overlaps_plane_sphere.h

// Description: Overlap tests between a plane and a sphere

#ifndef PASTELGEOMETRY_OVERLAPS_PLANE_SPHERE_H
#define PASTELGEOMETRY_OVERLAPS_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
{

    //! Tests if a plane and a sphere overlap.
    /*!
   Preconditions:
   plane.n() == sphere.n()

   Time complexity:
   O(n), where n is the dimension.

   Returns:
   Whether the plane and the sphere overlap.
   */
    template <typename Real, int N>
    bool overlaps(
        const Plane<Real, N>& plane,
        const Sphere<Real, N>& sphere)
    {
        // A plane intersects a sphere if
        // the distance of the sphere's center
        // point from the plane is smaller
        // than the sphere's radius.

        Real d2 = 
            distance2(plane, sphere.position());
        Real radius2 =
            square(sphere.radius());

        if (d2 >= radius2)
        {
            if (d2 > radius2 ||
                sphere.topology() == Topology::Open)
            {
                return false;
            }
        }

        return true;
    }

    //! Tests if a plane and a sphere overlap.
    /*!
   sphereOnPositiveSide: 
   Set true, if the center point of the box
   is on the positive side of the plane.
   Otherwise set to false.

   Returns:
   overlaps(plane, sphere)
   */
    template <typename Real, int N>
    bool overlaps(
        const Plane<Real, N>& plane,
        const Sphere<Real, N>& sphere,
        bool& sphereOnPositiveSide)
    {
        sphereOnPositiveSide = 
            dot(plane.normal(),   
            sphere.position() - plane.position()) > 0;

        return Pastel::overlaps(plane, sphere);
    }

}

#endif