halfplane.hpp

Go to the documentation of this file.

#pragma once
 
#include "shape/orientedsegment.hpp"

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

template <class PointType_, class TLabel>
struct Halfplane {
    using PointType = PointType_;
    using NumberType = PointType::NumberType;
    using LabelType = TLabel;
    using CoordinateType = detail::promoted_number_t<NumberType>;
 
    static_assert(detail::is_point_v<PointType>, "Halfplane requires pgl::Point defining points");

    constexpr Halfplane() = default;

    constexpr Halfplane(PointType source, PointType target)
        : points_{std::move(source), std::move(target)} {}

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

    template <class A>
        requires(detail::has_label_v<LabelType> && std::constructible_from<LabelType, A&&>)
    constexpr Halfplane(PointType source, PointType target, A&& label)
        : points_{std::move(source), std::move(target)}, label_(std::forward<A>(label)) {}

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

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

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

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

    constexpr PointType& operator[](std::size_t index) {
        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 PointType& get(std::ptrdiff_t index) {
        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& source() const {
        return points_[0];
    }
    constexpr PointType& source() {
        return points_[0];
    }

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

    constexpr const PointType& min() const {
        return target() < source() ? target() : source();
    }

    constexpr const PointType& max() const {
        return source() < target() ? target() : source();
    }

    constexpr Halfplane opposite() const {
        return Halfplane(target(), source());
    }

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

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

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

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

    [[nodiscard]] constexpr bool operator==(const Halfplane& other) const;

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

    [[nodiscard]] constexpr auto operator<=>(const Halfplane& other) const;

    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 explicit operator OrientedLine<PointType>() const;

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

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

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

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

    constexpr void rotate90(int k = 1);

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

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

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

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

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

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

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

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

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

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

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

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

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

    template<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool boundaryContains(const OtherPoint& point) const;
 
    // The boundary of a half-plane is its edge line. A 1D shape lies on the
    // boundary iff its defining points do; an area must additionally be
    // degenerate (collapsed onto that line). See the implementations.
    template<SegmentConcept OtherSegment>
    [[nodiscard]] constexpr bool boundaryContains(const OtherSegment& other) const;
    template<LineConcept OtherLine>
    [[nodiscard]] constexpr bool boundaryContains(const OtherLine& other) const;
    template<OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr bool boundaryContains(const OtherOrientedSegment& other) const;
    template<OrientedLineConcept OtherOrientedLine>
    [[nodiscard]] constexpr bool boundaryContains(const OtherOrientedLine& other) const;
    template<RayConcept OtherRay>
    [[nodiscard]] constexpr bool boundaryContains(const OtherRay& other) const;
    template<RectangleConcept OtherRectangle>
    [[nodiscard]] constexpr bool boundaryContains(const OtherRectangle& other) const;
    template<TriangleConcept OtherTriangle>
    [[nodiscard]] constexpr bool boundaryContains(const OtherTriangle& other) const;
    template<HalfplaneConcept OtherHalfplane>
    [[nodiscard]] constexpr bool boundaryContains(const OtherHalfplane& other) const;
    template<ConvexConcept OtherConvex>
    [[nodiscard]] constexpr bool boundaryContains(const OtherConvex& other) const {
        return detail::reduceDegenerateGuarded(
            other, [this](const auto& carrier) { return this->boundaryContains(carrier); });
    }

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

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

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

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

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

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

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

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

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

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

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

    [[nodiscard]] constexpr bool boundaryContains(const Shape<PointType>& 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<LineConcept OtherLine>
    [[nodiscard]] constexpr bool interiorContains(const OtherLine& other) const;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    template<typename OtherShape>
        requires (!PointConcept<OtherShape> && detail::shapeRank<OtherShape> > detail::shapeRank<Halfplane>)
    [[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<PointConcept OtherPoint>
    [[nodiscard]] constexpr bool interiorsIntersect(const OtherPoint& other) const;

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

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

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

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

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

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

    template<typename OtherShape>
        requires (!PointConcept<OtherShape> && detail::shapeRank<OtherShape> > detail::shapeRank<Halfplane>)
    [[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<LineConcept OtherLine>
    [[nodiscard]] constexpr bool separates(const OtherLine& other) const;

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

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

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

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

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

    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;

    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;
 
    // --- not-yet-implemented predicate pairs (throw); see implementation ---
    template<PolygonConcept OtherPolygon>
    [[nodiscard]] constexpr bool interiorContains(const OtherPolygon& other) const;
 

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

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

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

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

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

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

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

    template<typename OtherShape>
        requires (!PointConcept<OtherShape> && detail::shapeRank<OtherShape> > detail::shapeRank<Halfplane>)
    [[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 = NumberType, PointConcept OtherPoint>
    [[nodiscard]] constexpr std::optional<Point<ResultNumber, typename PointType::LabelType>>
    intersection(const OtherPoint& other) const;

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

    template <class ResultNumber = division_result_t<NumberType>, OrientedLineConcept OtherOrientedLine>
    [[nodiscard]] constexpr std::optional<std::variant<Point<ResultNumber, typename PointType::LabelType>, Line<Point<ResultNumber, typename PointType::LabelType>>, Ray<Point<ResultNumber, typename PointType::LabelType>>>>
    intersection(const OtherOrientedLine& 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>, OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr std::optional<std::variant<Point<ResultNumber, typename PointType::LabelType>, Segment<Point<ResultNumber, typename PointType::LabelType>>>>
    intersection(const OtherOrientedSegment& other) const;

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

    template <class ResultNumber = NumberType, HalfplaneConcept OtherHalfplane>
    [[nodiscard]] constexpr HalfplaneIntersection<Point<ResultNumber, typename PointType::LabelType>>
    intersection(const OtherHalfplane& other) const;

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

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

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires (!PointConcept<OtherShape>
                  && (detail::shapeRank<OtherShape> > detail::shapeRank<Halfplane>)
                  && requires(const OtherShape& o, const Halfplane& self) {
                         o.template regularizedIntersection<ResultNumber>(self);
                     })
    [[nodiscard]] constexpr auto regularizedIntersection(const OtherShape& other) const {
        return other.template regularizedIntersection<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>, 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>, OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr auto squaredDistance(const OtherOrientedSegment& other) const;

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

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

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

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

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires ((detail::shapeRank<OtherShape> > detail::shapeRank<Halfplane>)
                  && requires(const OtherShape& o, const Halfplane& 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 = division_result_t<NumberType>, class OtherShape>
        requires detail::ClosestPointsPairConcept<Halfplane<PointType_, 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>, OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr auto distanceL1(const OtherOrientedSegment& other) const;

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

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

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

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

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires ((detail::shapeRank<OtherShape> > detail::shapeRank<Halfplane>)
                  && requires(const OtherShape& o, const Halfplane& 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 = division_result_t<NumberType>, PointConcept OtherPoint>
    [[nodiscard]] auto regularizedIntersection(const Shape<OtherPoint>& other) const {
        return other.template regularizedIntersection<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>, OrientedSegmentConcept OtherOrientedSegment>
    [[nodiscard]] constexpr auto distanceLInf(const OtherOrientedSegment& other) const;

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

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

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

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

    template <class ResultNumber = division_result_t<NumberType>, typename OtherShape>
        requires ((detail::shapeRank<OtherShape> > detail::shapeRank<Halfplane>)
                  && requires(const OtherShape& o, const Halfplane& 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>>
    [[nodiscard]] constexpr ResultNumber slope() const;

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

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

    template <class ResultNumber = double, DiskConcept OtherDisk>
    [[nodiscard]] Halfplane<Point<ResultNumber, typename PointType_::LabelType>>
    minkowskiErosion(const OtherDisk& other) const;

    template <class ResultNumber = double, DiskConcept OtherDisk>
    [[nodiscard]] Halfplane<Point<ResultNumber, typename PointType_::LabelType>>
    minkowskiSum(const OtherDisk& other) const;

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

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

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

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

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

    template <class OtherShape>
    [[nodiscard]] constexpr bool pointInsideInteriorContainedIn(const OtherShape& shape) const;
 
  private:
 
    std::array<PointType, 2> points_{};
    [[no_unique_address]] mutable LabelType label_{};
};
 
template <class PointType, class LabelType, class TranslationNumber, class TranslationLabel>
constexpr auto operator-(const Halfplane<PointType, LabelType>& halfplane, const Point<TranslationNumber, TranslationLabel>& translation);
 
template <class PointType, class LabelType, class Scalar>
    requires(!detail::is_point_v<Scalar> && !TransformationConcept<Scalar>)
constexpr auto operator*(const Halfplane<PointType, LabelType>& halfplane, 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 Halfplane<PointType, LabelType>& halfplane);
 
template <class PointType, class LabelType, class Scalar>
    requires(!detail::is_point_v<Scalar> && !TransformationConcept<Scalar>)
constexpr auto operator/(const Halfplane<PointType, LabelType>& halfplane, const Scalar& scalar);
 
template <class PointType, class LabelType>
std::ostream& operator<<(std::ostream& stream, const Halfplane<PointType, LabelType>& halfplane);
 
}  // namespace pgl