// Sphere
template< typename Vector >
Sphere< Vector >::Sphere(
  const vector_type& centre,
  const value_type& radius,
  const size_t& index
  )
  : primitive::Sphere< Vector >( centre, radius ), index_( index )
{}

template< typename Vector >
Sphere< Vector >::~Sphere()
{}

template< typename Vector >
typename Sphere< Vector >::vector_type
Sphere< Vector >::low() const
{
  const value_type& radius = this->radius();
  vector_type radius_vector = vector_type( radius, radius, radius );
  return this->centre() - radius_vector;
}

template< typename Vector >
typename Sphere< Vector >::vector_type
Sphere< Vector >::high() const
{
  const value_type& radius = this->radius();
  vector_type radius_vector = vector_type( radius, radius, radius );
  return this->centre() + radius_vector;
}

template< typename Vector >
const size_t&
Sphere< Vector >::index() const
{
  return index_;
}

template< typename Vector >
Transform< Vector >::Transform(
  const vector_type& centre,
  const value_type& radius
  )
  : centre_( centre ), radius_( radius )
{}

// Transformation
template< typename Vector >
Transform< Vector >::~Transform()
{}

template< typename Vector >
typename Transform< Vector >::vector_type
Transform< Vector>::operator ()(const vector_type& point) const
{
  return radius_ * point + centre_;
}

// Overlap and equivalence
template< typename Object, typename Algorithm >
OverlapEqualityFilter< Object, Algorithm >::OverlapEqualityFilter(
  const object_type& object
  )
  : object_( object )
{}

template< typename Object, typename Algorithm >
OverlapEqualityFilter< Object, Algorithm >::~OverlapEqualityFilter()
{}

template< typename Object, typename Algorithm >
bool
OverlapEqualityFilter< Object, Algorithm >::operator ()(
  const object_type& other
  )
  const
{
  return ( other.index() != object_.index() ) && Algorithm::operator ()( object_, other );
}