CGAL 4.5.2 - dD Spatial Searching
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#include <CGAL/Weighted_Minkowski_distance.h>
The class Weighted_Minkowski_distance
provides an implementation of the concept OrthogonalDistance
, with a weighted Minkowski metric on \( d\)-dimensional points defined by \( l_p(w)(r,q)= ({\Sigma_{i=1}^{i=d} \, w_i(r_i-q_i)^p})^{1/p}\) for \( 0 < p <\infty\) and defined by \( l_{\infty}(w)(r,q)=max \{w_i |r_i-q_i| \mid 1 \leq i \leq d\}\).
For the purpose of the distance computations it is more efficient to compute the transformed distance \( {\sigma_{i=1}^{i=d} \, w_i(r_i-q_i)^p}\) instead of the actual distance.
Parameters
Expects for the template argument a model of the concept SearchTraits
, for example Search_traits_2<Kernel>
.
OrthogonalDistance
CGAL::Euclidean_distance<Traits>
Types | |
typedef Traits::FT | FT |
Number type. | |
typedef Traits::Point_d | Point_d |
Point type. | |
Creation | |
Weighted_Minkowski_distance (int d, Traits t=Traits()) | |
Constructor implementing \( l_2\) metric for \( d\)-dimensional points. | |
template<class InputIterator > | |
Weighted_Minkowski_distance (FT power, int dim, InputIterator wb, InputIterator we, Traits t=Traits()) | |
Constructor implementing the \( l_{power}(weights)\) metric. More... | |
Operations | |
FT | transformed_distance (Point_d q, Point_d r) const |
Returns \( d^{power}\), where \( d\) denotes the distance between q and r . | |
FT | min_distance_to_rectangle (Point_d q, Kd_tree_rectangle< FT > r;) const |
Returns \( d^{power}\), where \( d\) denotes the distance between the query item q and the point on the boundary of r closest to q . | |
FT | max_distance_to_rectangle (Point_d q, Kd_tree_rectangle< FT > r;) const |
Returns \( d^{power}\), where \( d\) denotes the distance between the query item q and the point on the boundary of r farthest to q . | |
FT | new_distance (FT dist, FT old_off, FT new_off, int cutting_dimension) const |
Updates dist incrementally and returns the updated distance. | |
FT | transformed_distance (FT d) const |
Returns \( d^p\) for \( 0 < p <\infty\) . More... | |
FT | inverse_of_transformed_distance (FT d) const |
Returns \( d^{1/p}\) for \( 0 < p <\infty\). More... | |
CGAL::Weighted_Minkowski_distance< Traits >::Weighted_Minkowski_distance | ( | FT | power, |
int | dim, | ||
InputIterator | wb, | ||
InputIterator | we, | ||
Traits | t = Traits() |
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) |
Constructor implementing the \( l_{power}(weights)\) metric.
\( power \leq0\) denotes the \( l_{\infty}(weights)\) metric. The values in the iterator range [wb,we)
are the weight.
FT CGAL::Weighted_Minkowski_distance< Traits >::inverse_of_transformed_distance | ( | FT | d) | const |
Returns \( d^{1/p}\) for \( 0 < p <\infty\).
Returns \( d\) for \( p=\infty\).
FT CGAL::Weighted_Minkowski_distance< Traits >::transformed_distance | ( | FT | d) | const |
Returns \( d^p\) for \( 0 < p <\infty\) .
Returns \( d\) for \( p=\infty\) .