plane.h

// Description: Plane

#ifndef PASTELGEOMETRY_PLANE_H
#define PASTELGEOMETRY_PLANE_H

#include "pastel/sys/mytypes.h"
#include "pastel/sys/vector.h"

#include <boost/operators.hpp>

namespace Pastel
{

    //! A plane.

    /*!
   A plane can be described by a position and a
   normal. The hyperplane is the set of all x's that satisfy
   the equation:
   dot(normal, x - position) = 0

   The plane passes through the given
   'position' point. This can be seen by substituting
   'x' = 'position'. Any other 'position' point on the plane
   describes the same plane. For consider any translation
   vector T on the plane, such that dot(normal, T) = 0.
   Then
   dot(normal, x - (position + T)) =
   dot(normal, x - position) - dot(normal, T) =
   dot(normal, x - position)

   For performance reasons it must
   be required that the plane normal is always of unit
   length. This is not enforced by the system, but it is
   required by the algorithms.
   */

    template <typename Real, integer N = Dynamic>
    class Plane
        : boost::multipliable<Plane<Real, N>, Real
        , boost::dividable<Plane<Real, N>, Real
        , boost::addable<Plane<Real, N>, Vector<Real, N>
        , boost::subtractable<Plane<Real, N>, Vector<Real, N>
        > > > >
    {
    public:
        using Real_ = Real;
        static constexpr integer N_ = N;

        // Using default copy constructor.
        // Using default assignment.

        //! Constructs an x-orthogonal plane at the origin.
        Plane();

        //! Constructs an x-orthogonal plane at the origin.
        explicit Plane(integer dimension);

        //! Constructs a plane given a position and a normal.
        Plane(const Vector<Real, N>& position,
            const Vector<Real, N>& unitNormal);

        //! Constructs a plane given a position and a normal.
        Plane(integer dimension,
            const Vector<Real, N>& position,
            const Vector<Real, N>& unitNormal);

        //! Used for concept checking.
        ~Plane();

        //! Swaps two planes.
        void swap(Plane<Real, N>& that);

        //! Returns the dimension of the plane.
        integer n() const;

        //! Sets the position and normal of the plane.
        void set(const Vector<Real, N>& position,
            const Vector<Real, N>& unitNormal);

        //! Sets the point which the plane must pass through.
        void setPosition(const Vector<Real, N>& position);

        //! Returns the point that the plane must pass through.
        const Vector<Real, N>& position() const;

        //! Sets the normal of the plane.
        void setNormal(const Vector<Real, N>& unitNormal);

        //! Returns the normal of the plane.
        const Vector<Real, N>& normal() const;

        //! Translates the plane by the given vector.
        Plane<Real, N>& operator+=(const Vector<Real, N>& that);

        //! Translates the plane backwards by the given vector.
        Plane<Real, N>& operator-=(const Vector<Real, N>& that);

        //! Scales up the plane without affecting position.
        Plane<Real, N>& operator*=(const Real& that);

        //! Scales down the plane without affecting position.
        Plane<Real, N>& operator/=(const Real& that);

    private:
        Vector<Real, N> position_;
        Vector<Real, N> normal_;
    };

    template <typename Real, integer N>
    void swap(Plane<Real, N>& left,
        Plane<Real, N>& right);

    using Plane1 = Plane<real, 1>;
    using Plane2 = Plane<real, 2>;
    using Plane3 = Plane<real, 3>;
    using Plane4 = Plane<real, 4>;
    using PlaneD = Plane<real, Dynamic>;

}

#include "pastel/geometry/shape/plane.hpp"

#endif