(
            other, [this](const auto& carrier) { return this->interiorContains(carrier); });
    }

    template<PolygonConcept OtherPolygon>
    [[nodiscard]] constexpr bool interiorContains(const OtherPolygon& other) const {
        return detail::reduceDegenerate(
            other, [this](const auto& carrier) { return this->interiorContains(carrier); });
    }

    template<DiskConcept OtherDisk>
    [[nodiscard]] constexpr bool interiorContains(const OtherDisk& other) const {
        return detail::reduceDegenerate(
            other, [this](const auto& carrier) { return this->interiorContains(carrier); });
    }

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool interiorContains(const Shape<OtherPoint>& other) const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool collinear(const OtherPoint& point) const;

    template<SegmentConcept OtherSegment>
    [[nodiscard]] constexpr bool collinear(const OtherSegment& other) const;

    template<OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr bool collinear(const OtherOrientedSegment& other) const;

    template<LineConcept OtherLine>
    [[nodiscard]] constexpr bool collinear(const OtherLine& other) const;

    template<OrientedLineConcept OtherOrientedLine>
    [[nodiscard]] constexpr bool collinear(const OtherOrientedLine& other) const;

    template<RayConcept OtherRay>
    [[nodiscard]] constexpr bool collinear(const OtherRay& other) const;

    template <class ResultNumber = division_result_t<NumberType>>
    [[nodiscard]] constexpr ResultNumber slope() const;

    template<SegmentConcept OtherSegment>
    [[nodiscard]] constexpr bool parallel(const OtherSegment& other) const;

    template<OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr bool parallel(const OtherOrientedSegment& other) const;

    template<LineConcept OtherLine>
    [[nodiscard]] constexpr bool parallel(const OtherLine& other) const;

    template<OrientedLineConcept OtherOrientedLine>
    [[nodiscard]] constexpr bool parallel(const OtherOrientedLine& other) const;

    template<RayConcept OtherRay>
    [[nodiscard]] constexpr bool parallel(const OtherRay& other) const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool intersects(const OtherPoint& other) const;

    template<SegmentConcept OtherSegment>
    [[nodiscard]] constexpr bool intersects(const OtherSegment& other) const;

    [[nodiscard]] constexpr bool intersects(const Shape<PointType>& other) const;

    template<typename OtherShape>
        requires (!PointConcept<OtherShape> && detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
    [[nodiscard]] constexpr bool intersects(const OtherShape& other) const {
        return other.intersects(*this);
    }

    template <class EmptyPoint>
    [[nodiscard]] constexpr bool intersects(const EmptyShape<EmptyPoint>&) const {
        return false;
    }

    template <class ResultNumber = NumberType, PointConcept OtherPoint>
    [[nodiscard]] constexpr std::optional<Point<ResultNumber, typename PointType::LabelType>>
    intersection(const OtherPoint& other) const;

    template <class ResultNumber = division_result_t<NumberType>, SegmentConcept OtherSegment>
    [[nodiscard]] constexpr std::optional<std::variant<Point<ResultNumber, typename PointType::LabelType>, Segment<Point<ResultNumber, typename PointType::LabelType>>>>
    intersection(const OtherSegment& other) const;

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires (!PointConcept<OtherShape>
                  && (detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
                  && requires(const OtherShape& o, const Segment& self) {
                         o.template intersection<ResultNumber>(self);
                     })
    [[nodiscard]] constexpr auto intersection(const OtherShape& other) const {
        return other.template intersection<ResultNumber>(*this);
    }

    template <class ResultNumber = NumberType, class EmptyPoint>
    [[nodiscard]] constexpr EmptyShape<EmptyPoint> intersection(const EmptyShape<EmptyPoint>&) const {
        return {};
    }

    template <class ResultNumber = division_result_t<NumberType>, class OtherNumber>
    [[nodiscard]] constexpr std::optional<ResultNumber>
    yAtX(const OtherNumber &x) const;

    template <class ResultNumber = division_result_t<NumberType>, class OtherNumber>
    [[nodiscard]] constexpr std::optional<ResultNumber>
    xAtY(const OtherNumber &y) const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool separates(const OtherPoint& other) const;

    template<SegmentConcept OtherSegment>
    [[nodiscard]] constexpr bool separates(const OtherSegment& other) const;

    template<OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr bool separates(const OtherOrientedSegment& other) const;

    template<LineConcept OtherLine>
    [[nodiscard]] constexpr bool separates(const OtherLine& other) const;

    template<OrientedLineConcept OtherOrientedLine>
    [[nodiscard]] constexpr bool separates(const OtherOrientedLine& other) const;

    template<RayConcept OtherRay>
    [[nodiscard]] constexpr bool separates(const OtherRay& other) const;

    template<RectangleConcept OtherRectangle>
    [[nodiscard]] constexpr bool separates(const OtherRectangle& other) const;

    template<TriangleConcept OtherTriangle>
    [[nodiscard]] constexpr bool separates(const OtherTriangle& other) const;

    template<HalfplaneConcept OtherHalfplane>
    [[nodiscard]] constexpr bool separates(const OtherHalfplane& other) const;

    template<ConvexConcept OtherConvex>
    [[nodiscard]] constexpr bool separates(const OtherConvex& other) const;

    template<PolygonConcept OtherPolygon>
    [[nodiscard]] constexpr bool separates(const OtherPolygon& other) const;

    template<MonotoneChainConcept OtherChain>
    [[nodiscard]] constexpr bool contains(const OtherChain& other) const;

    template<MonotoneChainConcept OtherChain>
    [[nodiscard]] constexpr bool boundaryContains(const OtherChain& other) const {
        return detail::reduceDegenerateToPoint(
            other, [this](const auto& vertex) { return this->boundaryContains(vertex); });
    }

    template<MonotoneChainConcept OtherChain>
    [[nodiscard]] constexpr bool interiorContains(const OtherChain& other) const;

    template<MonotoneChainConcept OtherChain>
    [[nodiscard]] constexpr bool separates(const OtherChain& other) const;

    template<PolylineConcept OtherPolyline>
    [[nodiscard]] constexpr bool contains(const OtherPolyline& other) const;

    template<PolylineConcept OtherPolyline>
    [[nodiscard]] constexpr bool boundaryContains(const OtherPolyline& other) const {
        return detail::reduceDegenerateToPoint(
            other, [this](const auto& vertex) { return this->boundaryContains(vertex); });
    }

    template<PolylineConcept OtherPolyline>
    [[nodiscard]] constexpr bool interiorContains(const OtherPolyline& other) const;

    template<PolylineConcept OtherPolyline>
    [[nodiscard]] constexpr bool separates(const OtherPolyline& other) const;

    template<HalfplaneIntersectionConcept OtherRegion>
    [[nodiscard]] constexpr bool contains(const OtherRegion& other) const;

    template<HalfplaneIntersectionConcept OtherRegion>
    [[nodiscard]] constexpr bool boundaryContains(const OtherRegion& other) const;

    template<HalfplaneIntersectionConcept OtherRegion>
    [[nodiscard]] constexpr bool interiorContains(const OtherRegion& other) const;

    template<HalfplaneIntersectionConcept OtherRegion>
    [[nodiscard]] constexpr bool separates(const OtherRegion& other) const;

    template<PolygonWithHolesConcept OtherRegion>
    [[nodiscard]] constexpr bool contains(const OtherRegion& other) const;

    template<PolygonWithHolesConcept OtherRegion>
    [[nodiscard]] constexpr bool boundaryContains(const OtherRegion& other) const;

    template<PolygonWithHolesConcept OtherRegion>
    [[nodiscard]] constexpr bool interiorContains(const OtherRegion& other) const;

    template<PolygonWithHolesConcept OtherRegion>
    [[nodiscard]] bool separates(const OtherRegion& other) const;
 
    // -------------------------------------------------------------------------
    // A set of regions
    //
    // It outranks every other shape, so the symmetric relations reach it through
    // the rank-based forwarders and only the asymmetric ones are answered here.
    // A set is the union of its components, so it is contained exactly when
    // every component is — no matter what this shape is.

    template<PolygonSetConcept OtherSet>
    [[nodiscard]] constexpr bool contains(const OtherSet& other) const {
        for (const auto& component : other) {
            if (!contains(component)) {
                return false;
            }
        }
        return true;
    }

    template<PolygonSetConcept OtherSet>
    [[nodiscard]] constexpr bool boundaryContains(const OtherSet& other) const {
        for (const auto& component : other) {
            if (!boundaryContains(component)) {
                return false;
            }
        }
        return true;
    }

    template<PolygonSetConcept OtherSet>
    [[nodiscard]] constexpr bool interiorContains(const OtherSet& other) const {
        for (const auto& component : other) {
            if (!interiorContains(component)) {
                return false;
            }
        }
        return true;
    }

    template<PolygonSetConcept OtherSet>
    [[nodiscard]] bool separates(const OtherSet& other) const;

    template<DiskConcept OtherDisk>
    [[nodiscard]] constexpr bool separates(const OtherDisk& other) const;

    [[nodiscard]] constexpr bool separates(const Shape<PointType>& other) const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool interiorsIntersect(const OtherPoint& other) const;

    template<SegmentConcept OtherSegment>
    [[nodiscard]] constexpr bool interiorsIntersect(const OtherSegment& other) const;

    template<typename OtherShape>
        requires (!PointConcept<OtherShape> && detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
    [[nodiscard]] constexpr bool interiorsIntersect(const OtherShape& other) const {
        return other.interiorsIntersect(*this);
    }

    template <class EmptyPoint>
    [[nodiscard]] constexpr bool interiorsIntersect(const EmptyShape<EmptyPoint>&) const {
        return false;
    }

    [[nodiscard]] constexpr bool interiorsIntersect(const Shape<PointType>& other) const;

    template<SegmentConcept OtherSegment>
    [[nodiscard]] constexpr bool crosses(const OtherSegment& other) const;

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool crosses(const OtherPoint& other) const;

    template<typename OtherShape>
        requires (!PointConcept<OtherShape> && detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
    [[nodiscard]] constexpr bool crosses(const OtherShape& other) const {
        return other.crosses(*this);
    }

    template <class EmptyPoint>
    [[nodiscard]] constexpr bool crosses(const EmptyShape<EmptyPoint>&) const {
        return false;
    }

    [[nodiscard]] constexpr bool crosses(const Shape<PointType>& other) const;

    template <class ResultNumber = division_result_t<NumberType>, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto squaredDistance(const OtherPoint& point) const;

    template <class ResultNumber = division_result_t<NumberType>, SegmentConcept OtherSegment>
    [[nodiscard]] constexpr auto squaredDistance(const OtherSegment& other) const;

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires ((detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
                  && requires(const OtherShape& o, const Segment& self) {
                         o.template squaredDistance<ResultNumber>(self);
                     })
    [[nodiscard]] constexpr auto squaredDistance(const OtherShape& other) const {
        return other.template squaredDistance<ResultNumber>(*this);
    }

    template <class ResultNumber = double, class DiskPointType, class DiskLabel>
    [[nodiscard]] detail::floating_result_t<ResultNumber> squaredDistance(const Disk<DiskPointType, DiskLabel>& disk) const {
        return disk.template squaredDistance<ResultNumber>(*this);
    }

    template <class ResultNumber = NumberType, BoundedPolygonalConcept OtherShape>
        requires detail::ClosestPairConcept<Segment<TPoint, TLabel>, OtherShape>
    [[nodiscard]] constexpr auto closestSegments(const OtherShape& other) const;

    template <class ResultNumber = division_result_t<NumberType>, class OtherShape>
        requires detail::ClosestPointsPairConcept<Segment<TPoint, TLabel>, OtherShape>
    [[nodiscard]] constexpr auto closestPoints(const OtherShape& other) const;

    template <class ResultNumber = division_result_t<NumberType>, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto distanceL1(const OtherPoint& point) const;

    template <class ResultNumber = division_result_t<NumberType>, SegmentConcept OtherSegment>
    [[nodiscard]] constexpr auto distanceL1(const OtherSegment& other) const;

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires ((detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
                  && requires(const OtherShape& o, const Segment& self) {
                         o.template distanceL1<ResultNumber>(self);
                     })
    [[nodiscard]] constexpr auto distanceL1(const OtherShape& other) const {
        return other.template distanceL1<ResultNumber>(*this);
    }

    template <class ResultNumber = division_result_t<NumberType>, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto intersection(const Shape<OtherPoint>& other) const {
        return other.template intersection<ResultNumber>(*this);
    }

    template <class ResultNumber = double, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto distanceL1(const Shape<OtherPoint>& other) const {
        return other.template distanceL1<ResultNumber>(*this);
    }

    template <class ResultNumber = division_result_t<NumberType>, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto distanceLInf(const OtherPoint& point) const;

    template <class ResultNumber = division_result_t<NumberType>, SegmentConcept OtherSegment>
    [[nodiscard]] constexpr auto distanceLInf(const OtherSegment& other) const;

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires ((detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
                  && requires(const OtherShape& o, const Segment& self) {
                         o.template distanceLInf<ResultNumber>(self);
                     })
    [[nodiscard]] constexpr auto distanceLInf(const OtherShape& other) const {
        return other.template distanceLInf<ResultNumber>(*this);
    }

    template <class ResultNumber = double, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto distanceLInf(const Shape<OtherPoint>& other) const {
        return other.template distanceLInf<ResultNumber>(*this);
    }

    template <class ResultNumber = division_result_t<NumberType>, SegmentConcept OtherSegment>
    [[nodiscard]] constexpr auto hausdorffDistanceL1(const OtherSegment& other) const;

    template <class ResultNumber = NumberType, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto hausdorffDistanceL1(const OtherPoint& point) const;

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires ((detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
                  && requires(const OtherShape& o, const Segment& self) {
                         o.template hausdorffDistanceL1<ResultNumber>(self);
                     })
    [[nodiscard]] constexpr auto hausdorffDistanceL1(const OtherShape& other) const {
        return other.template hausdorffDistanceL1<ResultNumber>(*this);
    }

    template <class ResultNumber = division_result_t<NumberType>, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto hausdorffDistanceL1(const Shape<OtherPoint>& other) const {
        return other.template hausdorffDistanceL1<ResultNumber>(*this);
    }

    template <class ResultNumber = division_result_t<NumberType>, SegmentConcept OtherSegment>
    [[nodiscard]] constexpr auto hausdorffDistanceLInf(const OtherSegment& other) const;

    template <class ResultNumber = NumberType, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto hausdorffDistanceLInf(const OtherPoint& point) const;

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires ((detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
                  && requires(const OtherShape& o, const Segment& self) {
                         o.template hausdorffDistanceLInf<ResultNumber>(self);
                     })
    [[nodiscard]] constexpr auto hausdorffDistanceLInf(const OtherShape& other) const {
        return other.template hausdorffDistanceLInf<ResultNumber>(*this);
    }

    template <class ResultNumber = division_result_t<NumberType>, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto hausdorffDistanceLInf(const Shape<OtherPoint>& other) const {
        return other.template hausdorffDistanceLInf<ResultNumber>(*this);
    }

    template <class ResultNumber = division_result_t<NumberType>, SegmentConcept OtherSegment>
    [[nodiscard]] constexpr auto squaredHausdorffDistance(const OtherSegment& other) const;

    template <class ResultNumber = NumberType, PointConcept OtherPoint>
    [[nodiscard]] constexpr auto squaredHausdorffDistance(const OtherPoint& point) const;

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires ((detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
                  && requires(const OtherShape& o, const Segment& self) {
                         o.template squaredHausdorffDistance<ResultNumber>(self);
                     })
    [[nodiscard]] constexpr auto squaredHausdorffDistance(const OtherShape& other) const {
        return other.template squaredHausdorffDistance<ResultNumber>(*this);
    }

    [[nodiscard]] constexpr Segment diameter() const;

    template <class ResultNumber = division_result_t<NumberType>>
    [[nodiscard]] constexpr Point<ResultNumber> midpoint() const;

    template <class ResultNumber = division_result_t<NumberType>>
    [[nodiscard]] constexpr Point<ResultNumber> pointInside() const;

    template <class OtherShape>
    [[nodiscard]] constexpr bool pointInsideInteriorContainedIn(const OtherShape& shape) const;

    template <class ResultNumber = grid_number_t<typename TPoint::NumberType>>
        requires(detail::extended_integral<ResultNumber> || std::same_as<ResultNumber, BigInt>)
    [[nodiscard]] std::vector<Point<ResultNumber, typename PointType::LabelType>>
    latticePoints() const;

    [[nodiscard]] constexpr Rectangle<PointType> bbox() const;

    template <std::floating_point ResultNumber = double>
    [[nodiscard]] constexpr Rectangle<Point<ResultNumber>> fbox() const;

    [[nodiscard]] constexpr std::array<PointType, 2> vertices() const;

    [[nodiscard]] constexpr Convex<PointType> convexHull() const {
        return Convex<PointType>(vertices());
    }

    [[nodiscard]] constexpr std::array<Segment, 1> edges() const;

    [[nodiscard]] constexpr std::array<OrientedSegment<PointType>, 1> orientedEdges() const;

    [[nodiscard]] constexpr Polyline<PointType> asPolyline() const;

    template <class OtherShape>
        requires MinkowskiSummableConcept<Segment<TPoint, TLabel>, OtherShape>
    [[nodiscard]] constexpr auto minkowskiSum(const OtherShape& other) const;

    template <class OtherShape>
        requires MinkowskiSummableConcept<Segment<TPoint, TLabel>, OtherShape>
    [[nodiscard]] constexpr auto minkowskiErosion(const OtherShape& other) const;

    template <class OtherShape>
        requires (!MinkowskiSummableConcept<Segment<TPoint, TLabel>, OtherShape> &&
                  BoundedPolygonalConcept<OtherShape>)
    [[nodiscard]] constexpr auto minkowskiErosion(const OtherShape& other) const;

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires (!MinkowskiSummableConcept<Segment<TPoint, TLabel>, OtherShape>
                  && (detail::shapeRank<OtherShape> > detail::shapeRank<Segment>)
                  && requires(const OtherShape& o, const Segment& self) {
                         o.template minkowskiSum<ResultNumber>(self);
                     })
    [[nodiscard]] auto minkowskiSum(const OtherShape& other) const {
        return other.template minkowskiSum<ResultNumber>(*this);
    }

    template<PointConcept OtherPoint>
    constexpr Segment& operator+=(const OtherPoint& translation);

    template<PointConcept OtherPoint>
    constexpr Segment& operator-=(const OtherPoint& translation);

    template <class Scalar>
        requires(!detail::is_point_v<Scalar> && !TransformationConcept<Scalar>)
    constexpr Segment& operator*=(const Scalar& scalar);

    template <class Scalar>
        requires(!detail::is_point_v<Scalar> && !TransformationConcept<Scalar>)
    constexpr Segment& operator/=(const Scalar& scalar);
 
   private:
    template <std::floating_point ResultNumber, class Value>
    static constexpr ResultNumber lowerCoordinateBound(const Value& value);
 
    template <std::floating_point ResultNumber, class Value>
    static constexpr ResultNumber upperCoordinateBound(const Value& value);
 
    template<SegmentConcept OtherSegment>
    constexpr bool boundingBoxesOverlap(const OtherSegment& other) const;
 
    // Returns 0 for no overlap, 1 for overlap but no cross, 2 for cross
    template<SegmentConcept OtherSegment>
    constexpr int boundingBoxesCross(const OtherSegment& other) const;
 
    std::array<PointType,2> points_{};
    [[no_unique_address]] mutable LabelType label_{};
};

template <class PointType, class LabelType, class TranslationNumber, class TranslationLabel>
constexpr auto operator-(const Segment<PointType, LabelType>& segment, const Point<TranslationNumber, TranslationLabel>& translation);

template <class PointType, class LabelType, class Scalar>
    requires(!detail::is_point_v<Scalar> && !TransformationConcept<Scalar>)
constexpr auto operator*(const Segment<PointType, LabelType>& segment, const Scalar& scalar);

template <class Scalar, class PointType, class LabelType>
    requires(!detail::is_point_v<Scalar> && !TransformationConcept<Scalar>)
constexpr auto operator*(const Scalar& scalar, const Segment<PointType, LabelType>& segment);

template <class PointType, class LabelType, class Scalar>
    requires(!detail::is_point_v<Scalar> && !TransformationConcept<Scalar>)
constexpr auto operator/(const Segment<PointType, LabelType>& segment, const Scalar& scalar);

template <class PointType, class LabelType>
std::ostream& operator<<(std::ostream& stream, const Segment<PointType, LabelType>& segment);
 
}  // pgl