distance_plane_sphere.h

// Description: Distance between a plane and a sphere

#ifndef PASTELGEOMETRY_DISTANCE_PLANE_SPHERE_H
#define PASTELGEOMETRY_DISTANCE_PLANE_SPHERE_H

#include "pastel/geometry/shape/plane.h"
#include "pastel/geometry/shape/sphere.h"
#include "pastel/geometry/distance/distance_plane_point.h"

namespace Pastel
{

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

   Time complexity:
   O(n), where n is the dimension.
   */
    template <typename Real, int N>
    auto distance2(
        const Plane<Real, N>& plane,
        const Sphere<Real, N>& sphere)
    {
        PENSURE_OP(plane.n(), ==, sphere.n());

        // Let
        // s = distance from sphere's center to the plane.
        // 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(plane, sphere.position());
        if (centerDistance <= sphere.radius()) return norm();
        return norm((Real)centerDistance - sphere.radius());
    }

}

#endif