distance_alignedbox_sphere.h

// Description: Distance between an aligned box and a sphere

#ifndef PASTELGEOMETRY_DISTANCE_ALIGNEDBOX_SPHERE_H
#define PASTELGEOMETRY_DISTANCE_ALIGNEDBOX_SPHERE_H

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

#include "pastel/geometry/distance/distance_alignedbox_point.h"
#include "pastel/math/norm/euclidean_norm.h"

namespace Pastel
{

    //! Euclidean distance between a box and a sphere.
    /*!
   Preconditions:
   box.n() == sphere.n()

   Time complexity: O(box.n())

   The box and the sphere are assumed to be solid.
   */
    template <typename Real, int N>
    auto distance2(
        const AlignedBox<Real, N>& box,
        const Sphere<Real, N>& sphere)
    {
        PENSURE_OP(box.n(), ==, sphere.n());

        // Let
        // s = distance from sphere's center to 'box'.
        // r = sphere's radius
        // Then the distance d is given by
        // d = s - r
        // Negative distance means overlapping,
        // so then zero distance is returned.

        auto norm = Euclidean_Norm<Real>();
        auto centerDistance = distance2(box, sphere.position());
        if (~centerDistance <= square(sphere.radius())) return norm();

        return norm((Real)centerDistance - sphere.radius());
    }

}

#endif