CGAL 5.5.1  dD Spatial Searching

Requirements of a distance class defining a distance between a query item denoting a spatial object and a point. To optimize distance computations transformed distances are used, e.g., for a Euclidean distance the transformed distance is the squared Euclidean distance.
Types  
typedef unspecified_type  D 
Dimension Tag.  
typedef unspecified_type  FT 
Number type.  
typedef unspecified_type  Point_d 
Point type.  
typedef unspecified_type  Query_item 
Query item type.  
Operations  
FT  transformed_distance (Query_item q, Point_d r) 
Returns the transformed distance between q and r .  
template<typename Coord_iterator >  
FT  transformed_distance_from_coordinates (Query_item q, Coord_iterator begin, Coord_iterator end) const 
Optional: must be defined when used with a Kd_tree where EnablePointsCache is set to Tag_true . More...  
template<typename Coord_iterator >  
FT  interruptible_transformed_distance (Query_item q, Coord_iterator begin, Coord_iterator end, FT stop_if_geq_to_this) const 
Optional: in most cases (e.g., Euclidean distance), the distance computation algorithm knows before its end that the distance will be greater than or equal to some given value. More...  
FT  min_distance_to_rectangle (Query_item q, Kd_tree_rectangle< FT, D > r) const 
Returns the transformed distance between q and the point on the boundary of r closest to q .  
FT  max_distance_to_rectangle (Query_item q, Kd_tree_rectangle< FT, D > r) const 
Returns the transformed distance between q and the point on the boundary of r furthest to q .  
FT  transformed_distance (FT d) const 
Returns the transformed distance.  
FT  inverse_of_transformed_distance (FT d) const 
Returns the inverse of the transformed distance.  
FT GeneralDistance::interruptible_transformed_distance  (  Query_item  q, 
Coord_iterator  begin,  
Coord_iterator  end,  
FT  stop_if_geq_to_this  
)  const 
Optional: in most cases (e.g., Euclidean distance), the distance computation algorithm knows before its end that the distance will be greater than or equal to some given value.
In this function, the computation can be stopped when the distance is going to be greater than or equal to stop_if_geq_to_this
. In this case, the only requirement of the return value it to be \( \geq \) stop_if_geq_to_this
. Note that points cache does not have to be activated to enable this optimization.
Returns the transformed distance between q
and the point whose Cartesian coordinates are contained in the range [begin
, end
), or any value \( \geq \) stop_if_geq_to_this
if the transformed distance is \( \geq \) stop_if_geq_to_this
.
FT GeneralDistance::transformed_distance_from_coordinates  (  Query_item  q, 
Coord_iterator  begin,  
Coord_iterator  end  
)  const 
Optional: must be defined when used with a Kd_tree
where EnablePointsCache
is set to Tag_true
.
Returns the transformed distance between q
and the point whose Cartesian coordinates are contained in the range [begin
, end
).