CGAL 6.2 - dD Spatial Searching

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OrthogonalDistance Concept Reference
Reference Manual » Concepts

## Definition

Requirements of an orthogonal distance class supporting incremental distance updates. To optimize distance computations transformed distances are used. E.g., for a Euclidean distance the transformed distance is the squared Euclidean distance.

Refines
  `GeneralDistance`

Has models
  `CGAL::Euclidean_distance<Traits>`
  `CGAL::Weighted_Minkowski_distance<Traits>`

## 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.

## Creation
| OrthogonalDistance ()
| Constructor implementing distance for `d`-dimensional points.

## Operations
FT | transformed_distance (Query_item q, Point_d r) const
| Returns the transformed distance between `q` and `r`.
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 | min_distance_to_rectangle (Query_item q, Kd_tree_rectangle< FT, D > r, std::vector< FT > &dists)
| 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` farthest to `q`.
FT | max_distance_to_rectangle (Query_item q, Kd_tree_rectangle< FT, D > r, std::vector< FT > &dists)
| Returns the transformed distance between `q` and the point on the boundary of `r` farthest 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 | new_distance (FT dist, FT old_off, FT new_off, int cutting_dimension) const
| Updates `dist` incrementally and returns the updated distance.

## Member Function Documentation

## ◆ max_distance_to_rectangle()

FT OrthogonalDistance::max_distance_to_rectangle | ( | Query_item | q,
|  | Kd_tree_rectangle< FT, D > | r,
|  | std::vector< FT > & | dists
| ) |  |

Returns the transformed distance between `q` and the point on the boundary of `r` farthest to `q`.

The vector `dists` has the size of the dimension of the data points and is filled with the distance in each dimension.

## ◆ min_distance_to_rectangle()

FT OrthogonalDistance::min_distance_to_rectangle | ( | Query_item | q,
|  | Kd_tree_rectangle< FT, D > | r,
|  | std::vector< FT > & | dists
| ) |  |

Returns the transformed distance between `q` and the point on the boundary of `r` closest to `q`.

The vector `dists` has the size of the dimension of the data points and is filled with the distance in each dimension.