polytope.h

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#ifndef REPRESENTATION_GEOMETRIC_POLYTOPE_H
#define REPRESENTATION_GEOMETRIC_POLYTOPE_H

#include <vector>
#include <iostream>
#include <capd/capdlib.h>
#include <irafhy/representation/geometric/geometry.h>
#include <irafhy/representation/geometric/basic/point.h>
#include <irafhy/representation/geometric/basic/halfSpace.h>
#include <irafhy/utility/compGeometry/convexHull.hpp>

namespace irafhy
{
    class Polytope : public Geometry<Polytope>
    {
    private:
        std::vector<Point> pointConstraints_;
        std::vector<HalfSpace> halfSpaceConstraints_;
        double volume_ = 0.0;
        int dimension_ = 0;

    private:
        Polytope(const std::vector<Point>&   pointConstraints,
                 const std::vector<HalfSpace>& halfSpaceConstraints,
                 double                        volume,
                 int                           dimension);
        void init(const convexConstraints& constraints);
        std::vector<Point> verticesEnumerationDualPly(const std::vector<HalfSpace>& halfSpaces);
        std::vector<Point> verticesEnumerationIntersect(const std::vector<HalfSpace>& halfSpaces);
        std::vector<Point> verticesEnumeration(const std::vector<capd::interval>& constraints);
        std::vector<Point> verticesEnumeration(const Eigen::VectorXd& center, double radius);

    public:
        static Polytope Empty(std::size_t dimension = 0);

    public:
        Polytope();
        Polytope(const Polytope& polytope) = default;
        Polytope(Polytope&& polytope) noexcept = default;
        explicit Polytope(const std::vector<Point>& points);
        explicit Polytope(const std::vector<HalfSpace>& halfSpaces);
        explicit Polytope(const std::vector<capd::interval>& constraints);
        explicit Polytope(const capd::C0Rect2Set& set);
        Polytope(const Point& center, double radius);
        Polytope(const Eigen::VectorXd& center, double radius);
        ~Polytope() override = default;
        [[nodiscard]] std::vector<Point> pointConstraints() const;
        [[nodiscard]] std::vector<HalfSpace> halfSpaceConstraints() const;
        [[nodiscard]] Point centroid() const;
        [[nodiscard]] std::vector<capd::interval> constraints() const;
        [[nodiscard]] bool empty() const override;
        [[nodiscard]] int dimension() const override;
        [[nodiscard]] double volume() const;
        bool intersect(const Polytope& rhs, Polytope& result) const override;
        [[nodiscard]] Polytope unite(const Polytope& rhs) const override;
        [[nodiscard]] bool contains(const Point& point) const override;
        [[nodiscard]] bool contains(const Eigen::VectorXd& coordinate) const override;
        Polytope& operator=(const Polytope& rhs) = default;
        Polytope& operator=(Polytope&& rhs) noexcept = default;
    };

    std::ostream& operator<<(std::ostream& out, const Polytope& rhs);
} // namespace irafhy
#endif //REPRESENTATION_GEOMETRIC_POLYTOPE_H