euclidean_normbijection.h

// Description: Euclidean_NormBijection class
// Detail: A norm bijection of the Euclidean norm
// Documentation: normbijection.txt

#ifndef PASTELMATH_EUCLIDEAN_NORMBIJECTION_H
#define PASTELMATH_EUCLIDEAN_NORMBIJECTION_H

#include "pastel/sys/vector/vector_tools.h"
#include "pastel/math/normbijection/normbijection_concept.h"
#include "pastel/geometry/volume/sphere_volume.h"

namespace Pastel
{

    template <typename Real_>
    class Euclidean_NormBijection
    {
    public:
        using Real = Real_;

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

        Real lnVolumeUnitSphere(integer dimension) const
        {
            return Pastel::lnVolumeUnitSphere<Real>(dimension);
        }

        Real toNorm(const Real& normBijection) const
        {
            return std::sqrt(normBijection);
        }

        Real toLnNorm(const Real& normBijection) const
        {
            return 0.5 * std::log(normBijection);
        }

        Real toBijection(const Real& norm) const
        {
            PENSURE(norm >= 0);
            return square(norm);
        }

        Real scalingFactor(
            const Real& scaling) const
        {
            return square(scaling);
        }

        Real axis(
            const Real& axisDistance) const
        {
            return square(axisDistance);
        }

        Real signedAxis(
            const Real& axisDistance) const
        {
            return square(axisDistance);
        }

        Real addAxis(
            const Real& distance, 
            const Real& newAxisDistance) const
        {
            PENSURE(newAxisDistance >= 0);

            return distance + 
                newAxisDistance;
        }

        Real replaceAxis(
            const Real& distance, 
            const Real& oldAxisDistance,
            const Real& newAxisDistance) const
        {
            PENSURE(oldAxisDistance >= 0);
            PENSURE(newAxisDistance >= 0);

            return (distance - oldAxisDistance) + 
                newAxisDistance;
        }
    };

}

#endif