distance_alignedbox_alignedbox.h

// Description: Distance between two aligned boxes

#ifndef PASTELGEOMETRY_DISTANCE_ALIGNEDBOX_ALIGNEDBOX_H
#define PASTELGEOMETRY_DISTANCE_ALIGNEDBOX_ALIGNEDBOX_H

#include "pastel/geometry/shape/alignedbox.h"

#include "pastel/math/norm/norm_concept.h"
#include "pastel/math/norm/euclidean_norm.h"

#include "pastel/geometry/distance/distance_alignedbox_alignedbox.h"
#include "pastel/geometry/distance/distance_point_point.h"

namespace Pastel
{

    //! Computes the norm-bijection distance between two aligned boxes.
    /*!
   Preconditions:
   aBox.n() == bBox.n()

   Time complexity: O(aBox.n())

   The distance is computed assuming that the boxes are solid. 
   */
    template <
        typename Real, int N, 
        Norm_Concept Norm = Euclidean_Norm<Real>
    >
    auto distance2(
        const AlignedBox<Real, N>& aBox,
        const AlignedBox<Real, N>& bBox,
        const Norm& norm = Norm())
    {
        PENSURE_OP(aBox.n(), ==, bBox.n());

        auto distance = norm();

        integer n = aBox.n();
        for (integer i = 0;i < n;++i)
        {
            const Real& aMin = aBox.min()[i];
            const Real& aMax = aBox.max()[i];
            const Real& bMin = bBox.min()[i];
            const Real& bMax = bBox.max()[i];

            if (aMin > bMax)
            {
                distance.set(i, aMin - bMax);
            }
            else if (bMin > aMax)
            {
                distance.set(i, bMin - aMax);
            }
            // else the projection intervals overlap.
        }

        return distance;
    }

    //! Computes the farthest norm-bijection distance between two aligned boxes.
    /*!
   Preconditions:
   aBox.n() == bBox.n()

   Time complexity: O(aBox.n())

   The distance is computed assuming that the boxes are solid. 
   */
    template <
        typename Real, int N, 
        Norm_Concept Norm = Euclidean_Norm<Real>
    >
    auto farthestDistance2(
        const AlignedBox<Real, N>& aBox,
        const AlignedBox<Real, N>& bBox,
        const Norm& norm = Norm())
    {
        PENSURE_OP(aBox.n(), ==, bBox.n());

        auto distance = norm();

        integer n = aBox.n();
        for (integer i = 0;i < n;++i)
        {
            const Real& aMin = aBox.min()[i];
            const Real& aMax = aBox.max()[i];
            const Real& bMin = bBox.min()[i];
            const Real& bMax = bBox.max()[i];

            if (aMin > bMin)
            {
                if (bMax > aMax)
                {
                    distance.set(i, std::max(bMax - aMin, aMax - bMin));
                }
                else
                {
                    distance.set(i, aMax - bMin);
                }
            }
            else 
            {
                if (bMax > aMax)
                {
                    distance.set(i, bMax - aMin);
                }
                else
                {
                    distance.set(i, std::max(bMax - aMin, aMax - bMin));
                }                
            }
        }

        return distance;
    }

}

#endif