overlaps_sphere_point.h

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

#ifndef PASTELGEOMETRY_OVERLAPS_SPHERE_POINT_H
#define PASTELGEOMETRY_OVERLAPS_SPHERE_POINT_H

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

#include "pastel/sys/vector.h"
#include "pastel/sys/math_functions.h"

namespace Pastel
{

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

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

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

        // A point intersects a sphere if
        // the distance of the point from
        // the sphere's center is less or 
        // equal than the sphere's radius.

        Real d2 = 
            dot(point - sphere.position());
        Real radius2 =
            square(sphere.radius());

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

        return true;
    }

}

#endif