overlaps_sphere_sphere.h

// Description: Overlap tests between two spheres

#ifndef PASTELGEOMETRY_OVERLAPS_SPHERE_SPHERE_H
#define PASTELGEOMETRY_OVERLAPS_SPHERE_SPHERE_H

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

namespace Pastel
{

    //! Tests if two solid spheres intersect.
    /*!
   Preconditions:
   aSphere.n() == bSphere.n()

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

   Returns:
   Whether the spheres overlap.
   */
    template <typename Real, int N>
    bool overlaps(
        const Sphere<Real, N>& aSphere,
        const Sphere<Real, N>& bSphere)
    {
        PENSURE_OP(aSphere.n(), ==, bSphere.n());

        // Two spheres intersect if the distance
        // between their center points is
        // less than or equal to the sum of their radii.

        Real centerDistance2 =
            dot(bSphere.position() - aSphere.position());
        Real radiusSum2 =
            square(aSphere.radius() + bSphere.radius());

        if (centerDistance2 >= radiusSum2)
        {
            if (centerDistance2 > radiusSum2 ||
                aSphere.topology() == Topology::Open ||
                bSphere.topology() == Topology::Open)
            {
                return false;
            }
        }

        return true;
    }

}

#endif